├── .devcontainer ├── Dockerfile ├── devcontainer.json └── noop.txt ├── .gitignore ├── 2020_PendData ├── TestPend.ipynb ├── alex1.csv ├── dimitris1.csv ├── dimitris2.csv ├── mitchell1.csv ├── soren1.csv └── soren2.csv ├── Iris.csv ├── LICENSE ├── P00-Intro.ipynb ├── P01-Euler.ipynb ├── P02-The-Heun-Method.ipynb ├── P02b-ClassicalConstForceMotion.ipynb ├── P03-TaylorSeries.ipynb ├── P03-TaylorSeriesWarmUpA.ipynb ├── P03-TaylorSeriesWarmUpB.ipynb ├── P04-HigherOrderMethods.ipynb ├── P04b-Symplectic.ipynb ├── P05-DemonAlgorithm.ipynb ├── P06-MatrixMethodsOptics.ipynb ├── P06a-SVDExample.ipynb ├── P07-Parameter Estimation (Zipf's Law).ipynb ├── P08-LargeAmplitudePendulum.ipynb ├── P09-RootFinding.ipynb ├── P10-CoupledMasses.ipynb ├── P10b-StochasticMatrices.ipynb ├── P11-FourierSeries.ipynb ├── P12-MachineLearning.ipynb ├── P12b-MLTensorFlow.ipynb ├── P12c-Perceptron_CF.ipynb ├── P13-ParallelCode.ipynb ├── README.md ├── ReportOutline.ipynb ├── buildPDFs.py ├── imgs ├── SwingRideRootFinding.png ├── butcher-tab.png ├── einst.png ├── heun1.png ├── heun2.png ├── heun3.png └── rk4-table.png ├── myData.csv ├── p8-data.zip ├── p8-data ├── raw-data.csv ├── track270.csv └── track_full_lowamp.csv ├── pendulum.ino ├── report_rubric.pdf ├── requirements.txt ├── titanic_survived.csv ├── titanic_test_set.csv └── titanic_train_set.csv /.devcontainer/Dockerfile: -------------------------------------------------------------------------------- 1 | FROM mcr.microsoft.com/devcontainers/anaconda:0-3 2 | 3 | # Copy environment.yml (if found) to a temp location so we update the environment. Also 4 | # copy "noop.txt" so the COPY instruction does not fail if no environment.yml exists. 5 | COPY environment.yml* .devcontainer/noop.txt /tmp/conda-tmp/ 6 | RUN if [ -f "/tmp/conda-tmp/environment.yml" ]; then umask 0002 && /opt/conda/bin/conda env update -n base -f /tmp/conda-tmp/environment.yml; fi \ 7 | && rm -rf /tmp/conda-tmp 8 | 9 | # [Optional] Uncomment this section to install additional OS packages. 10 | # RUN apt-get update && export DEBIAN_FRONTEND=noninteractive \ 11 | # && apt-get -y install --no-install-recommends 12 | -------------------------------------------------------------------------------- /.devcontainer/devcontainer.json: -------------------------------------------------------------------------------- 1 | // For format details, see https://aka.ms/devcontainer.json. For config options, see the 2 | // README at: https://github.com/devcontainers/templates/tree/main/src/anaconda 3 | { 4 | "name": "Anaconda (Python 3)", 5 | "build": { 6 | "context": "..", 7 | "dockerfile": "Dockerfile" 8 | }, 9 | "customizations": { 10 | "vscode": { 11 | "extensions": [ 12 | "ms-python.python", 13 | "dbaeumer.vscode-eslint", 14 | "ms-toolsai.jupyter", 15 | "ms-toolsai.vscode-jupyter-cell-tags", 16 | "ms-toolsai.jupyter-keymap", 17 | "ms-toolsai.jupyter-renderers", 18 | "ms-toolsai.vscode-jupyter-slideshow", 19 | "ms-python.vscode-pylance", 20 | "mechatroner.rainbow-csv" 21 | ] 22 | } 23 | }, 24 | 25 | // Features to add to the dev container. More info: https://containers.dev/features. 26 | // "features": {}, 27 | 28 | // Use 'forwardPorts' to make a list of ports inside the container available locally. 29 | // "forwardPorts": [], 30 | 31 | // Use 'postCreateCommand' to run commands after the container is created. 32 | "postCreateCommand": "python -m pip install -r requirements.txt", 33 | 34 | // Configure tool-specific properties. 35 | // "customizations": {}, 36 | 37 | // Uncomment to connect as root instead. More info: https://aka.ms/dev-containers-non-root. 38 | // "remoteUser": "root" 39 | } 40 | -------------------------------------------------------------------------------- /.devcontainer/noop.txt: -------------------------------------------------------------------------------- 1 | This file copied into the container along with environment.yml* from the parent 2 | folder. This file is included to prevents the Dockerfile COPY instruction from 3 | failing if no environment.yml is found. -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | .ipynb* 2 | Icon* 3 | *~ 4 | 5 | /build 6 | /cython_ext 7 | *.so 8 | 9 | .DS_Store 10 | 11 | 12 | -------------------------------------------------------------------------------- /2020_PendData/alex1.csv: -------------------------------------------------------------------------------- 1 | time,angle 2 | 0.000,0.000 3 | 0.001,0.000 4 | 0.002,0.000 5 | 0.003,0.000 6 | 0.003,0.000 7 | 0.004,0.000 8 | 0.014,0.000 9 | 0.028,0.000 10 | 0.041,0.000 11 | 0.055,0.000 12 | 0.068,0.000 13 | 0.081,0.000 14 | 0.096,0.000 15 | 0.109,0.000 16 | 0.122,0.000 17 | 0.136,0.000 18 | 0.149,0.000 19 | 0.163,0.000 20 | 0.177,0.000 21 | 0.190,0.000 22 | 0.203,0.000 23 | 0.216,0.000 24 | 0.231,0.000 25 | 0.244,0.000 26 | 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5.620,28.828 417 | 5.635,29.004 418 | 5.649,29.004 419 | 5.665,29.180 420 | 5.679,29.355 421 | 5.693,29.883 422 | 5.708,31.816 423 | 5.723,31.816 424 | 5.737,31.992 425 | 5.752,31.992 426 | 5.766,31.992 427 | 5.780,31.992 428 | 5.796,31.992 429 | 5.810,32.168 430 | 5.824,32.168 431 | 5.839,32.168 432 | 5.854,32.344 433 | 5.868,32.344 434 | 5.883,32.520 435 | 5.897,32.520 436 | 5.911,32.695 437 | 5.927,32.695 438 | 5.941,32.871 439 | 5.955,33.047 440 | 5.970,33.223 441 | 5.984,33.398 442 | 5.999,33.398 443 | 6.014,33.574 444 | 6.028,33.750 445 | 6.042,33.750 446 | 6.058,33.926 447 | 6.072,34.102 448 | 6.086,34.277 449 | 6.101,34.277 450 | 6.115,34.453 451 | 6.130,34.629 452 | 6.145,34.629 453 | 6.159,34.805 454 | 6.173,34.805 455 | 6.189,34.805 456 | 6.203,34.805 457 | 6.217,34.980 458 | 6.232,34.980 459 | 6.246,34.980 460 | 6.262,34.980 461 | 6.276,35.156 462 | 6.290,35.156 463 | 6.305,35.156 464 | 6.320,35.332 465 | 6.334,35.332 466 | 6.349,35.332 467 | 6.363,35.332 468 | 6.377,35.508 469 | 6.393,35.508 470 | 6.407,35.508 471 | 6.421,35.684 472 | 6.436,35.684 473 | 6.450,35.684 474 | 6.465,35.859 475 | 6.480,35.859 476 | 6.494,35.859 477 | 6.508,36.035 478 | 6.524,36.035 479 | 6.538,36.035 480 | 6.552,36.035 481 | 6.567,36.211 482 | 6.581,36.211 483 | 6.596,36.211 484 | 6.611,36.211 485 | 6.625,36.211 486 | 6.639,36.211 487 | 6.655,36.387 488 | 6.669,36.387 489 | 6.683,36.387 490 | 6.698,36.387 491 | 6.712,36.387 492 | 6.727,36.562 493 | 6.742,36.562 494 | 6.756,36.562 495 | 6.770,36.738 496 | 6.786,36.738 497 | 6.800,36.914 498 | 6.814,36.914 499 | 6.829,37.090 500 | 6.843,37.266 501 | 6.858,37.266 502 | 6.873,37.441 503 | 6.887,37.617 504 | 6.902,37.617 505 | 6.916,37.793 506 | 6.931,37.793 507 | 6.946,37.969 508 | 6.960,38.145 509 | 6.974,38.496 510 | 6.990,40.605 511 | 7.004,40.781 512 | 7.018,40.781 513 | 7.033,40.781 514 | 7.047,40.781 515 | 7.062,40.781 516 | 7.077,40.781 517 | 7.091,40.957 518 | 7.105,40.957 519 | 7.121,40.957 520 | 7.135,40.957 521 | 7.149,40.957 522 | 7.164,40.957 523 | 7.178,40.957 524 | 7.193,40.957 525 | 7.208,40.957 526 | 7.222,40.957 527 | 7.236,40.957 528 | 7.252,40.957 529 | 7.266,40.957 530 | 7.280,40.957 531 | 7.295,41.133 532 | 7.309,41.133 533 | 7.324,41.133 534 | 7.339,41.133 535 | 7.353,41.133 536 | 7.367,41.133 537 | 7.382,41.133 538 | 7.397,41.309 539 | 7.411,41.309 540 | 7.426,41.309 541 | 7.440,41.309 542 | 7.455,41.309 543 | 7.470,41.309 544 | 7.484,41.309 545 | 7.498,41.309 546 | 7.513,41.309 547 | 7.528,41.484 548 | 7.543,41.484 549 | 7.557,41.484 550 | 7.571,41.484 551 | 7.587,41.484 552 | 7.601,41.660 553 | 7.615,41.660 554 | 7.630,41.836 555 | 7.644,41.836 556 | 7.659,42.012 557 | 7.674,42.539 558 | 7.688,44.121 559 | 7.702,44.121 560 | 7.718,44.121 561 | 7.732,44.121 562 | 7.746,44.121 563 | 7.761,44.121 564 | 7.775,44.121 565 | 7.790,44.121 566 | 7.805,44.121 567 | 7.819,44.121 568 | 7.833,44.121 569 | 7.848,44.121 570 | 7.863,44.121 571 | 7.877,44.121 572 | 7.892,44.297 573 | 7.906,44.297 574 | 7.921,44.297 575 | 7.936,44.297 576 | 7.950,44.297 577 | 7.964,44.297 578 | 7.979,44.297 579 | 7.994,44.297 580 | 8.008,44.473 581 | 8.023,44.473 582 | 8.037,44.473 583 | 8.052,44.473 584 | 8.067,44.473 585 | 8.081,44.473 586 | 8.095,44.648 587 | 8.110,44.648 588 | 8.125,44.648 589 | 8.140,44.648 590 | 8.154,44.648 591 | 8.168,44.648 592 | 8.184,44.648 593 | 8.198,44.648 594 | 8.212,44.648 595 | 8.227,44.648 596 | 8.241,44.648 597 | 8.256,44.648 598 | 8.271,44.648 599 | 8.285,44.824 600 | 8.299,44.824 601 | 8.314,44.824 602 | 8.329,44.824 603 | 8.343,44.824 604 | 8.358,44.824 605 | 8.372,45.000 606 | 8.387,45.000 607 | 8.402,45.000 608 | 8.416,45.176 609 | 8.430,45.176 610 | 8.445,45.176 611 | 8.460,45.176 612 | 8.474,45.176 613 | 8.489,45.352 614 | 8.503,45.352 615 | 8.518,45.352 616 | 8.533,45.352 617 | 8.547,45.352 618 | 8.561,45.352 619 | 8.576,45.352 620 | 8.591,45.352 621 | 8.605,45.352 622 | 8.620,45.352 623 | 8.634,45.352 624 | 8.649,45.352 625 | 8.664,45.527 626 | 8.678,45.527 627 | 8.692,45.527 628 | 8.707,45.527 629 | 8.722,45.527 630 | 8.737,45.527 631 | 8.751,45.527 632 | 8.765,45.527 633 | 8.780,45.527 634 | 8.795,45.527 635 | 8.809,45.527 636 | 8.824,45.527 637 | 8.838,45.527 638 | 8.853,45.527 639 | 8.868,45.527 640 | 8.882,45.527 641 | 8.896,45.527 642 | 8.911,45.703 643 | 8.926,45.703 644 | 8.940,45.703 645 | 8.955,45.703 646 | 8.969,45.703 647 | 8.984,45.703 648 | 8.999,45.703 649 | 9.013,45.703 650 | 9.027,45.703 651 | 9.042,45.703 652 | 9.057,45.879 653 | 9.071,45.879 654 | 9.086,45.879 655 | 9.100,45.879 656 | 9.115,45.879 657 | 9.130,45.879 658 | 9.144,46.055 659 | 9.158,46.055 660 | 9.173,46.055 661 | 9.188,46.055 662 | 9.202,46.230 663 | 9.217,46.230 664 | 9.231,46.406 665 | 9.245,46.582 666 | 9.261,46.758 667 | 9.275,47.988 668 | 9.289,48.340 669 | 9.304,48.340 670 | 9.319,48.340 671 | 9.334,48.340 672 | 9.348,48.340 673 | 9.362,48.516 674 | 9.377,48.516 675 | 9.392,48.516 676 | 9.406,48.516 677 | 9.421,48.516 678 | 9.435,48.516 679 | 9.450,48.516 680 | 9.465,48.516 681 | 9.479,48.516 682 | 9.493,48.516 683 | 9.508,48.516 684 | 9.523,48.516 685 | 9.537,48.516 686 | 9.552,48.516 687 | 9.566,48.516 688 | 9.581,48.516 689 | 9.596,48.516 690 | 9.610,48.691 691 | 9.624,48.691 692 | 9.639,48.691 693 | 9.654,48.691 694 | 9.668,48.691 695 | 9.683,48.691 696 | 9.697,48.691 697 | 9.711,48.691 698 | 9.727,48.691 699 | 9.741,48.691 700 | 9.755,48.691 701 | 9.770,48.691 702 | 9.785,48.691 703 | 9.799,48.691 704 | 9.814,48.691 705 | 9.828,48.691 706 | 9.842,48.867 707 | 9.858,48.867 708 | 9.872,48.867 709 | 9.886,48.867 710 | 9.901,48.867 711 | 9.916,48.867 712 | 9.930,48.867 713 | 9.945,48.867 714 | 9.959,48.867 715 | 9.974,48.867 716 | 9.989,48.867 717 | 10.003,48.867 718 | 10.019,49.043 719 | 10.034,49.043 720 | 10.050,49.043 721 | 10.066,49.043 722 | 10.081,49.043 723 | 10.096,49.043 724 | 10.112,49.043 725 | 10.128,49.043 726 | 10.143,49.043 727 | 10.159,49.043 728 | 10.174,49.043 729 | 10.191,49.043 730 | 10.206,49.043 731 | 10.221,49.043 732 | 10.237,49.043 733 | 10.253,49.043 734 | 10.268,49.043 735 | 10.284,49.043 736 | 10.299,49.043 737 | 10.316,49.043 738 | 10.331,49.043 739 | 10.346,49.219 740 | 10.362,49.219 741 | 10.377,49.219 742 | 10.393,49.219 743 | 10.409,49.219 744 | 10.424,49.219 745 | 10.439,49.219 746 | 10.456,49.219 747 | 10.471,49.219 748 | 10.487,49.219 749 | 10.502,49.219 750 | 10.518,49.395 751 | 10.534,49.395 752 | 10.549,49.395 753 | 10.564,49.395 754 | 10.581,49.395 755 | 10.596,49.395 756 | 10.611,49.395 757 | 10.627,49.395 758 | 10.642,49.395 759 | 10.659,49.395 760 | 10.674,49.395 761 | 10.689,49.395 762 | 10.705,49.395 763 | 10.721,49.395 764 | 10.736,49.395 765 | 10.752,49.395 766 | 10.767,49.395 767 | 10.783,49.395 768 | 10.799,49.395 769 | 10.814,49.395 770 | 10.830,49.219 771 | 10.846,48.867 772 | 10.861,48.516 773 | 10.877,47.637 774 | 10.892,43.770 775 | 10.907,44.121 776 | 10.924,43.242 777 | 10.939,40.430 778 | 10.954,40.078 779 | 10.970,33.398 780 | 10.986,33.398 781 | 11.002,31.816 782 | 11.017,28.828 783 | 11.032,26.895 784 | 11.049,26.367 785 | 11.064,18.633 786 | 11.079,17.402 787 | 11.095,15.293 788 | 11.110,14.590 789 | 11.127,7.910 790 | 11.141,6.680 791 | 11.155,4.922 792 | 11.170,4.219 793 | 11.185,-1.582 794 | 11.200,-2.461 795 | 11.216,-7.559 796 | 11.231,-8.262 797 | 11.247,-13.184 798 | 11.264,-13.184 799 | 11.280,-15.645 800 | 11.297,-20.391 801 | 11.314,-21.094 802 | 11.330,-25.664 803 | 11.347,-26.543 804 | 11.363,-31.113 805 | 11.380,-31.816 806 | 11.397,-33.223 807 | 11.413,-36.738 808 | 11.430,-36.914 809 | 11.447,-38.496 810 | 11.463,-42.363 811 | 11.480,-42.539 812 | 11.496,-42.715 813 | 11.514,-42.891 814 | 11.530,-46.758 815 | 11.546,-47.109 816 | 11.563,-47.285 817 | 11.580,-47.461 818 | 11.597,-47.988 819 | 11.613,-49.746 820 | 11.629,-49.922 821 | 11.647,-49.922 822 | 11.663,-49.922 823 | 11.679,-49.922 824 | 11.696,-49.746 825 | 11.713,-49.570 826 | 11.730,-49.395 827 | 11.746,-48.516 828 | 11.762,-46.406 829 | 11.780,-45.703 830 | 11.796,-43.594 831 | 11.813,-41.484 832 | 11.829,-41.133 833 | 11.846,-39.375 834 | 11.863,-36.035 835 | 11.879,-34.980 836 | 11.896,-31.465 837 | 11.913,-29.707 838 | 11.929,-26.191 839 | 11.946,-24.609 840 | 11.962,-20.215 841 | 11.980,-18.105 842 | 11.996,-17.402 843 | 12.012,-10.898 844 | 12.029,-8.965 845 | 12.045,-6.680 846 | 12.060,-5.625 847 | 12.076,-0.703 848 | 12.091,0.703 849 | 12.105,7.207 850 | 12.121,7.910 851 | 12.135,10.020 852 | 12.151,11.777 853 | 12.166,16.172 854 | 12.182,17.227 855 | 12.198,22.500 856 | 12.213,22.676 857 | 12.228,26.191 858 | 12.245,27.949 859 | 12.260,28.477 860 | 12.275,33.047 861 | 12.291,35.859 862 | 12.306,36.211 863 | 12.323,37.441 864 | 12.338,40.957 865 | 12.353,41.309 866 | 12.369,41.484 867 | 12.385,44.648 868 | 12.400,45.176 869 | 12.416,45.352 870 | 12.431,45.527 871 | 12.447,45.879 872 | 12.463,46.934 873 | 12.478,48.691 874 | 12.494,48.691 875 | 12.510,48.691 876 | 12.525,48.691 877 | 12.541,48.867 878 | 12.556,48.867 879 | 12.571,48.867 880 | 12.588,48.867 881 | 12.603,48.691 882 | 12.618,48.691 883 | 12.634,48.691 884 | 12.650,48.516 885 | 12.666,48.164 886 | 12.681,46.582 887 | 12.696,44.297 888 | 12.713,43.945 889 | 12.728,40.078 890 | 12.743,40.254 891 | 12.759,39.375 892 | 12.774,34.453 893 | 12.791,33.574 894 | 12.806,31.289 895 | 12.821,27.246 896 | 12.837,26.719 897 | 12.853,25.664 898 | 12.868,20.742 899 | 12.884,16.348 900 | 12.899,15.293 901 | 12.915,14.238 902 | 12.931,7.207 903 | 12.945,5.977 904 | 12.959,5.098 905 | 12.974,0.703 906 | 12.989,-1.582 907 | 13.005,-2.812 908 | 13.020,-6.855 909 | 13.035,-8.086 910 | 13.052,-12.480 911 | 13.068,-13.535 912 | 13.084,-17.930 913 | 13.101,-20.918 914 | 13.118,-21.445 915 | 13.135,-26.543 916 | 13.151,-26.895 917 | 13.167,-32.168 918 | 13.185,-32.344 919 | 13.201,-33.926 920 | 13.218,-36.914 921 | 13.234,-37.090 922 | 13.251,-37.441 923 | 13.268,-43.242 924 | 13.284,-43.242 925 | 13.300,-43.594 926 | 13.318,-45.879 927 | 13.334,-46.406 928 | 13.351,-46.582 929 | 13.367,-46.758 930 | 13.384,-46.934 931 | 13.401,-47.109 932 | 13.417,-47.285 933 | 13.434,-47.461 934 | 13.451,-47.637 935 | 13.467,-47.637 936 | 13.484,-47.637 937 | 13.500,-47.461 938 | 13.518,-47.285 939 | 13.534,-46.934 940 | 13.550,-46.758 941 | 13.567,-46.230 942 | 13.584,-44.648 943 | 13.601,-41.836 944 | 13.617,-41.484 945 | 13.633,-40.605 946 | 13.651,-35.859 947 | 13.667,-36.035 948 | 13.683,-32.871 949 | 13.700,-30.937 950 | 13.717,-29.004 951 | 13.734,-25.664 952 | 13.750,-23.027 953 | 13.766,-20.039 954 | 13.784,-17.754 955 | 13.800,-15.820 956 | 13.817,-11.250 957 | 13.833,-6.328 958 | 13.849,-6.328 959 | 13.865,-2.812 960 | 13.880,0.176 961 | 13.894,1.055 962 | 13.910,7.031 963 | 13.924,7.910 964 | 13.938,10.547 965 | 13.954,14.941 966 | 13.969,16.699 967 | 13.986,17.402 968 | 14.001,21.797 969 | 14.016,22.676 970 | 14.032,27.246 971 | 14.048,28.125 972 | 14.063,28.652 973 | 14.079,35.332 974 | 14.094,35.508 975 | 14.110,36.211 976 | 14.126,37.617 977 | 14.141,40.957 978 | 14.157,41.309 979 | 14.172,41.660 980 | 14.188,43.418 981 | 14.204,45.527 982 | 14.219,45.527 983 | 14.234,45.703 984 | 14.251,45.879 985 | 14.266,46.230 986 | 14.281,48.691 987 | 14.297,48.867 988 | 14.313,48.867 989 | 14.329,48.867 990 | 14.344,48.867 991 | 14.359,48.867 992 | 14.376,48.867 993 | 14.391,48.867 994 | 14.406,48.867 995 | 14.422,48.867 996 | 14.437,48.691 997 | 14.454,48.516 998 | 14.469,47.637 999 | 14.484,44.824 1000 | 14.500,44.473 1001 | 14.516,43.594 1002 | 14.531,40.430 1003 | 14.547,39.902 1004 | 14.562,35.508 1005 | 14.578,34.102 1006 | 14.594,32.695 1007 | 14.609,29.883 1008 | 14.625,26.895 1009 | 14.641,26.367 1010 | 14.656,20.742 1011 | 14.672,19.863 1012 | 14.687,15.293 1013 | 14.702,14.941 1014 | 14.719,12.480 1015 | 14.734,7.383 1016 | 14.748,5.625 1017 | 14.763,4.570 1018 | 14.778,-0.879 1019 | 14.793,-1.934 1020 | 14.809,-6.152 1021 | 14.824,-7.383 1022 | 14.841,-9.141 1023 | 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-------------------------------------------------------------------------------- /Iris.csv: -------------------------------------------------------------------------------- 1 | Id,SepalLengthCm,SepalWidthCm,PetalLengthCm,PetalWidthCm,Species 2 | 1,5.1,3.5,1.4,0.2,Iris-setosa 3 | 2,4.9,3.0,1.4,0.2,Iris-setosa 4 | 3,4.7,3.2,1.3,0.2,Iris-setosa 5 | 4,4.6,3.1,1.5,0.2,Iris-setosa 6 | 5,5.0,3.6,1.4,0.2,Iris-setosa 7 | 6,5.4,3.9,1.7,0.4,Iris-setosa 8 | 7,4.6,3.4,1.4,0.3,Iris-setosa 9 | 8,5.0,3.4,1.5,0.2,Iris-setosa 10 | 9,4.4,2.9,1.4,0.2,Iris-setosa 11 | 10,4.9,3.1,1.5,0.1,Iris-setosa 12 | 11,5.4,3.7,1.5,0.2,Iris-setosa 13 | 12,4.8,3.4,1.6,0.2,Iris-setosa 14 | 13,4.8,3.0,1.4,0.1,Iris-setosa 15 | 14,4.3,3.0,1.1,0.1,Iris-setosa 16 | 15,5.8,4.0,1.2,0.2,Iris-setosa 17 | 16,5.7,4.4,1.5,0.4,Iris-setosa 18 | 17,5.4,3.9,1.3,0.4,Iris-setosa 19 | 18,5.1,3.5,1.4,0.3,Iris-setosa 20 | 19,5.7,3.8,1.7,0.3,Iris-setosa 21 | 20,5.1,3.8,1.5,0.3,Iris-setosa 22 | 21,5.4,3.4,1.7,0.2,Iris-setosa 23 | 22,5.1,3.7,1.5,0.4,Iris-setosa 24 | 23,4.6,3.6,1.0,0.2,Iris-setosa 25 | 24,5.1,3.3,1.7,0.5,Iris-setosa 26 | 25,4.8,3.4,1.9,0.2,Iris-setosa 27 | 26,5.0,3.0,1.6,0.2,Iris-setosa 28 | 27,5.0,3.4,1.6,0.4,Iris-setosa 29 | 28,5.2,3.5,1.5,0.2,Iris-setosa 30 | 29,5.2,3.4,1.4,0.2,Iris-setosa 31 | 30,4.7,3.2,1.6,0.2,Iris-setosa 32 | 31,4.8,3.1,1.6,0.2,Iris-setosa 33 | 32,5.4,3.4,1.5,0.4,Iris-setosa 34 | 33,5.2,4.1,1.5,0.1,Iris-setosa 35 | 34,5.5,4.2,1.4,0.2,Iris-setosa 36 | 35,4.9,3.1,1.5,0.1,Iris-setosa 37 | 36,5.0,3.2,1.2,0.2,Iris-setosa 38 | 37,5.5,3.5,1.3,0.2,Iris-setosa 39 | 38,4.9,3.1,1.5,0.1,Iris-setosa 40 | 39,4.4,3.0,1.3,0.2,Iris-setosa 41 | 40,5.1,3.4,1.5,0.2,Iris-setosa 42 | 41,5.0,3.5,1.3,0.3,Iris-setosa 43 | 42,4.5,2.3,1.3,0.3,Iris-setosa 44 | 43,4.4,3.2,1.3,0.2,Iris-setosa 45 | 44,5.0,3.5,1.6,0.6,Iris-setosa 46 | 45,5.1,3.8,1.9,0.4,Iris-setosa 47 | 46,4.8,3.0,1.4,0.3,Iris-setosa 48 | 47,5.1,3.8,1.6,0.2,Iris-setosa 49 | 48,4.6,3.2,1.4,0.2,Iris-setosa 50 | 49,5.3,3.7,1.5,0.2,Iris-setosa 51 | 50,5.0,3.3,1.4,0.2,Iris-setosa 52 | 51,7.0,3.2,4.7,1.4,Iris-versicolor 53 | 52,6.4,3.2,4.5,1.5,Iris-versicolor 54 | 53,6.9,3.1,4.9,1.5,Iris-versicolor 55 | 54,5.5,2.3,4.0,1.3,Iris-versicolor 56 | 55,6.5,2.8,4.6,1.5,Iris-versicolor 57 | 56,5.7,2.8,4.5,1.3,Iris-versicolor 58 | 57,6.3,3.3,4.7,1.6,Iris-versicolor 59 | 58,4.9,2.4,3.3,1.0,Iris-versicolor 60 | 59,6.6,2.9,4.6,1.3,Iris-versicolor 61 | 60,5.2,2.7,3.9,1.4,Iris-versicolor 62 | 61,5.0,2.0,3.5,1.0,Iris-versicolor 63 | 62,5.9,3.0,4.2,1.5,Iris-versicolor 64 | 63,6.0,2.2,4.0,1.0,Iris-versicolor 65 | 64,6.1,2.9,4.7,1.4,Iris-versicolor 66 | 65,5.6,2.9,3.6,1.3,Iris-versicolor 67 | 66,6.7,3.1,4.4,1.4,Iris-versicolor 68 | 67,5.6,3.0,4.5,1.5,Iris-versicolor 69 | 68,5.8,2.7,4.1,1.0,Iris-versicolor 70 | 69,6.2,2.2,4.5,1.5,Iris-versicolor 71 | 70,5.6,2.5,3.9,1.1,Iris-versicolor 72 | 71,5.9,3.2,4.8,1.8,Iris-versicolor 73 | 72,6.1,2.8,4.0,1.3,Iris-versicolor 74 | 73,6.3,2.5,4.9,1.5,Iris-versicolor 75 | 74,6.1,2.8,4.7,1.2,Iris-versicolor 76 | 75,6.4,2.9,4.3,1.3,Iris-versicolor 77 | 76,6.6,3.0,4.4,1.4,Iris-versicolor 78 | 77,6.8,2.8,4.8,1.4,Iris-versicolor 79 | 78,6.7,3.0,5.0,1.7,Iris-versicolor 80 | 79,6.0,2.9,4.5,1.5,Iris-versicolor 81 | 80,5.7,2.6,3.5,1.0,Iris-versicolor 82 | 81,5.5,2.4,3.8,1.1,Iris-versicolor 83 | 82,5.5,2.4,3.7,1.0,Iris-versicolor 84 | 83,5.8,2.7,3.9,1.2,Iris-versicolor 85 | 84,6.0,2.7,5.1,1.6,Iris-versicolor 86 | 85,5.4,3.0,4.5,1.5,Iris-versicolor 87 | 86,6.0,3.4,4.5,1.6,Iris-versicolor 88 | 87,6.7,3.1,4.7,1.5,Iris-versicolor 89 | 88,6.3,2.3,4.4,1.3,Iris-versicolor 90 | 89,5.6,3.0,4.1,1.3,Iris-versicolor 91 | 90,5.5,2.5,4.0,1.3,Iris-versicolor 92 | 91,5.5,2.6,4.4,1.2,Iris-versicolor 93 | 92,6.1,3.0,4.6,1.4,Iris-versicolor 94 | 93,5.8,2.6,4.0,1.2,Iris-versicolor 95 | 94,5.0,2.3,3.3,1.0,Iris-versicolor 96 | 95,5.6,2.7,4.2,1.3,Iris-versicolor 97 | 96,5.7,3.0,4.2,1.2,Iris-versicolor 98 | 97,5.7,2.9,4.2,1.3,Iris-versicolor 99 | 98,6.2,2.9,4.3,1.3,Iris-versicolor 100 | 99,5.1,2.5,3.0,1.1,Iris-versicolor 101 | 100,5.7,2.8,4.1,1.3,Iris-versicolor 102 | 101,6.3,3.3,6.0,2.5,Iris-virginica 103 | 102,5.8,2.7,5.1,1.9,Iris-virginica 104 | 103,7.1,3.0,5.9,2.1,Iris-virginica 105 | 104,6.3,2.9,5.6,1.8,Iris-virginica 106 | 105,6.5,3.0,5.8,2.2,Iris-virginica 107 | 106,7.6,3.0,6.6,2.1,Iris-virginica 108 | 107,4.9,2.5,4.5,1.7,Iris-virginica 109 | 108,7.3,2.9,6.3,1.8,Iris-virginica 110 | 109,6.7,2.5,5.8,1.8,Iris-virginica 111 | 110,7.2,3.6,6.1,2.5,Iris-virginica 112 | 111,6.5,3.2,5.1,2.0,Iris-virginica 113 | 112,6.4,2.7,5.3,1.9,Iris-virginica 114 | 113,6.8,3.0,5.5,2.1,Iris-virginica 115 | 114,5.7,2.5,5.0,2.0,Iris-virginica 116 | 115,5.8,2.8,5.1,2.4,Iris-virginica 117 | 116,6.4,3.2,5.3,2.3,Iris-virginica 118 | 117,6.5,3.0,5.5,1.8,Iris-virginica 119 | 118,7.7,3.8,6.7,2.2,Iris-virginica 120 | 119,7.7,2.6,6.9,2.3,Iris-virginica 121 | 120,6.0,2.2,5.0,1.5,Iris-virginica 122 | 121,6.9,3.2,5.7,2.3,Iris-virginica 123 | 122,5.6,2.8,4.9,2.0,Iris-virginica 124 | 123,7.7,2.8,6.7,2.0,Iris-virginica 125 | 124,6.3,2.7,4.9,1.8,Iris-virginica 126 | 125,6.7,3.3,5.7,2.1,Iris-virginica 127 | 126,7.2,3.2,6.0,1.8,Iris-virginica 128 | 127,6.2,2.8,4.8,1.8,Iris-virginica 129 | 128,6.1,3.0,4.9,1.8,Iris-virginica 130 | 129,6.4,2.8,5.6,2.1,Iris-virginica 131 | 130,7.2,3.0,5.8,1.6,Iris-virginica 132 | 131,7.4,2.8,6.1,1.9,Iris-virginica 133 | 132,7.9,3.8,6.4,2.0,Iris-virginica 134 | 133,6.4,2.8,5.6,2.2,Iris-virginica 135 | 134,6.3,2.8,5.1,1.5,Iris-virginica 136 | 135,6.1,2.6,5.6,1.4,Iris-virginica 137 | 136,7.7,3.0,6.1,2.3,Iris-virginica 138 | 137,6.3,3.4,5.6,2.4,Iris-virginica 139 | 138,6.4,3.1,5.5,1.8,Iris-virginica 140 | 139,6.0,3.0,4.8,1.8,Iris-virginica 141 | 140,6.9,3.1,5.4,2.1,Iris-virginica 142 | 141,6.7,3.1,5.6,2.4,Iris-virginica 143 | 142,6.9,3.1,5.1,2.3,Iris-virginica 144 | 143,5.8,2.7,5.1,1.9,Iris-virginica 145 | 144,6.8,3.2,5.9,2.3,Iris-virginica 146 | 145,6.7,3.3,5.7,2.5,Iris-virginica 147 | 146,6.7,3.0,5.2,2.3,Iris-virginica 148 | 147,6.3,2.5,5.0,1.9,Iris-virginica 149 | 148,6.5,3.0,5.2,2.0,Iris-virginica 150 | 149,6.2,3.4,5.4,2.3,Iris-virginica 151 | 150,5.9,3.0,5.1,1.8,Iris-virginica 152 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | The MIT License (MIT) 2 | 3 | Copyright (c) 2014 Steve Spicklemire 4 | 5 | Permission is hereby granted, free of charge, to any person obtaining a copy 6 | of this software and associated documentation files (the "Software"), to deal 7 | in the Software without restriction, including without limitation the rights 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 9 | copies of the Software, and to permit persons to whom the Software is 10 | furnished to do so, subject to the following conditions: 11 | 12 | The above copyright notice and this permission notice shall be included in all 13 | copies or substantial portions of the Software. 14 | 15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 21 | SOFTWARE. -------------------------------------------------------------------------------- /P02b-ClassicalConstForceMotion.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "metadata": {}, 6 | "source": [ 7 | "Classical 1-D acceleration with The Heun Method\n", 8 | "-----------------------------------------------\n", 9 | "\n", 10 | "Suppose we have a constant force $F_0$ acting on a fixed mass for a period of time. At low speeds the momentum principle gives us:\n", 11 | "\n", 12 | "$$\\frac{dv}{dt} = \\frac{F_0}{m}$$\n", 13 | "\n", 14 | "and we also know that\n", 15 | "\n", 16 | "$$\\frac{dx}{dt} = v$$\n", 17 | "\n", 18 | "which form a set of two coupled differential equations to be solved for the position and velocity of the mass." 19 | ] 20 | }, 21 | { 22 | "cell_type": "code", 23 | "execution_count": 1, 24 | "metadata": {}, 25 | "outputs": [ 26 | { 27 | "name": "stdout", 28 | "output_type": "stream", 29 | "text": [ 30 | "Populating the interactive namespace from numpy and matplotlib\n" 31 | ] 32 | } 33 | ], 34 | "source": [ 35 | "%pylab inline" 36 | ] 37 | }, 38 | { 39 | "cell_type": "code", 40 | "execution_count": 2, 41 | "metadata": {}, 42 | "outputs": [ 43 | { 44 | "data": { 45 | "text/plain": [ 46 | "[]" 47 | ] 48 | }, 49 | "execution_count": 2, 50 | "metadata": {}, 51 | "output_type": "execute_result" 52 | }, 53 | { 54 | "data": { 55 | "image/png": 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JaVV6nSbp/KIDMzOz1svTpzAbOCoiFkTEAuBo4P31PiRpgaSnJD1YY/ssSRsl3Zte5zQWupmZNVuu5iNgF+CZ9H7nnJ+5HLgEWDhGmTsiws9kMDPrEHmSwvlkz2leDIisb+HMeh+KiCWSBicUnZmZtVSeu4+uknQb8K606nMR8WSTjj9T0n3Az4HPRMTKaoUkzQPmAcyYMaNJhzYzs0pjPY5zn/TvwWQP2FmbXruldRO1AtgjIg4ALgaur1UwIuZHxFBEDA0MDDTh0GZmVs1YVwqfJvt1fkGVbQEcMZEDR8Smsvc3SfqWpCkR8fRE9mtmTeZ5jPpKzaQQEfPS2/dFxIvl2yRtP9EDS3oL8IuICEmHkl21bJjofs2siTyPUd/Jc0vqXTnXvYakq4ClwDskrZV0sqRTJJ2SihwHPJj6FC4C5ka9B0abWWt5HqO+U/NKIf2Snwa8XtJBZHceAewEvKHejiPig3W2X0J2y6qZdarReYxGrxQ8j1HPG6tP4U+AE4HdgQvL1m8Gzi4wJjPrFJ7HqO+M1adwBXCFpGMj4roWxmRmncTzGPWVsZqPPhIR/wgMSvp05faIuLDKx8zMrIuN1Xz0xvTvDq0IxMzM2m+s5qPvpH+/1LpwzMysnfJMnf23knaSNFnSLZJGJH2kFcGZmVlr5Rmn8Mdp9PEHgMeAtwGfLTIoMyvQ0qVw/vnZv2YV8sySOlrm/cA/R8RGSWOVN7NO5RHKVkeeK4UbJT0EHALcImkAeLHOZ8ysE3mEstVRNylExJnA7wFDEfEb4FfAnKIDM7MCjI5QnjTJI5StqrrNR5ImAx8B3puajW4HLi04LjMrgkcoWx15+hS+DUwGvpWWT0jrPl5UUGZWII9QtjHkSQrvSg/CGXVrmtnUzMx6TJ6O5pcl7TW6IGlP4OXiQjIzs3bJc6XwWWCxpEfJps/eAzip0KjMzKwt6iaFiLhF0t7AO9KqhyPipWLDMjOzdshz99H2wCeB3yd7NvMdki6tfESnmbWJn6FsTZSn+Wgh2YN1Lk7LHwKuBI4vKigzy8kjlK3J8iSFd0bEvmXLiyWtKiogM2tAtRHKTgo2AXnuPloh6fDRBUmHAcPFhWRmuXmEsjVZniuFQ4C7JP0sLc8AHpb0ABARsX9h0ZnZ2DxC2ZosT1I4uvAozGz8PELZmijPLamPtyIQMzNrvzx9CuMiaYGkpyQ9WGO7JF0kaY2k+yUdXFQsZmaWT2FJAbicsZue3gfsnV7zyCbZMzOzNiosKUTEEuCZMYrMARZG5m5gF0lTi4rHrGv4cZnWRnk6mosyDXiibHltWre+sqCkeWRXE8yYMaMlwZm1hQejWZsV2XzUNBExPyKGImJoYGCg3eGYFcePy7Q2a2dSWAdML1vePa0z618ejGZt1s7mo0XAqZKuBg4DNkbEVk1HZn3Fg9GszQpLCpKuAmYBUyStBb5A9lhPIuJS4CZgNrAGeB4/o8Es48Fo1kaFJYWI+GCd7QF8qqjjm5lZ47qio9nMzFrDScGsaB53YF2knR3NZr3P4w6sy/hKwaxIHndgXcZJwaxIHndgXcbNR2ZF8rgD6zJOCmZF87gD6yJuPjIzsxInBTMzK3FSMGuUxx1YD3OfglkjPO7AepyvFMwa4XEH1uOcFMwa4XEH1uPcfGTWCI87sB7npGDWKI87sB7m5iMzMytxUjAzsxInBetvHnNg9hruU7D+5TEHZlvxlYL1L485MNuKk4L1L485MNuKm4+sf3nMgdlWCr1SkHS0pIclrZF0ZpXtJ0oakXRven28yHjMtjJzJpx1lhOCWVLYlYKkScA3gaOAtcA9khZFxKqKotdExKlFxWF9ZulS//I3m4Aim48OBdZExKMAkq4G5gCVScGsOXw3kdmEFdl8NA14omx5bVpX6VhJ90u6VtL0ajuSNE/SsKThkZGRImK1XuC7icwmrN13H90ADEbE/sDNwBXVCkXE/IgYioihgYGBlgZoXcR3E5lNWJHNR+uA8l/+u6d1JRGxoWzxH4C/LTAe63W+m8hswopMCvcAe0t6K1kymAt8qLyApKkRsT4tHgOsLjAe6weewdRsQgpLChGxRdKpwA+BScCCiFgp6VxgOCIWAX8l6RhgC/AMcGJR8ViX8t1EZi2liGh3DA0ZGhqK4eHhdodhreC7icyaRtLyiBiqV67dHc1mtfluIrOWc1KwzuW7icxaznMfWefy3URmLeekYJ3NdxOZtZSbj6y1/KQzs47mKwVrHd9NZNbxfKVgreO7icw6npOCtY7vJjLreG4+solpZMSx7yYy63hOCjZ+4+kj8N1EZh3NzUc2fu4jMOs5Tgo2fu4jMOs5bj6y8XMfgVnPcVKwV41nmmr3EZj1FCcFy3hgmZnhPgUb5U5jM8NJobc1Ms+QO43NDDcf9a5Gm4PcaWxmOCn0rmrNQR5YZmZ1uPmom7g5yMwK5iuFbuHmIDNrASeFdmpkXICbg8ysBZwU2qXRX/6jzUGj5d0cZGYFKLRPQdLRkh6WtEbSmVW2byfpmrR9maTBIuMpXCNt/o2OCxhtDjrvPA8sM7PCFHalIGkS8E3gKGAtcI+kRRGxqqzYycAvI+JtkuYCXwP+rJCAxjOFQyOfacUvfzcHmVnBimw+OhRYExGPAki6GpgDlCeFOcAX0/trgUskKSKiqZGMZwqHRj/TaJu/O4LNrAMV2Xw0DXiibHltWle1TERsATYCu1buSNI8ScOShkdGRhqPZDxTODT6mfHcAjpzJpx1lhOCmXWMruhojoj5wHyAoaGhxq8ixtNU0+hn/MvfzHpAkUlhHTC9bHn3tK5ambWStgF2BjY0PZLx/MEe72ecDMysixWZFO4B9pb0VrI//nOBD1WUWQR8DFgKHAfc2vT+hFHj+YPtP/Jm1mcKSwoRsUXSqcAPgUnAgohYKelcYDgiFgGXAVdKWgM8Q5Y4zMysTQrtU4iIm4CbKtadU/b+ReD4ImMwM7P8PCGemZmVOCmYmVmJk4KZmZU4KZiZWYmKugO0KJJGgMfH+fEpwNNNDKcbuM79wXXuDxOp8x4RMVCvUNclhYmQNBwRQ+2Oo5Vc5/7gOveHVtTZzUdmZlbipGBmZiX9lhTmtzuANnCd+4Pr3B8Kr3Nf9SmYmdnY+u1KwczMxuCkYGZmJT2ZFCQdLelhSWsknVll+3aSrknbl0kabH2UzZWjzidKGpF0b3p9vB1xNoukBZKekvRgje2SdFH6Pu6XdHCrY2y2HHWeJWlj2Tk+p1q5biJpuqTFklZJWinptCpleupc56xzcec6InrqRTZN9yPAnsC2wH3AvhVlPglcmt7PBa5pd9wtqPOJwCXtjrWJdX4vcDDwYI3ts4EfAAIOB5a1O+YW1HkWcGO742xynacCB6f3OwL/WeW/7Z461znrXNi57sUrhUOBNRHxaET8GrgamFNRZg5wRXp/LXCkJLUwxmbLU+eeEhFLyJ7BUcscYGFk7gZ2kTS1NdEVI0ede05ErI+IFen9ZmA1Wz/rvafOdc46F6YXk8I04Imy5bVs/YWWykTEFmAjsGtLoitGnjoDHJsur6+VNL3K9l6S9zvpNTMl3SfpB5L2a3cwzZSaeQ8CllVs6tlzPUadoaBz3YtJwaq7ARiMiP2Bm3n1Ssl6xwqy+W0OAC4Grm9zPE0jaQfgOuD0iNjU7nhaoU6dCzvXvZgU1gHlv4J3T+uqlpG0DbAzsKEl0RWjbp0jYkNEvJQW/wE4pEWxtUue/w56SkRsiojn0vubgMmSprQ5rAmTNJnsj+N3I+L7VYr03LmuV+ciz3UvJoV7gL0lvVXStmQdyYsqyiwCPpbeHwfcGqn3pkvVrXNFG+sxZO2UvWwR8NF0Z8rhwMaIWN/uoIok6S2jfWOSDiX7/7ubf+yQ6nMZsDoiLqxRrKfOdZ46F3muC31GcztExBZJpwI/JLsrZ0FErJR0LjAcEYvIvvArJa0h67ib276IJy5nnf9K0jHAFrI6n9i2gJtA0lVkd2BMkbQW+AIwGSAiLiV7NvhsYA3wPHBSeyJtnhx1Pg74hKQtwAvA3C7/sQPwbuAE4AFJ96Z1ZwMzoGfPdZ46F3auPc2FmZmV9GLzkZmZjZOTgpmZlTgpmJlZiZOCmZmVOCmYmVmJk4L1NUm7SPpk2fJukq4t6Fj/fazZLCX9rqTLizi2WV6+JdX6Wppb5saIeGcLjnUXcExEPD1GmR8Bfx4RPys6HrNqfKVg/e6rwF5pTvqvSxocfV5BegbF9ZJulvSYpFMlfVrSTyTdLem3Urm9JP2bpOWS7pC0T+VBJL0deGk0IUg6XtKDaUKzJWVFb6DLB1Nad3NSsH53JvBIRBwYEZ+tsv2dwP8A3gX8DfB8RBwELAU+msrMB/4yIg4BPgN8q8p+3k02idmoc4A/SROaHVO2fhh4zwTqYzYhPTfNhVmTLU5z2m+WtJHslzzAA8D+aSbL3wP+ueyRHNtV2c9UYKRs+T+AyyV9Dyif8OwpYLcmxm/WECcFs7G9VPb+lbLlV8j+/3kd8GxEHFhnPy+QzcYLQEScIukw4P3AckmHRMQGYPtU1qwt3Hxk/W4z2SMPxyXNc/9fko6H0vOCD6hSdDXwttEFSXtFxLKIOIfsCmJ06ue3A1WfwWzWCk4K1tfSr/P/SJ2+Xx/nbj4MnCzpPmAl1R+FugQ4qOyxr1+X9EDq1L6L7LnaAH8I/Os44zCbMN+SatYikv4euCEiflRj+3bA7cDvp8fEmrWcrxTMWucrwBvG2D4DONMJwdrJVwpmZlbiKwUzMytxUjAzsxInBTMzK3FSMDOzEicFMzMr+f81+KcIumYK6QAAAABJRU5ErkJggg==\n", 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" 58 | ] 59 | }, 60 | "metadata": {}, 61 | "output_type": "display_data" 62 | } 63 | ], 64 | "source": [ 65 | "m=1.0 # assume one kilogram\n", 66 | "F0=1.0 # and one newton, just for illustration\n", 67 | "\n", 68 | "v0 = 0.0 # start at rest\n", 69 | "x0 = 0.0 # at the origin\n", 70 | "xf = 3.0 # go to 3.0m\n", 71 | "dt = 0.1 # 0.1 sec intervals\n", 72 | "t = 0.0 # start at t=0.0s\n", 73 | "\n", 74 | "s=array([x0, v0]) # the \"state\" will be position and velocity\n", 75 | "\n", 76 | "def derivs_F(s, t):\n", 77 | "\n", 78 | " x=s[0] # extract position and velocity from the \"state\"\n", 79 | " v=s[1]\n", 80 | " \n", 81 | " dxdt=v # use the recipe here to get dvdt \n", 82 | " dvdt=F0/m # and dxdt\n", 83 | " \n", 84 | " return array([dxdt, dvdt])\n", 85 | "\n", 86 | "def HeunStep(s, t, derivs, dt):\n", 87 | " f1=derivs(s,t)\n", 88 | " f2=derivs(s+f1*dt,t+dt)\n", 89 | " return s + 0.5*(f1+f2)*dt\n", 90 | "\n", 91 | "xlist = [x0]\n", 92 | "tlist = [t]\n", 93 | "\n", 94 | "while s[0] < xf:\n", 95 | " s = HeunStep(s, t, derivs_F, dt)\n", 96 | " t += dt\n", 97 | " xlist.append(s[0])\n", 98 | " tlist.append(t)\n", 99 | "\n", 100 | "title('Motion with constant force')\n", 101 | "xlabel('time (s)')\n", 102 | "ylabel('position (m)')\n", 103 | "plot(tlist, xlist, 'r.')" 104 | ] 105 | }, 106 | { 107 | "cell_type": "code", 108 | "execution_count": null, 109 | "metadata": {}, 110 | "outputs": [], 111 | "source": [] 112 | }, 113 | { 114 | "cell_type": "code", 115 | "execution_count": null, 116 | "metadata": {}, 117 | "outputs": [], 118 | "source": [] 119 | } 120 | ], 121 | "metadata": { 122 | "kernelspec": { 123 | "display_name": "Python 3", 124 | "language": "python", 125 | "name": "python3" 126 | }, 127 | "language_info": { 128 | "codemirror_mode": { 129 | "name": "ipython", 130 | "version": 3 131 | }, 132 | "file_extension": ".py", 133 | "mimetype": "text/x-python", 134 | "name": "python", 135 | "nbconvert_exporter": "python", 136 | "pygments_lexer": "ipython3", 137 | "version": "3.8.3" 138 | } 139 | }, 140 | "nbformat": 4, 141 | "nbformat_minor": 1 142 | } 143 | -------------------------------------------------------------------------------- /P03-TaylorSeries.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "metadata": {}, 6 | "source": [ 7 | "Taylor Series\n", 8 | "=============\n", 9 | "\n", 10 | "Suppose you have some function that may be expensive or difficult to evaluate and so you’d like to find an easy approximation for that function in some limited domain. One particularly nice way to handle that is with a polynomial approximation since they are easy to compute. The question is: How can we find such a polynomial? One easy answer is called the \"Taylor Series\" set up like so:\n", 11 | "\n", 12 | "$$f(x) = A + B(x-x_0) + C(x-x_0)^2 + D(x-x_0)^3 + \\cdots$$\n", 13 | "\n", 14 | "So.. $x_0$ is the point around which we are interested in finding an approximation, but what are the values coefficients $A$, $B$, $C$, etc. of the binomials $(x-x_0)^n$ ? There are many ways to answer that question but *Taylor* *Series* answer is that the value of the function, and all of its derivatives *must* *match* the value of the *series* and all of *its* derivatives at the point x0. Let’s try it and see what happens: Just substitute $x \\rightarrow x_0$ in the expression.\n", 15 | "\n", 16 | "What happens? Well.. $x_0 - x_0$ is nothing but $0$ so all but the first term go to zeor and we just get:\n", 17 | "\n", 18 | "$$f(x_0) = A$$\n", 19 | "\n", 20 | "We have our first coefficient, $A=f(x_0)$, so $A$ is simply equal to the *value* of the function at the point of interest.\n", 21 | "\n", 22 | "What about $B$, $C$, and all the rest? Let’s demand that the first derivative of $f(x)$ match the first derivative of the series and see what we discover. What is the first derivative of the series?\n", 23 | "\n", 24 | "$$f'(x) = 0 + B + 2C(x-x_0) + 3D(x-x_0)^2 + \\cdots $$\n", 25 | "\n", 26 | "Now, put $x \\rightarrow x_0$ and see what we get:\n", 27 | "\n", 28 | "$$f'(x_0) = 0 + B + 0 + \\cdots $$\n", 29 | "\n", 30 | "so $B = f'(x_0)$, see how easy this is!\n", 31 | "\n", 32 | "Now try the second derivative:\n", 33 | "\n", 34 | "$$f''(x) = 0 + 0 + 2C + 6D(x-x_0) + \\cdots $$\n", 35 | "\n", 36 | "putting $x \\rightarrow x_0$ and we see:\n", 37 | "\n", 38 | "$$f''(x_0) = 2C$$\n", 39 | "\n", 40 | "so $C=f''(x_0)/2$. If you carry this on for a bit you can see you get:\n", 41 | "\n", 42 | "$$f(x) \\approx f(x_0) + f'(x_0)(x-x_0) + \\frac{1}{2}f''(x_0)(x-x_0)^2 + \\cdots$$\n", 43 | "\n", 44 | "or more generally:\n", 45 | "\n", 46 | "$$f(x) = \\sum_{n=0}^{n=\\infty} \\frac{f^{(n)}(x_0)}{n!}(x-x_0)^n$$\n", 47 | "\n", 48 | "Morse Potential\n", 49 | "===============\n", 50 | "\n", 51 | "Let's use this technique to analyze the motion of nitrogen atoms in a nitrogen molecule. The atoms live in an attractive potential of the form:\n", 52 | "\n", 53 | "$$U(x) = U_m \\left( \\left(1-e^{-\\alpha(x-x_0)}\\right)^2 - 1\\right)$$\n", 54 | "\n", 55 | "Let's load up sympy and define all the symbols we need: $U_m$, $x$, $x_0$ and $\\alpha$:\n" 56 | ] 57 | }, 58 | { 59 | "cell_type": "code", 60 | "execution_count": 1, 61 | "metadata": {}, 62 | "outputs": [], 63 | "source": [ 64 | "import sympy as sp\n", 65 | "sp.init_printing()" 66 | ] 67 | }, 68 | { 69 | "cell_type": "code", 70 | "execution_count": 3, 71 | "metadata": {}, 72 | "outputs": [], 73 | "source": [ 74 | "Um,x,x0,alpha=sp.symbols('Um x x_0 alpha', real=True)" 75 | ] 76 | }, 77 | { 78 | "cell_type": "markdown", 79 | "metadata": {}, 80 | "source": [ 81 | "Next let's define the Morse Potential function $U(x)$:" 82 | ] 83 | }, 84 | { 85 | "cell_type": "code", 86 | "execution_count": 4, 87 | "metadata": {}, 88 | "outputs": [ 89 | { 90 | "data": { 91 | "image/png": "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\n", 92 | "text/latex": [ 93 | "$\\displaystyle Um \\left(\\left(1 - e^{- \\alpha \\left(x - x_{0}\\right)}\\right)^{2} - 1\\right)$" 94 | ], 95 | "text/plain": [ 96 | " ⎛ 2 ⎞\n", 97 | " ⎜⎛ -α⋅(x - x₀)⎞ ⎟\n", 98 | "Um⋅⎝⎝1 - ℯ ⎠ - 1⎠" 99 | ] 100 | }, 101 | "execution_count": 4, 102 | "metadata": {}, 103 | "output_type": "execute_result" 104 | } 105 | ], 106 | "source": [ 107 | "U = Um*((1-sp.exp(-alpha*(x-x0)))**2-1)\n", 108 | "U" 109 | ] 110 | }, 111 | { 112 | "cell_type": "markdown", 113 | "metadata": {}, 114 | "source": [ 115 | "Next, Let's take the derivatite of $U(x)$ with respect to $x$: $U'(x)$. \n", 116 | "\n", 117 | "Remember the force is $-U'(x)$ so the point in space where $U'(x)=0$ is the equilibrium position." 118 | ] 119 | }, 120 | { 121 | "cell_type": "code", 122 | "execution_count": 5, 123 | "metadata": {}, 124 | "outputs": [ 125 | { 126 | "name": "stdout", 127 | "output_type": "stream", 128 | "text": [ 129 | "Python expression for Force:\n", 130 | "Force is: -2*Um*alpha*(1 - exp(-alpha*(x - x_0)))*exp(-alpha*(x - x_0))\n", 131 | "Latex: 2 Um \\alpha \\left(1 - e^{- \\alpha \\left(x - x_{0}\\right)}\\right) e^{- \\alpha \\left(x - x_{0}\\right)}\n", 132 | "Pretty math\n" 133 | ] 134 | }, 135 | { 136 | "data": { 137 | "image/png": "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\n", 138 | "text/latex": [ 139 | "$\\displaystyle 2 Um \\alpha \\left(1 - e^{- \\alpha \\left(x - x_{0}\\right)}\\right) e^{- \\alpha \\left(x - x_{0}\\right)}$" 140 | ], 141 | "text/plain": [ 142 | " ⎛ -α⋅(x - x₀)⎞ -α⋅(x - x₀)\n", 143 | "2⋅Um⋅α⋅⎝1 - ℯ ⎠⋅ℯ " 144 | ] 145 | }, 146 | "execution_count": 5, 147 | "metadata": {}, 148 | "output_type": "execute_result" 149 | } 150 | ], 151 | "source": [ 152 | "Up=U.diff(x)\n", 153 | "print(\"Python expression for Force:\")\n", 154 | "print(\"Force is:\",-Up)\n", 155 | "print(\"Latex:\", sp.latex(Up))\n", 156 | "print(\"Pretty math\")\n", 157 | "Up" 158 | ] 159 | }, 160 | { 161 | "cell_type": "markdown", 162 | "metadata": {}, 163 | "source": [ 164 | "Next we can solve for the value of x where $\\frac{dU}{dx} = 0$." 165 | ] 166 | }, 167 | { 168 | "cell_type": "code", 169 | "execution_count": 6, 170 | "metadata": {}, 171 | "outputs": [ 172 | { 173 | "data": { 174 | "image/png": "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\n", 175 | "text/latex": [ 176 | "$\\displaystyle \\left[ x_{0}\\right]$" 177 | ], 178 | "text/plain": [ 179 | "[x₀]" 180 | ] 181 | }, 182 | "execution_count": 6, 183 | "metadata": {}, 184 | "output_type": "execute_result" 185 | } 186 | ], 187 | "source": [ 188 | "sp.solve(Up,x)" 189 | ] 190 | }, 191 | { 192 | "cell_type": "markdown", 193 | "metadata": {}, 194 | "source": [ 195 | "Aha! So the function has a minimum at $x=x_0$. Now take the *second* derivative of $U(x)$ with respect to $x$: $U''(x)$" 196 | ] 197 | }, 198 | { 199 | "cell_type": "code", 200 | "execution_count": 7, 201 | "metadata": {}, 202 | "outputs": [ 203 | { 204 | "data": { 205 | "image/png": "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\n", 206 | "text/latex": [ 207 | "$\\displaystyle - 2 Um \\alpha^{2} \\left(1 - e^{- \\alpha \\left(x - x_{0}\\right)}\\right) e^{- \\alpha \\left(x - x_{0}\\right)} + 2 Um \\alpha^{2} e^{- 2 \\alpha \\left(x - x_{0}\\right)}$" 208 | ], 209 | "text/plain": [ 210 | " 2 ⎛ -α⋅(x - x₀)⎞ -α⋅(x - x₀) 2 -2⋅α⋅(x - x₀)\n", 211 | "- 2⋅Um⋅α ⋅⎝1 - ℯ ⎠⋅ℯ + 2⋅Um⋅α ⋅ℯ " 212 | ] 213 | }, 214 | "execution_count": 7, 215 | "metadata": {}, 216 | "output_type": "execute_result" 217 | } 218 | ], 219 | "source": [ 220 | "Upp=Up.diff(x)\n", 221 | "Upp" 222 | ] 223 | }, 224 | { 225 | "cell_type": "markdown", 226 | "metadata": {}, 227 | "source": [ 228 | "OK, we can use the `subs` method to evalute $U''(x)$ where $x=x_0$:" 229 | ] 230 | }, 231 | { 232 | "cell_type": "code", 233 | "execution_count": 8, 234 | "metadata": {}, 235 | "outputs": [ 236 | { 237 | "data": { 238 | "image/png": "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\n", 239 | "text/latex": [ 240 | "$\\displaystyle 2 Um \\alpha^{2}$" 241 | ], 242 | "text/plain": [ 243 | " 2\n", 244 | "2⋅Um⋅α " 245 | ] 246 | }, 247 | "execution_count": 8, 248 | "metadata": {}, 249 | "output_type": "execute_result" 250 | } 251 | ], 252 | "source": [ 253 | "Upp.subs(x,x0)" 254 | ] 255 | }, 256 | { 257 | "cell_type": "markdown", 258 | "metadata": {}, 259 | "source": [ 260 | "So, we see now that:\n", 261 | "\n", 262 | "$$\\frac{d^2U}{dx^2}\\bigg|_{x_0} = 2 U_m \\alpha^2$$\n", 263 | "\n", 264 | "so we can connect the parameters of the Morse Potential to the Taylor Series coefficients near the minimum of the Potential.\n", 265 | "\n", 266 | "Project 3\n", 267 | "===========\n", 268 | "\n", 269 | "See the podcast! But basically the project is to use the experimental data, the analytical approximation (Taylor Series) to the Morse Potential and the Heun Method to:\n", 270 | "\n", 271 | "* Verify/show that the experimental data is consistent with the Morse Potential model.\n", 272 | "\n", 273 | "* Use the Heun Method to compute the period of small oscillations about the equilibrium position and compare that to the experimental data *and* the Taylor Series result.\n", 274 | "\n", 275 | "$U_m$ = 7.37 eV\n", 276 | "\n", 277 | "$x_0$ = 1.2 A\n", 278 | "\n", 279 | "$\\alpha = 2.287\\ A^{-1}$\n", 280 | "\n", 281 | "$f$ = $5.19\\times 10^{13}$ Hz\n", 282 | "\n", 283 | "IMPORTANT NOTES\n", 284 | "---------------\n", 285 | "\n", 286 | "1) Without careful attention to keeping the namespaces separate it's not really practical to use sympy and pylab at the same time in the same notebook. If you're interested in this, I have a notebook that illustrates how this can be done, but I don't want overload you with too many new concepts in this one lesson. If you're already confused just take my advice and don't mix them. Doing this is easy: Create *one* notebook for sympy. Take the *result* of that notebook and use it to produce the python expression you need for the numerial algorithm. Then create a *second* notebook and simply *paste* python expression produced by the first notebook in the evaluation of the force for the second notebook. Simple.\n", 287 | "\n", 288 | "2) This project is meant to add two tools to your toolbox 1: sympy, 2: Talor Series expansion. Both of these are really just analytical tools that work with algebra and calculus. We're going to use these tools to understand and approximate the low amplitude behavior system interacting under the Morse Potential. Then we're going to *check* our understanding and approximation by calculating the (arbitrary amplitude) behavior of a system interacting under the Morse Potential numericaly and evaluating the frequency at various amplitudes. So:\n", 289 | "\n", 290 | " a) Use sympy/Taylor series to estimate the low-amplitude frequency of the system\n", 291 | " b) Use sympy to get a python expression for the Force of interaction\n", 292 | " c) Use a numerical method (e.g., Heun Algorithm) to compute the time evolution (frequency) of the system\n", 293 | " d) Compare the results of (c) and (a)\n", 294 | " e) Once you've validated the code in step \"d\" experiment with increasing the amplitude of motion. \n", 295 | " f) Describe how the period and trajectory of the particle changes.\n", 296 | "\n", 297 | "Please ask if you have questions!\n" 298 | ] 299 | }, 300 | { 301 | "cell_type": "code", 302 | "execution_count": null, 303 | "metadata": {}, 304 | "outputs": [], 305 | "source": [] 306 | } 307 | ], 308 | "metadata": { 309 | "kernelspec": { 310 | "display_name": "Python 3", 311 | "language": "python", 312 | "name": "python3" 313 | }, 314 | "language_info": { 315 | "codemirror_mode": { 316 | "name": "ipython", 317 | "version": 3 318 | }, 319 | "file_extension": ".py", 320 | "mimetype": "text/x-python", 321 | "name": "python", 322 | "nbconvert_exporter": "python", 323 | "pygments_lexer": "ipython3", 324 | "version": "3.7.6" 325 | } 326 | }, 327 | "nbformat": 4, 328 | "nbformat_minor": 1 329 | } 330 | -------------------------------------------------------------------------------- /P06-MatrixMethodsOptics.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "metadata": {}, 6 | "source": [ 7 | "\n", 8 | "Matrix Methods\n", 9 | "==============\n", 10 | "\n", 11 | "\n", 12 | "This project involves performing thin lens calculations using a matrix representation of optical elements. See the slides for an explanation of the details. The end result is that we have two matrix operators for refraction and translation transitions:\n", 13 | "\n", 14 | "Refraction:\n", 15 | "-----------\n", 16 | "\n", 17 | "$$\\hat{R}\\left|r_0\\right\\rangle = \\begin{bmatrix} 1 & 0 \\\\ \\frac{n_l - n_r}{R n_r} & \\frac{n_l}{n_r} \\end{bmatrix} \\begin{bmatrix} y_0 \\\\ \\alpha_0\\end{bmatrix}$$\n", 18 | "\n", 19 | "Translation\n", 20 | "-----------\n", 21 | "\n", 22 | "$$\\hat{T}\\left|r_0\\right\\rangle = \\begin{bmatrix} 1 & L \\\\ 0 & 1 \\end{bmatrix} \\begin{bmatrix} y_0 \\\\ \\alpha_0\\end{bmatrix}$$\n", 23 | "\n", 24 | "Where $n_l$ and $n_r$ are the indices of refraction on the left and right (respectively) of the refractive interface. $R$ is the radius of curvature of the refractive interface (positive if the center of curvature is to the right, negative to the left). $y_0$ is the height of the ray before the transition, $\\alpha_0$ is the angle (in radians) of the ray before the transition. $L$ is the length of the translation. Various combinations of these two operators can describe very complicated lens systems easily!\n", 25 | "\n", 26 | "Here's the example worked out in the slides:" 27 | ] 28 | }, 29 | { 30 | "cell_type": "code", 31 | "execution_count": 1, 32 | "metadata": {}, 33 | "outputs": [], 34 | "source": [ 35 | "import numpy as np\n", 36 | "import matplotlib.pyplot as pl" 37 | ] 38 | }, 39 | { 40 | "cell_type": "code", 41 | "execution_count": 2, 42 | "metadata": {}, 43 | "outputs": [ 44 | { 45 | "data": { 46 | "text/plain": [ 47 | "array([[0.01],\n", 48 | " [0. ]])" 49 | ] 50 | }, 51 | "execution_count": 2, 52 | "metadata": {}, 53 | "output_type": "execute_result" 54 | } 55 | ], 56 | "source": [ 57 | "ng=1.5 # index of glass\n", 58 | "na=1.0 # index of air\n", 59 | "h=0.01 # start with ray 1.0 cm above axis\n", 60 | "R=0.15 # radius of curvature of lens\n", 61 | "\n", 62 | "ray1 = np.array([[h],[0.0]])\n", 63 | "\n", 64 | "ray1" 65 | ] 66 | }, 67 | { 68 | "cell_type": "code", 69 | "execution_count": 3, 70 | "metadata": {}, 71 | "outputs": [ 72 | { 73 | "data": { 74 | "text/plain": [ 75 | "array([[1., 3.],\n", 76 | " [0., 1.]])" 77 | ] 78 | }, 79 | "execution_count": 3, 80 | "metadata": {}, 81 | "output_type": "execute_result" 82 | } 83 | ], 84 | "source": [ 85 | "T1 = np.array([[1.0, 3.0],\n", 86 | " [0.0, 1.0]\n", 87 | " ])\n", 88 | "T1" 89 | ] 90 | }, 91 | { 92 | "cell_type": "code", 93 | "execution_count": 4, 94 | "metadata": {}, 95 | "outputs": [ 96 | { 97 | "data": { 98 | "text/plain": [ 99 | "array([[0.01],\n", 100 | " [0. ]])" 101 | ] 102 | }, 103 | "execution_count": 4, 104 | "metadata": {}, 105 | "output_type": "execute_result" 106 | } 107 | ], 108 | "source": [ 109 | "ray2 = T1.dot(ray1) # matrix multiplication is handled by the \"dot\" method of an array\n", 110 | "ray2" 111 | ] 112 | }, 113 | { 114 | "cell_type": "code", 115 | "execution_count": 5, 116 | "metadata": {}, 117 | "outputs": [ 118 | { 119 | "data": { 120 | "text/plain": [ 121 | "array([[ 1. , 0. ],\n", 122 | " [-2.22222222, 0.66666667]])" 123 | ] 124 | }, 125 | "execution_count": 5, 126 | "metadata": {}, 127 | "output_type": "execute_result" 128 | } 129 | ], 130 | "source": [ 131 | "R1 = np.array([[1.0, 0.0], # entering the curved surface\n", 132 | " [(na-ng)/(ng*R), na/ng]])\n", 133 | "R1" 134 | ] 135 | }, 136 | { 137 | "cell_type": "code", 138 | "execution_count": 6, 139 | "metadata": {}, 140 | "outputs": [ 141 | { 142 | "data": { 143 | "text/plain": [ 144 | "array([[ 0.01 ],\n", 145 | " [-0.02222222]])" 146 | ] 147 | }, 148 | "execution_count": 6, 149 | "metadata": {}, 150 | "output_type": "execute_result" 151 | } 152 | ], 153 | "source": [ 154 | "ray3 = R1.dot(ray2)\n", 155 | "ray3" 156 | ] 157 | }, 158 | { 159 | "cell_type": "code", 160 | "execution_count": 7, 161 | "metadata": {}, 162 | "outputs": [ 163 | { 164 | "data": { 165 | "text/plain": [ 166 | "array([[1. , 0. ],\n", 167 | " [0. , 1.5]])" 168 | ] 169 | }, 170 | "execution_count": 7, 171 | "metadata": {}, 172 | "output_type": "execute_result" 173 | } 174 | ], 175 | "source": [ 176 | "R2 = np.array([[1.0,0.0], # exiting the planer surface\n", 177 | " [0.0, ng/na]])\n", 178 | "R2" 179 | ] 180 | }, 181 | { 182 | "cell_type": "code", 183 | "execution_count": 8, 184 | "metadata": {}, 185 | "outputs": [ 186 | { 187 | "data": { 188 | "text/plain": [ 189 | "array([[ 0.01 ],\n", 190 | " [-0.03333333]])" 191 | ] 192 | }, 193 | "execution_count": 8, 194 | "metadata": {}, 195 | "output_type": "execute_result" 196 | } 197 | ], 198 | "source": [ 199 | "ray4=R2.dot(ray3)\n", 200 | "ray4" 201 | ] 202 | }, 203 | { 204 | "cell_type": "code", 205 | "execution_count": 9, 206 | "metadata": {}, 207 | "outputs": [ 208 | { 209 | "data": { 210 | "text/plain": [ 211 | "0.3" 212 | ] 213 | }, 214 | "execution_count": 9, 215 | "metadata": {}, 216 | "output_type": "execute_result" 217 | } 218 | ], 219 | "source": [ 220 | "fl=-ray4[0,0]/ray4[1,0] # calculate the focal length from the height and angle of the ray.\n", 221 | "fl" 222 | ] 223 | }, 224 | { 225 | "cell_type": "code", 226 | "execution_count": 10, 227 | "metadata": {}, 228 | "outputs": [ 229 | { 230 | "data": { 231 | "text/plain": [ 232 | "0.3" 233 | ] 234 | }, 235 | "execution_count": 10, 236 | "metadata": {}, 237 | "output_type": "execute_result" 238 | } 239 | ], 240 | "source": [ 241 | "na*R/(ng-na) # compare to the \"lens makers\" equation result." 242 | ] 243 | }, 244 | { 245 | "cell_type": "code", 246 | "execution_count": 11, 247 | "metadata": {}, 248 | "outputs": [ 249 | { 250 | "data": { 251 | "text/plain": [ 252 | "array([[ 1. , 3. ],\n", 253 | " [-3.33333333, -9. ]])" 254 | ] 255 | }, 256 | "execution_count": 11, 257 | "metadata": {}, 258 | "output_type": "execute_result" 259 | } 260 | ], 261 | "source": [ 262 | "M = R2.dot(R1.dot(T1)) # system matrix\n", 263 | "M" 264 | ] 265 | }, 266 | { 267 | "cell_type": "code", 268 | "execution_count": 12, 269 | "metadata": {}, 270 | "outputs": [ 271 | { 272 | "data": { 273 | "text/plain": [ 274 | "array([[ 0.01 ],\n", 275 | " [-0.03333333]])" 276 | ] 277 | }, 278 | "execution_count": 12, 279 | "metadata": {}, 280 | "output_type": "execute_result" 281 | } 282 | ], 283 | "source": [ 284 | "M.dot(ray1) # system acting on ray1" 285 | ] 286 | }, 287 | { 288 | "cell_type": "markdown", 289 | "metadata": {}, 290 | "source": [ 291 | "Project 6\n", 292 | "==========\n", 293 | "\n", 294 | "We'll measure the properties of a *thick* lens in class. We'll measure a laser beam passing through this lens. Using these ideas, compute the trajectory of a ray through the lens. Compare the computed trajectory to your measured values." 295 | ] 296 | }, 297 | { 298 | "cell_type": "code", 299 | "execution_count": 12, 300 | "metadata": {}, 301 | "outputs": [], 302 | "source": [] 303 | } 304 | ], 305 | "metadata": { 306 | "kernelspec": { 307 | "display_name": "Python 3", 308 | "language": "python", 309 | "name": "python3" 310 | }, 311 | "language_info": { 312 | "codemirror_mode": { 313 | "name": "ipython", 314 | "version": 3 315 | }, 316 | "file_extension": ".py", 317 | "mimetype": "text/x-python", 318 | "name": "python", 319 | "nbconvert_exporter": "python", 320 | "pygments_lexer": "ipython3", 321 | "version": "3.7.6" 322 | } 323 | }, 324 | "nbformat": 4, 325 | "nbformat_minor": 1 326 | } 327 | -------------------------------------------------------------------------------- /P10b-StochasticMatrices.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "code", 5 | "execution_count": 3, 6 | "metadata": {}, 7 | "outputs": [], 8 | "source": [ 9 | "import numpy as np" 10 | ] 11 | }, 12 | { 13 | "cell_type": "markdown", 14 | "metadata": {}, 15 | "source": [ 16 | "# Stochastic Matrices\n", 17 | "\n", 18 | "These guys are matrices that predict a probability distribution iteratively. You present a \"current\" distribution, then you multiply by the \"transition matrix\" and it tells you the \"next\" distribution.\n" 19 | ] 20 | }, 21 | { 22 | "cell_type": "code", 23 | "execution_count": 4, 24 | "metadata": {}, 25 | "outputs": [ 26 | { 27 | "data": { 28 | "text/plain": [ 29 | "array([[0.1, 0.2, 0.3],\n", 30 | " [0.5, 0.3, 0.6],\n", 31 | " [0.4, 0.5, 0.1]])" 32 | ] 33 | }, 34 | "execution_count": 4, 35 | "metadata": {}, 36 | "output_type": "execute_result" 37 | } 38 | ], 39 | "source": [ 40 | "#\n", 41 | "# define a transition matrix\n", 42 | "#\n", 43 | "T = np.array([[0.1, 0.2, 0.3],\n", 44 | " [0.5,0.3,0.6],\n", 45 | " [0.4,0.5,0.1]])\n", 46 | "T" 47 | ] 48 | }, 49 | { 50 | "cell_type": "code", 51 | "execution_count": 5, 52 | "metadata": {}, 53 | "outputs": [ 54 | { 55 | "data": { 56 | "text/plain": [ 57 | "array([[0.01285965],\n", 58 | " [0.31088394],\n", 59 | " [0.67625641]])" 60 | ] 61 | }, 62 | "execution_count": 5, 63 | "metadata": {}, 64 | "output_type": "execute_result" 65 | } 66 | ], 67 | "source": [ 68 | "#\n", 69 | "# Start out with a random prob distribution vector\n", 70 | "#\n", 71 | "\n", 72 | "x0 = np.array([np.random.rand(3)]).T\n", 73 | "x0 = x0/x0.sum()\n", 74 | "x0" 75 | ] 76 | }, 77 | { 78 | "cell_type": "code", 79 | "execution_count": 6, 80 | "metadata": {}, 81 | "outputs": [ 82 | { 83 | "data": { 84 | "text/plain": [ 85 | "array([[0.26633968],\n", 86 | " [0.50544885],\n", 87 | " [0.22821147]])" 88 | ] 89 | }, 90 | "execution_count": 6, 91 | "metadata": {}, 92 | "output_type": "execute_result" 93 | } 94 | ], 95 | "source": [ 96 | "x1 = T.dot(x0)\n", 97 | "x1" 98 | ] 99 | }, 100 | { 101 | "cell_type": "code", 102 | "execution_count": 7, 103 | "metadata": {}, 104 | "outputs": [ 105 | { 106 | "data": { 107 | "text/plain": [ 108 | "array([[0.19618718],\n", 109 | " [0.42173138],\n", 110 | " [0.38208144]])" 111 | ] 112 | }, 113 | "execution_count": 7, 114 | "metadata": {}, 115 | "output_type": "execute_result" 116 | } 117 | ], 118 | "source": [ 119 | "x2 = T.dot(x1)\n", 120 | "x2" 121 | ] 122 | }, 123 | { 124 | "cell_type": "code", 125 | "execution_count": 8, 126 | "metadata": {}, 127 | "outputs": [ 128 | { 129 | "data": { 130 | "text/plain": [ 131 | "array([[0.21858943],\n", 132 | " [0.45386187],\n", 133 | " [0.3275487 ]])" 134 | ] 135 | }, 136 | "execution_count": 8, 137 | "metadata": {}, 138 | "output_type": "execute_result" 139 | } 140 | ], 141 | "source": [ 142 | "x3 = T.dot(x2)\n", 143 | "x3" 144 | ] 145 | }, 146 | { 147 | "cell_type": "code", 148 | "execution_count": 9, 149 | "metadata": {}, 150 | "outputs": [ 151 | { 152 | "data": { 153 | "text/plain": [ 154 | "array([[0.21290323],\n", 155 | " [0.44516129],\n", 156 | " [0.34193548]])" 157 | ] 158 | }, 159 | "execution_count": 9, 160 | "metadata": {}, 161 | "output_type": "execute_result" 162 | } 163 | ], 164 | "source": [ 165 | "xn = x3\n", 166 | "for i in range(100):\n", 167 | " xn = T.dot(xn)\n", 168 | " \n", 169 | "xn\n", 170 | " " 171 | ] 172 | }, 173 | { 174 | "cell_type": "code", 175 | "execution_count": 10, 176 | "metadata": {}, 177 | "outputs": [ 178 | { 179 | "data": { 180 | "text/plain": [ 181 | "array([ 1. , -0.1381966, -0.3618034])" 182 | ] 183 | }, 184 | "execution_count": 10, 185 | "metadata": {}, 186 | "output_type": "execute_result" 187 | } 188 | ], 189 | "source": [ 190 | "vals, vecs = np.linalg.eig(T)\n", 191 | "vals" 192 | ] 193 | }, 194 | { 195 | "cell_type": "code", 196 | "execution_count": 48, 197 | "metadata": {}, 198 | "outputs": [ 199 | { 200 | "data": { 201 | "text/plain": [ 202 | "array([0.21290323, 0.44516129, 0.34193548])" 203 | ] 204 | }, 205 | "execution_count": 48, 206 | "metadata": {}, 207 | "output_type": "execute_result" 208 | } 209 | ], 210 | "source": [ 211 | "vecs[:,0]/vecs[:,0].sum()" 212 | ] 213 | }, 214 | { 215 | "cell_type": "code", 216 | "execution_count": 12, 217 | "metadata": {}, 218 | "outputs": [ 219 | { 220 | "data": { 221 | "text/plain": [ 222 | "array([ 1.66570400e+00, -8.32667268e-16, 1.11022302e-16])" 223 | ] 224 | }, 225 | "execution_count": 12, 226 | "metadata": {}, 227 | "output_type": "execute_result" 228 | } 229 | ], 230 | "source": [ 231 | "vecs.sum(axis=0)" 232 | ] 233 | }, 234 | { 235 | "cell_type": "code", 236 | "execution_count": 13, 237 | "metadata": {}, 238 | "outputs": [ 239 | { 240 | "data": { 241 | "text/plain": [ 242 | "array([[ 0.21290323, 0.48569073, -0.18551735],\n", 243 | " [ 0.44516129, -0.30017338, -0.30017338],\n", 244 | " [ 0.34193548, -0.18551735, 0.48569073]])" 245 | ] 246 | }, 247 | "execution_count": 13, 248 | "metadata": {}, 249 | "output_type": "execute_result" 250 | } 251 | ], 252 | "source": [ 253 | "vecs/vecs.sum(axis=0)[0]" 254 | ] 255 | }, 256 | { 257 | "cell_type": "code", 258 | "execution_count": 16, 259 | "metadata": {}, 260 | "outputs": [ 261 | { 262 | "data": { 263 | "text/plain": [ 264 | "array([[0.33333333],\n", 265 | " [0.33333333],\n", 266 | " [0.33333333]])" 267 | ] 268 | }, 269 | "execution_count": 16, 270 | "metadata": {}, 271 | "output_type": "execute_result" 272 | } 273 | ], 274 | "source": [ 275 | "x0 = np.array([[1/3,1/3,1/3]]).T\n", 276 | "x0" 277 | ] 278 | }, 279 | { 280 | "cell_type": "code", 281 | "execution_count": 18, 282 | "metadata": {}, 283 | "outputs": [ 284 | { 285 | "data": { 286 | "text/plain": [ 287 | "array([0.35463375, 0.74150694, 0.5695633 ])" 288 | ] 289 | }, 290 | "execution_count": 18, 291 | "metadata": {}, 292 | "output_type": "execute_result" 293 | } 294 | ], 295 | "source": [ 296 | "vecs[:,0]" 297 | ] 298 | }, 299 | { 300 | "cell_type": "code", 301 | "execution_count": 22, 302 | "metadata": {}, 303 | "outputs": [ 304 | { 305 | "data": { 306 | "text/plain": [ 307 | "array([ 0.80901699, -0.5 , -0.30901699])" 308 | ] 309 | }, 310 | "execution_count": 22, 311 | "metadata": {}, 312 | "output_type": "execute_result" 313 | } 314 | ], 315 | "source": [ 316 | "vecs[:,1]" 317 | ] 318 | }, 319 | { 320 | "cell_type": "code", 321 | "execution_count": 20, 322 | "metadata": {}, 323 | "outputs": [ 324 | { 325 | "data": { 326 | "text/plain": [ 327 | "array([-0.30901699, -0.5 , 0.80901699])" 328 | ] 329 | }, 330 | "execution_count": 20, 331 | "metadata": {}, 332 | "output_type": "execute_result" 333 | } 334 | ], 335 | "source": [ 336 | "vecs[:,2]" 337 | ] 338 | }, 339 | { 340 | "cell_type": "markdown", 341 | "metadata": {}, 342 | "source": [ 343 | "x0 = c0*vecs[:,0] + c1*vecs[:,1] + c2*vecs[:,2]\n", 344 | "\n", 345 | "T*x0 = T*(c0*vecs[:,0] + c1*vecs[:,1] + c2*vecs[:,2])\n", 346 | "\n", 347 | " = c0*1*v0 + c1*(-0.138)*v1 + c2*(-0.3618)*v2\n", 348 | " \n", 349 | "\n", 350 | "T*T*x0 = c0*1*1*v0 + c1*(-0.138)**2*v1 + c2*(-0.3618)**2*v2\n", 351 | "T*T*T*x0 = c0*1**3*v0 + c1*((-0.138)**3*v1 + c2*(-0.3618)**3*v2\n", 352 | "(T**100)x0 = c0*1**100*v0 + c1*((-0.138)**100*v1 + c2*(-0.3618)**100*v2" 353 | ] 354 | }, 355 | { 356 | "cell_type": "code", 357 | "execution_count": 47, 358 | "metadata": {}, 359 | "outputs": [ 360 | { 361 | "data": { 362 | "text/plain": [ 363 | "-7.028396476918598e-45" 364 | ] 365 | }, 366 | "execution_count": 47, 367 | "metadata": {}, 368 | "output_type": "execute_result" 369 | } 370 | ], 371 | "source": [ 372 | "-0.3618**100" 373 | ] 374 | }, 375 | { 376 | "cell_type": "code", 377 | "execution_count": 25, 378 | "metadata": {}, 379 | "outputs": [ 380 | { 381 | "data": { 382 | "text/plain": [ 383 | "array([0.35463375, 0.74150694, 0.5695633 ])" 384 | ] 385 | }, 386 | "execution_count": 25, 387 | "metadata": {}, 388 | "output_type": "execute_result" 389 | } 390 | ], 391 | "source": [ 392 | "T.dot(vecs[:,0])" 393 | ] 394 | }, 395 | { 396 | "cell_type": "code", 397 | "execution_count": 38, 398 | "metadata": {}, 399 | "outputs": [ 400 | { 401 | "data": { 402 | "text/plain": [ 403 | "(array([-0.1118034, 0.0690983, 0.0427051]),\n", 404 | " array([ 0.80901699, -0.5 , -0.30901699]))" 405 | ] 406 | }, 407 | "execution_count": 38, 408 | "metadata": {}, 409 | "output_type": "execute_result" 410 | } 411 | ], 412 | "source": [ 413 | "T.dot(vecs[:,1]), vecs[:,1]," 414 | ] 415 | }, 416 | { 417 | "cell_type": "code", 418 | "execution_count": 30, 419 | "metadata": {}, 420 | "outputs": [ 421 | { 422 | "data": { 423 | "text/plain": [ 424 | "array([ 0.80901699, -0.5 , -0.30901699])" 425 | ] 426 | }, 427 | "execution_count": 30, 428 | "metadata": {}, 429 | "output_type": "execute_result" 430 | } 431 | ], 432 | "source": [ 433 | "vecs[:,1]" 434 | ] 435 | }, 436 | { 437 | "cell_type": "code", 438 | "execution_count": 33, 439 | "metadata": {}, 440 | "outputs": [ 441 | { 442 | "data": { 443 | "text/plain": [ 444 | "(-0.13819530284301607, -0.1381966, -0.13819660854246235)" 445 | ] 446 | }, 447 | "execution_count": 33, 448 | "metadata": {}, 449 | "output_type": "execute_result" 450 | } 451 | ], 452 | "source": [ 453 | "-.1118/.8090, 0.0690983/ -0.5, 0.0427051/-0.30901699" 454 | ] 455 | }, 456 | { 457 | "cell_type": "code", 458 | "execution_count": 34, 459 | "metadata": {}, 460 | "outputs": [], 461 | "source": [ 462 | "a = np.array([1,2,3])\n", 463 | "b = np.array([2,4,6])" 464 | ] 465 | }, 466 | { 467 | "cell_type": "code", 468 | "execution_count": 35, 469 | "metadata": {}, 470 | "outputs": [ 471 | { 472 | "data": { 473 | "text/plain": [ 474 | "array([0.5, 0.5, 0.5])" 475 | ] 476 | }, 477 | "execution_count": 35, 478 | "metadata": {}, 479 | "output_type": "execute_result" 480 | } 481 | ], 482 | "source": [ 483 | "a/b" 484 | ] 485 | }, 486 | { 487 | "cell_type": "code", 488 | "execution_count": 40, 489 | "metadata": {}, 490 | "outputs": [ 491 | { 492 | "data": { 493 | "text/plain": [ 494 | "(array([[0.6],\n", 495 | " [1.4],\n", 496 | " [1. ]]),\n", 497 | " array([[0.33333333],\n", 498 | " [0.33333333],\n", 499 | " [0.33333333]]))" 500 | ] 501 | }, 502 | "execution_count": 40, 503 | "metadata": {}, 504 | "output_type": "execute_result" 505 | } 506 | ], 507 | "source": [ 508 | "T.dot(x0)/x0, x0" 509 | ] 510 | }, 511 | { 512 | "cell_type": "code", 513 | "execution_count": null, 514 | "metadata": {}, 515 | "outputs": [], 516 | "source": [] 517 | } 518 | ], 519 | "metadata": { 520 | "kernelspec": { 521 | "display_name": "Python 3", 522 | "language": "python", 523 | "name": "python3" 524 | }, 525 | "language_info": { 526 | "codemirror_mode": { 527 | "name": "ipython", 528 | "version": 3 529 | }, 530 | "file_extension": ".py", 531 | "mimetype": "text/x-python", 532 | "name": "python", 533 | "nbconvert_exporter": "python", 534 | "pygments_lexer": "ipython3", 535 | "version": "3.8.5" 536 | } 537 | }, 538 | "nbformat": 4, 539 | "nbformat_minor": 2 540 | } 541 | -------------------------------------------------------------------------------- /P13-ParallelCode.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "metadata": { 3 | "name": "", 4 | "signature": "sha256:5f6686c8e8c4452fd6727485f7030a0dba1d4e5fd3127159a4d67d88d965719c" 5 | }, 6 | "nbformat": 3, 7 | "nbformat_minor": 0, 8 | "worksheets": [ 9 | { 10 | "cells": [ 11 | { 12 | "cell_type": "markdown", 13 | "metadata": {}, 14 | "source": [ 15 | "IPython Notebooks for Parallel Computing\n", 16 | "========================================\n", 17 | "\n", 18 | "This is simply an example notbook illustrating the \"cluster\" tab of the ipython notebook. You can use this as a starter project for developing simple parallel codes in a notebook.\n", 19 | "\n", 20 | "First start up a cluster using the \"Cluster\" tab. Then try these cells." 21 | ] 22 | }, 23 | { 24 | "cell_type": "code", 25 | "collapsed": false, 26 | "input": [ 27 | "from IPython.parallel import Client\n", 28 | "rc=Client()\n", 29 | "view = rc[:]\n", 30 | "print rc.ids" 31 | ], 32 | "language": "python", 33 | "metadata": {}, 34 | "outputs": [ 35 | { 36 | "output_type": "stream", 37 | "stream": "stdout", 38 | "text": [ 39 | "[0, 1, 2, 3]\n" 40 | ] 41 | } 42 | ], 43 | "prompt_number": 1 44 | }, 45 | { 46 | "cell_type": "markdown", 47 | "metadata": {}, 48 | "source": [ 49 | "Use the %px magic to import methods on the nodes" 50 | ] 51 | }, 52 | { 53 | "cell_type": "code", 54 | "collapsed": false, 55 | "input": [ 56 | "%px from pylab import arccos, rand\n", 57 | "from numpy import array" 58 | ], 59 | "language": "python", 60 | "metadata": {}, 61 | "outputs": [], 62 | "prompt_number": 2 63 | }, 64 | { 65 | "cell_type": "markdown", 66 | "metadata": {}, 67 | "source": [ 68 | "Next, use the `%%px` magic to define a function on the nodes" 69 | ] 70 | }, 71 | { 72 | "cell_type": "code", 73 | "collapsed": false, 74 | "input": [ 75 | "%%px\n", 76 | "\n", 77 | "def f(N):\n", 78 | " y=arccos(1.0-2*rand(N))\n", 79 | " return 2.0*y.sum()/N\n" 80 | ], 81 | "language": "python", 82 | "metadata": {}, 83 | "outputs": [], 84 | "prompt_number": 3 85 | }, 86 | { 87 | "cell_type": "code", 88 | "collapsed": false, 89 | "input": [ 90 | "x = view.map(lambda N: f(N), 10*[1000000]).result\n", 91 | "x" 92 | ], 93 | "language": "python", 94 | "metadata": {}, 95 | "outputs": [ 96 | { 97 | "metadata": {}, 98 | "output_type": "pyout", 99 | "prompt_number": 4, 100 | "text": [ 101 | "[3.1405796297219211,\n", 102 | " 3.1426586695423637,\n", 103 | " 3.1398369967668183,\n", 104 | " 3.1420250074438467,\n", 105 | " 3.1427624932300482,\n", 106 | " 3.1410966404557557,\n", 107 | " 3.1431271009553994,\n", 108 | " 3.141158465309319,\n", 109 | " 3.1426331913328771,\n", 110 | " 3.1436420212612775]" 111 | ] 112 | } 113 | ], 114 | "prompt_number": 4 115 | }, 116 | { 117 | "cell_type": "code", 118 | "collapsed": false, 119 | "input": [ 120 | "array(x).sum()/len(x)" 121 | ], 122 | "language": "python", 123 | "metadata": {}, 124 | "outputs": [ 125 | { 126 | "metadata": {}, 127 | "output_type": "pyout", 128 | "prompt_number": 5, 129 | "text": [ 130 | "3.1419520216019627" 131 | ] 132 | } 133 | ], 134 | "prompt_number": 5 135 | }, 136 | { 137 | "cell_type": "code", 138 | "collapsed": false, 139 | "input": [], 140 | "language": "python", 141 | "metadata": {}, 142 | "outputs": [] 143 | } 144 | ], 145 | "metadata": {} 146 | } 147 | ] 148 | } -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | sci-comp-notebooks 2 | ================== 3 | 4 | A collection of scientific computing notebooks. 5 | 6 | These are notebooks I've used for my scientific computing class at the University of Indianapolis. 7 | 8 | Hopefully others will find them useful for some purpose. ;-) 9 | 10 | [![Binder](https://mybinder.org/badge.svg)](https://mybinder.org/v2/gh/sspickle/sci-comp-notebooks/master) 11 | 12 | -------------------------------------------------------------------------------- /ReportOutline.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "metadata": {}, 6 | "source": [ 7 | "# Computational Narrative Report" 8 | ] 9 | }, 10 | { 11 | "cell_type": "markdown", 12 | "metadata": {}, 13 | "source": [ 14 | "## Abstract\n", 15 | "\n", 16 | "This is where you describe *briefly* what you're doing and why. What's the point? What's the approach? What's the basic result (value +/- uncertainty)? That's it." 17 | ] 18 | }, 19 | { 20 | "cell_type": "markdown", 21 | "metadata": {}, 22 | "source": [ 23 | "## Description\n", 24 | "\n", 25 | "This is where you go more in depth regarding background information, references, etc. What does the reader need to know to make sense of your project? What is the significance of the project. What did you learn? Stuff like that.\n" 26 | ] 27 | }, 28 | { 29 | "cell_type": "markdown", 30 | "metadata": {}, 31 | "source": [ 32 | "## Algorithm and Discussion\n", 33 | "\n", 34 | "This is where you describe your computational approach. How are you going to address this problem computationally? How is your approach particularly suitable to this problem? What does the reader need to know or understand to make sense of your *code*." 35 | ] 36 | }, 37 | { 38 | "cell_type": "markdown", 39 | "metadata": {}, 40 | "source": [ 41 | "## Implementation and Code\n", 42 | "\n", 43 | "This is the part where you actually solve the problem. Try to make your code clear and readable if possible. The idea is to mix in enough comments and narrative (in Markdown sections) to help the reader understand how your code actually solves the problem at hand. Explain how you're *validating* the code you've written." 44 | ] 45 | }, 46 | { 47 | "cell_type": "markdown", 48 | "metadata": {}, 49 | "source": [ 50 | "## Results\n", 51 | "\n", 52 | "This is where to interpret the results of your calculation. Show how they solve the problem. Explain how you might improve the calculation if you had more time, resources, etc.. Explain how your approach to validation did or did not show your code is producing reasonable results." 53 | ] 54 | }, 55 | { 56 | "cell_type": "markdown", 57 | "metadata": {}, 58 | "source": [ 59 | "## Conclusion\n", 60 | "\n", 61 | "This is a *brief* summary of the whole report. You don't need to *repeat* everything, but a person should be able to read the conclusion and know the basic findings, including numerical results and some indication of uncertainty. An overall assessment of the succcess or failure of the project should be provided." 62 | ] 63 | }, 64 | { 65 | "cell_type": "code", 66 | "execution_count": null, 67 | "metadata": {}, 68 | "outputs": [], 69 | "source": [] 70 | } 71 | ], 72 | "metadata": { 73 | "kernelspec": { 74 | "display_name": "Python 3", 75 | "language": "python", 76 | "name": "python3" 77 | }, 78 | "language_info": { 79 | "codemirror_mode": { 80 | "name": "ipython", 81 | "version": 3 82 | }, 83 | "file_extension": ".py", 84 | "mimetype": "text/x-python", 85 | "name": "python", 86 | "nbconvert_exporter": "python", 87 | "pygments_lexer": "ipython3", 88 | "version": "3.6.5" 89 | } 90 | }, 91 | "nbformat": 4, 92 | "nbformat_minor": 2 93 | } 94 | -------------------------------------------------------------------------------- /buildPDFs.py: -------------------------------------------------------------------------------- 1 | """ 2 | Build pdfs from student notebooks. You need a 'report_rubric.pdf' in the same directory as this file. 3 | """ 4 | import sys 5 | import os 6 | import glob 7 | import re 8 | 9 | if len(sys.argv)>1: 10 | paths=sys.argv[1:] 11 | else: 12 | paths=[os.curdir] 13 | 14 | files = [] 15 | skiprubric = False 16 | 17 | for path in paths: 18 | if path.startswith('--skip'): 19 | skiprubric = True 20 | continue 21 | if os.path.isdir(path): 22 | files += glob.glob(os.path.join(path,'*.ipynb')) 23 | elif os.path.isfile(path): 24 | files += [path] 25 | 26 | rubricPath = os.path.join(os.path.dirname(sys.argv[0]),'report_rubric.pdf') 27 | 28 | print("Files:",files) 29 | 30 | for afile in files: 31 | 32 | blocks = afile.split('/') 33 | print("Found blocks:", blocks) 34 | fname = blocks[-1] 35 | print("Searching for username in ", blocks[1]) 36 | userRE = re.compile("\((.+)\)") 37 | m = userRE.search(blocks[1]) 38 | username = m.group(1) 39 | print("found username:", username) 40 | #codeDir = '/'.join(blocks[:-1]) 41 | #os.chdir(os.path.join(cwd, codeDir)) 42 | #print("Checking %s" % codeDir) 43 | 44 | fpath, fsrc = os.path.split(afile) 45 | fRoot = os.path.splitext(fsrc)[0] 46 | fPDF = os.path.join(fpath, fRoot + '.pdf') 47 | fDest = '.'.join(['./output/' + username,'out','pdf']) 48 | 49 | if not os.path.exists(fDest): 50 | cmd = 'jupyter nbconvert --to PDF "%s"' % afile 51 | print("executing:", cmd) 52 | result = os.system(cmd) 53 | if not result: 54 | if skiprubric: 55 | cmd = 'mv "%s" "%s"' % (fPDF, fDest) 56 | else: 57 | cmd = 'gs -dBATCH -dNOPAUSE -q -sDEVICE=pdfwrite -sOutputFile="%s" "%s" "%s"' % (fDest, rubricPath, fPDF) 58 | print("executing:", cmd) 59 | result = os.system(cmd) 60 | if not result: 61 | print("Complete!", fDest) 62 | if not skiprubric: 63 | os.unlink(fPDF) 64 | else: 65 | print("Ack") 66 | else: 67 | print("Ack Ack!") 68 | else: 69 | print("%s already exists" % fDest) 70 | -------------------------------------------------------------------------------- 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706,23.5581,55.5399,25.1512,54.7086 12 | 754,25.1512,54.7086,26.7425,53.6776 13 | 802,26.7425,53.6776,28.3313,52.8859 14 | 850,28.3313,52.8859,29.9178,52.0349 15 | 898,29.9178,52.0349,31.5009,51.1840 16 | 946,31.5009,51.1840,33.0813,50.3555 17 | 994,33.0813,50.3555,34.6601,49.7643 18 | 1038,34.6601,49.7643,36.2348,49.0897 19 | 1085,36.2348,49.0897,37.8089,48.2261 20 | 1131,37.8089,48.2261,39.3823,47.8323 21 | 1179,39.3823,47.8323,40.9522,47.1996 22 | 2115,70.5354,38.4092,72.0815,37.9136 23 | 2901,96.7421,32.9455,98.2783,32.6774 -------------------------------------------------------------------------------- /p8-data/track270.csv: -------------------------------------------------------------------------------- 1 | mass_A 2 | t,x,y 3 | 8.910000000E0,2.251872769E1,-5.339492132E1 4 | 8.943333333E0,2.042936120E1,-5.432352864E1 5 | 8.976666667E0,1.930729401E1,-5.474914033E1 6 | 9.010000000E0,1.938467796E1,-5.474914033E1 7 | 9.043333333E0,2.042936120E1,-5.436222062E1 8 | 9.076666667E0,2.217049994E1,-5.354968920E1 9 | -------------------------------------------------------------------------------- /p8-data/track_full_lowamp.csv: -------------------------------------------------------------------------------- 1 | mass_A 2 | t,x,y 3 | 1.221950000E2,5.794963014E1,6.547194533E0 4 | 1.222283333E2,5.799838353E1,6.400934354E0 5 | 1.222616667E2,5.794963014E1,6.205920781E0 6 | 1.222950000E2,5.799838353E1,5.767140243E0 7 | 1.223283333E2,5.799838353E1,5.230852918E0 8 | 1.223616667E2,5.809589032E1,4.548305414E0 9 | 1.223950000E2,5.809589032E1,3.817004517E0 10 | 1.224283333E2,5.819339710E1,2.988196834E0 11 | 1.224616667E2,5.804713692E1,2.208142544E0 12 | 1.224950000E2,5.804713692E1,7.942941427E-1 13 | 1.225283333E2,5.824215050E1,1.117466387E-1 14 | 1.225616667E2,5.819339710E1,-9.120746172E-1 15 | 1.225950000E2,5.819339710E1,-1.935895873E0 16 | 1.226283333E2,5.809589032E1,-2.959717129E0 17 | 1.226616667E2,5.799838353E1,-4.032291778E0 18 | 1.226950000E2,5.799838353E1,-5.056113034E0 19 | 1.227283333E2,5.785212335E1,-5.787413931E0 20 | 1.227616667E2,5.785212335E1,-6.664975008E0 21 | 1.227950000E2,5.770586317E1,-7.250015725E0 22 | 1.228283333E2,5.770586317E1,-7.981316622E0 23 | 1.228616667E2,5.775461657E1,-8.371343767E0 24 | 1.228950000E2,5.770586317E1,-8.566357340E0 25 | 1.229300000E2,5.770586317E1,-8.761370912E0 26 | 1.229633333E2,5.770586317E1,-8.761370912E0 27 | 1.229966667E2,5.775461657E1,-8.566357340E0 28 | 1.230300000E2,5.775461657E1,-8.322590374E0 29 | 1.230633333E2,5.780336996E1,-7.981316622E0 30 | 1.230966667E2,5.785212335E1,-7.347522511E0 31 | 1.231300000E2,5.780336996E1,-6.616221614E0 32 | 1.231633333E2,5.785212335E1,-5.884920717E0 33 | 1.231966667E2,5.799838353E1,-5.007359641E0 34 | 1.232300000E2,5.794963014E1,-3.983538385E0 35 | 1.232633333E2,5.790087675E1,-3.057223915E0 36 | 1.232966667E2,5.790087675E1,-2.033402659E0 37 | 1.233300000E2,5.804713692E1,-8.633212240E-1 38 | 1.233633333E2,5.790087675E1,2.092534250E-1 39 | 1.233966667E2,5.799838353E1,9.405543221E-1 40 | 1.234300000E2,5.785212335E1,1.769362005E0 41 | 1.234633333E2,5.780336996E1,2.939443441E0 42 | 1.234966667E2,5.775461657E1,3.768251124E0 43 | 1.235300000E2,5.760835639E1,4.450798628E0 44 | 1.235633333E2,5.760835639E1,5.133346132E0 45 | 1.235966667E2,5.770586317E1,5.669633457E0 46 | 1.236300000E2,5.760835639E1,6.010907208E0 47 | 1.236633333E2,5.755960299E1,6.254674174E0 48 | 1.236966667E2,5.755960299E1,6.400934354E0 49 | 1.237300000E2,5.760835639E1,6.303427567E0 50 | 1.237633333E2,5.770586317E1,6.205920781E0 51 | 1.237966667E2,5.775461657E1,5.913400422E0 52 | 1.238300000E2,5.775461657E1,5.425866491E0 53 | 1.238633333E2,5.780336996E1,4.889579166E0 54 | 1.238966667E2,5.794963014E1,4.060771483E0 55 | 1.239300000E2,5.785212335E1,3.329470586E0 56 | 1.239633333E2,5.785212335E1,2.305649330E0 57 | 1.239966667E2,5.794963014E1,1.379334860E0 58 | 1.240300000E2,5.804713692E1,3.067602113E-1 59 | -------------------------------------------------------------------------------- /pendulum.ino: -------------------------------------------------------------------------------- 1 | #define LED 13 2 | 3 | #define IPIN0 2 // CHANNEL B 4 | #define IPIN1 3 // CHANNEL A 5 | 6 | volatile int angle; // What is the current angle? 7 | 8 | volatile int state0 = LOW; // what is the state of pin 0? 9 | volatile int state1 = LOW; // what is the state of pin 1? 10 | 11 | long int t0; 12 | 13 | int going=0; 14 | 15 | void blink0() { 16 | state0 = digitalRead(IPIN0); // state0 has changed. check state0 and state1 and update angle. 17 | state1 = digitalRead(IPIN1); 18 | 19 | digitalWrite(LED,state0); // let the LED know we're here. 20 | 21 | if (state0) { 22 | if (state1) { 23 | angle -= 1; 24 | } else { 25 | angle += 1; 26 | } 27 | } else { 28 | if (state1) { 29 | angle += 1; 30 | } else { 31 | angle -= 1; 32 | } 33 | } 34 | } 35 | 36 | void blink1() { 37 | state0 = digitalRead(IPIN0); // state1 has changed. check state0 and state1 and update angle. 38 | state1 = digitalRead(IPIN1); 39 | if (state0) { 40 | if (state1) { 41 | angle += 1; 42 | } else { 43 | angle -= 1; 44 | } 45 | } else { 46 | if (state1) { 47 | angle -= 1; 48 | } else { 49 | angle += 1; 50 | } 51 | } 52 | } 53 | 54 | void setup() { 55 | pinMode(LED, OUTPUT); 56 | Serial.begin(9600); 57 | attachInterrupt(digitalPinToInterrupt(IPIN0), blink0, CHANGE); 58 | attachInterrupt(digitalPinToInterrupt(IPIN1), blink1, CHANGE); 59 | Serial.println("Ready"); // tell the computer we're ready 60 | Serial.println("Time,Angle"); 61 | } 62 | 63 | void loop() { 64 | char command; 65 | if (Serial.available()>0) { // are there characters to read? 66 | command = (char)Serial.read(); // grab one 67 | if (command=='g') { // check it 68 | going=1; 69 | angle=0; 70 | t0=millis(); 71 | } else if (command=='s') { 72 | going=0; 73 | } 74 | } 75 | if (going) { 76 | Serial.print(1.0*(millis()-t0)/1000,3); 77 | Serial.print(","); 78 | Serial.println(360.0*angle/2048,3); 79 | } 80 | } 81 | 82 | 83 | -------------------------------------------------------------------------------- /report_rubric.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/sspickle/sci-comp-notebooks/ec0b5c28ff76d228066337a8181be69b5d9c2b7b/report_rubric.pdf -------------------------------------------------------------------------------- /requirements.txt: -------------------------------------------------------------------------------- 1 | Cython 2 | jupyter 3 | matplotlib 4 | numpy 5 | pandas 6 | scipy 7 | sympy 8 | tensorflow 9 | xlrd 10 | openpyxl 11 | -------------------------------------------------------------------------------- /titanic_survived.csv: -------------------------------------------------------------------------------- 1 | PassengerId,Survived 2 | 892,0 3 | 893,1 4 | 894,0 5 | 895,0 6 | 896,1 7 | 897,0 8 | 898,1 9 | 899,0 10 | 900,1 11 | 901,0 12 | 902,0 13 | 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104 | 994,0 105 | 995,0 106 | 996,1 107 | 997,0 108 | 998,0 109 | 999,0 110 | 1000,0 111 | 1001,0 112 | 1002,0 113 | 1003,1 114 | 1004,1 115 | 1005,1 116 | 1006,1 117 | 1007,0 118 | 1008,0 119 | 1009,1 120 | 1010,0 121 | 1011,1 122 | 1012,1 123 | 1013,0 124 | 1014,1 125 | 1015,0 126 | 1016,0 127 | 1017,1 128 | 1018,0 129 | 1019,1 130 | 1020,0 131 | 1021,0 132 | 1022,0 133 | 1023,0 134 | 1024,1 135 | 1025,0 136 | 1026,0 137 | 1027,0 138 | 1028,0 139 | 1029,0 140 | 1030,1 141 | 1031,0 142 | 1032,1 143 | 1033,1 144 | 1034,0 145 | 1035,0 146 | 1036,0 147 | 1037,0 148 | 1038,0 149 | 1039,0 150 | 1040,0 151 | 1041,0 152 | 1042,1 153 | 1043,0 154 | 1044,0 155 | 1045,1 156 | 1046,0 157 | 1047,0 158 | 1048,1 159 | 1049,1 160 | 1050,0 161 | 1051,1 162 | 1052,1 163 | 1053,0 164 | 1054,1 165 | 1055,0 166 | 1056,0 167 | 1057,1 168 | 1058,0 169 | 1059,0 170 | 1060,1 171 | 1061,1 172 | 1062,0 173 | 1063,0 174 | 1064,0 175 | 1065,0 176 | 1066,0 177 | 1067,1 178 | 1068,1 179 | 1069,0 180 | 1070,1 181 | 1071,1 182 | 1072,0 183 | 1073,0 184 | 1074,1 185 | 1075,0 186 | 1076,1 187 | 1077,0 188 | 1078,1 189 | 1079,0 190 | 1080,1 191 | 1081,0 192 | 1082,0 193 | 1083,0 194 | 1084,0 195 | 1085,0 196 | 1086,0 197 | 1087,0 198 | 1088,0 199 | 1089,1 200 | 1090,0 201 | 1091,1 202 | 1092,1 203 | 1093,0 204 | 1094,0 205 | 1095,1 206 | 1096,0 207 | 1097,0 208 | 1098,1 209 | 1099,0 210 | 1100,1 211 | 1101,0 212 | 1102,0 213 | 1103,0 214 | 1104,0 215 | 1105,1 216 | 1106,1 217 | 1107,0 218 | 1108,1 219 | 1109,0 220 | 1110,1 221 | 1111,0 222 | 1112,1 223 | 1113,0 224 | 1114,1 225 | 1115,0 226 | 1116,1 227 | 1117,1 228 | 1118,0 229 | 1119,1 230 | 1120,0 231 | 1121,0 232 | 1122,0 233 | 1123,1 234 | 1124,0 235 | 1125,0 236 | 1126,0 237 | 1127,0 238 | 1128,0 239 | 1129,0 240 | 1130,1 241 | 1131,1 242 | 1132,1 243 | 1133,1 244 | 1134,0 245 | 1135,0 246 | 1136,0 247 | 1137,0 248 | 1138,1 249 | 1139,0 250 | 1140,1 251 | 1141,1 252 | 1142,1 253 | 1143,0 254 | 1144,0 255 | 1145,0 256 | 1146,0 257 | 1147,0 258 | 1148,0 259 | 1149,0 260 | 1150,1 261 | 1151,0 262 | 1152,0 263 | 1153,0 264 | 1154,1 265 | 1155,1 266 | 1156,0 267 | 1157,0 268 | 1158,0 269 | 1159,0 270 | 1160,1 271 | 1161,0 272 | 1162,0 273 | 1163,0 274 | 1164,1 275 | 1165,1 276 | 1166,0 277 | 1167,1 278 | 1168,0 279 | 1169,0 280 | 1170,0 281 | 1171,0 282 | 1172,1 283 | 1173,0 284 | 1174,1 285 | 1175,1 286 | 1176,1 287 | 1177,0 288 | 1178,0 289 | 1179,0 290 | 1180,0 291 | 1181,0 292 | 1182,0 293 | 1183,1 294 | 1184,0 295 | 1185,0 296 | 1186,0 297 | 1187,0 298 | 1188,1 299 | 1189,0 300 | 1190,0 301 | 1191,0 302 | 1192,0 303 | 1193,0 304 | 1194,0 305 | 1195,0 306 | 1196,1 307 | 1197,1 308 | 1198,0 309 | 1199,0 310 | 1200,0 311 | 1201,1 312 | 1202,0 313 | 1203,0 314 | 1204,0 315 | 1205,1 316 | 1206,1 317 | 1207,1 318 | 1208,0 319 | 1209,0 320 | 1210,0 321 | 1211,0 322 | 1212,0 323 | 1213,0 324 | 1214,0 325 | 1215,0 326 | 1216,1 327 | 1217,0 328 | 1218,1 329 | 1219,0 330 | 1220,0 331 | 1221,0 332 | 1222,1 333 | 1223,0 334 | 1224,0 335 | 1225,1 336 | 1226,0 337 | 1227,0 338 | 1228,0 339 | 1229,0 340 | 1230,0 341 | 1231,0 342 | 1232,0 343 | 1233,0 344 | 1234,0 345 | 1235,1 346 | 1236,0 347 | 1237,1 348 | 1238,0 349 | 1239,1 350 | 1240,0 351 | 1241,1 352 | 1242,1 353 | 1243,0 354 | 1244,0 355 | 1245,0 356 | 1246,1 357 | 1247,0 358 | 1248,1 359 | 1249,0 360 | 1250,0 361 | 1251,1 362 | 1252,0 363 | 1253,1 364 | 1254,1 365 | 1255,0 366 | 1256,1 367 | 1257,1 368 | 1258,0 369 | 1259,1 370 | 1260,1 371 | 1261,0 372 | 1262,0 373 | 1263,1 374 | 1264,0 375 | 1265,0 376 | 1266,1 377 | 1267,1 378 | 1268,1 379 | 1269,0 380 | 1270,0 381 | 1271,0 382 | 1272,0 383 | 1273,0 384 | 1274,1 385 | 1275,1 386 | 1276,0 387 | 1277,1 388 | 1278,0 389 | 1279,0 390 | 1280,0 391 | 1281,0 392 | 1282,0 393 | 1283,1 394 | 1284,0 395 | 1285,0 396 | 1286,0 397 | 1287,1 398 | 1288,0 399 | 1289,1 400 | 1290,0 401 | 1291,0 402 | 1292,1 403 | 1293,0 404 | 1294,1 405 | 1295,0 406 | 1296,0 407 | 1297,0 408 | 1298,0 409 | 1299,0 410 | 1300,1 411 | 1301,1 412 | 1302,1 413 | 1303,1 414 | 1304,1 415 | 1305,0 416 | 1306,1 417 | 1307,0 418 | 1308,0 419 | 1309,0 --------------------------------------------------------------------------------