├── .codespell-ignore-words ├── .codespellrc ├── .github ├── dependabot.yml └── workflows │ ├── codespell.yml │ ├── linkcheck.yml │ └── main.yml ├── .gitignore ├── LICENSE ├── README.md ├── applications.txt ├── content ├── ODEs │ ├── ODEs-conservation.ipynb │ ├── ODEs-euler.ipynb │ ├── ODEs-implicit-nonlinear-systems.ipynb │ ├── ODEs-implicit-systems.ipynb │ ├── ODEs-implicit.ipynb │ ├── ODEs-midpoint.ipynb │ ├── ODEs-rk4.ipynb │ ├── ODEs-scipy.ipynb │ ├── ODEs-timereverse.ipynb │ ├── adaptive-orbits.ipynb │ ├── adaptive_stepping.md │ ├── adaptive_timestep.png │ ├── application-CNO-network.ipynb │ ├── application-few-body.ipynb │ ├── application-lane-emden.ipynb │ ├── application-planetary-stability.ipynb │ ├── application-xrb-one-zone.ipynb │ ├── applications.md │ ├── boundary-value-problems.ipynb │ ├── ellipse_initial_cond_e0.0.png │ ├── ellipse_initial_cond_e0.4.png │ ├── example-lorenz.ipynb │ ├── exercises.ipynb │ ├── more-applications.md │ ├── orbit.py │ ├── orbit_adaptive.py │ ├── orbit_util.py │ ├── rk2_Euler.png │ ├── rk2_final.png │ ├── rk2_halfEuler.png │ ├── rk4_final.png │ ├── rk4_k1.png │ ├── rk4_k2.png │ ├── rk4_k3.png │ ├── rk4_k4.png │ └── three_body.py ├── _config.yml ├── _static │ └── myfile.css ├── _toc.yml ├── _toc_all.yml ├── advection │ ├── advection-intro.md │ ├── advection-more.md │ ├── advection │ │ ├── advection-convergence.ipynb │ │ ├── advection-finite-volumes.md │ │ ├── advection-partI.ipynb │ │ ├── advection-second-order.ipynb │ │ ├── advection-states.png │ │ ├── advection-upwind.ipynb │ │ ├── array-labels.png │ │ ├── fd_ghost.png │ │ ├── fd_ghost_lohi.png │ │ ├── fd_grid.png │ │ ├── fd_grid_basic.png │ │ ├── fv_ghost.png │ │ ├── fv_grid.png │ │ ├── generalgrid.png │ │ ├── grids.png │ │ ├── riemann-adv-mol.png │ │ ├── riemann-mol.png │ │ └── riemann.png │ ├── burgers │ │ ├── advection-characteristics.png │ │ ├── burgers-characteristics-rare.png │ │ ├── burgers-characteristics-shock.png │ │ ├── burgers-methods.ipynb │ │ ├── burgers-riemann.md │ │ ├── burgers.md │ │ ├── exercises.ipynb │ │ └── rh.png │ └── pdes.md ├── basics │ ├── diff-int │ │ ├── 3alpha.cpp │ │ ├── application-blackbody.ipynb │ │ ├── application-rate-temperature-sensitivity.ipynb │ │ ├── application-stellar-colors.ipynb │ │ ├── compound.png │ │ ├── compound2.png │ │ ├── derivs.png │ │ ├── differentiation.ipynb │ │ ├── example-second-deriv.ipynb │ │ ├── exercises.ipynb │ │ ├── fd_grid.png │ │ ├── going-further.md │ │ ├── integration-composite.ipynb │ │ ├── integration-scipy.ipynb │ │ ├── integration-simpsons.ipynb │ │ ├── integration.ipynb │ │ ├── rectangle_N1.png │ │ ├── rectangle_N6.png │ │ ├── simpsons_N1.png │ │ ├── simpsons_N6.png │ │ ├── trapezoid_N1.png │ │ └── trapezoid_N6.png │ ├── floating-point │ │ ├── 1024px-IEEE_754_Double_Floating_Point_Format.svg.png │ │ ├── floating-point-details.md │ │ └── numerical_error.ipynb │ ├── linear-algebra │ │ ├── application-lorenz.ipynb │ │ ├── condition-number.ipynb │ │ ├── gaussian_elimination.md │ │ ├── gaussian_elimination_python.ipynb │ │ ├── going-further.md │ │ ├── la-basics.ipynb │ │ ├── la-cxx.md │ │ ├── la-overview.md │ │ ├── linear-algebra-libraries.ipynb │ │ ├── linear-system-example.md │ │ └── multivariate-roots.md │ └── roots │ │ ├── application-degeneracy.ipynb │ │ ├── application-wiens.ipynb │ │ ├── newton_00.png │ │ ├── newton_01.png │ │ ├── newton_02.png │ │ ├── root-finding.ipynb │ │ └── roots-scipy.ipynb ├── diffusion │ ├── diffusion-explicit.ipynb │ ├── diffusion-going-further.md │ ├── diffusion-implicit-direct.ipynb │ ├── diffusion-implicit-intro.md │ ├── diffusion-implicit-relax.ipynb │ ├── diffusion.md │ ├── phi_analytic_t.png │ └── tridiagonal-system.md ├── elliptic_multigrid │ ├── intro │ │ └── elliptic-problems.md │ ├── multigrid │ │ ├── __pycache__ │ │ │ ├── grid.cpython-39.pyc │ │ │ └── multigrid.cpython-39.pyc │ │ ├── fvrestrict.png │ │ ├── grid.py │ │ ├── mg_error_vs_cycle.png │ │ ├── mg_test.py │ │ ├── mgtower.png │ │ ├── multigrid-restrict-prolong.ipynb │ │ ├── multigrid-two-grid.ipynb │ │ ├── multigrid-vcycles.ipynb │ │ ├── multigrid.md │ │ ├── multigrid.py │ │ ├── phi_analytic.png │ │ └── vcycle.png │ └── relaxation │ │ ├── __pycache__ │ │ └── smoothing.cpython-39.pyc │ │ ├── ccfd_ghost.png │ │ ├── ccfd_grid_bnd.png │ │ ├── elliptic-modes.ipynb │ │ ├── elliptic-relaxation.ipynb │ │ ├── elliptic-residual.ipynb │ │ ├── fd_grid_bnd.png │ │ ├── relaxation.md │ │ └── smoothing.py ├── euler │ ├── euler-eigen.ipynb │ ├── euler-riemann-sampling.ipynb │ ├── euler-riemann.ipynb │ ├── euler-solver.ipynb │ ├── euler.md │ ├── fv_grid.png │ ├── rarefaction_span.png │ ├── riemann-mol.png │ ├── riemann-sod.png │ ├── riemann-waves-jump.png │ ├── riemann-waves.png │ ├── riemann_exact.py │ ├── riemann_state.png │ ├── simplegrid_gc.png │ └── sod-exact.out ├── ffts │ ├── 4u1728_burstdata.txt │ ├── application-lightcurves.ipynb │ ├── application-planets-fft.ipynb │ ├── dft-tests.ipynb │ ├── dft.ipynb │ ├── example-turbulent-power-spectrum.ipynb │ ├── fft-multid.ipynb │ ├── fft.ipynb │ ├── fourier.md │ ├── freq.py │ ├── inclass-filter.ipynb │ ├── inclass-pendulum.ipynb │ ├── luna_bw.png │ ├── non-periodic.md │ ├── planet_positions.dat │ ├── planetary_stability.dat │ ├── power_spectrum2.png │ ├── radial_velocity.dat │ └── sine-k.png ├── fitting │ ├── SCPUnion2_mu_vs_z.txt │ ├── application-snia-h0.ipynb │ ├── fitting-illustration.png │ ├── fitting-nonlinear.ipynb │ ├── fitting-scipy.ipynb │ ├── fitting-to-a-line.ipynb │ ├── generalized-linear-least-squares-tests.ipynb │ ├── generalized-linear-least-squares.md │ ├── illustration.py │ └── least_squares.md ├── git │ ├── distributed_version_control.png │ ├── git-branches.md │ ├── git-remotes.md │ ├── git.md │ ├── github-clone.png │ ├── github-copy-ssh.png │ ├── github-create.png │ ├── github-fork.png │ ├── github-new.png │ ├── github-pr.png │ ├── github-pr2.png │ ├── github-workflow.odg │ ├── github-workflow.pdf │ ├── github-workflow.png │ ├── github.md │ ├── pull-requests.md │ └── version-control.md ├── homework │ ├── 2023 │ │ ├── bilinear_eos.png │ │ ├── homework1.md │ │ ├── homework2.md │ │ ├── homework3.md │ │ ├── homework4.md │ │ ├── homework5.md │ │ ├── homework6.md │ │ ├── homework7.md │ │ ├── hw1-solutions.ipynb │ │ ├── hw2-solutions.ipynb │ │ ├── hw3-solutions.ipynb │ │ ├── hw4-solutions.ipynb │ │ ├── hw5-solutions.ipynb │ │ ├── hw6-solutions.ipynb │ │ ├── hw7-solutions.ipynb │ │ ├── project.md │ │ └── signal.txt │ ├── cepheids.txt │ ├── homework1-solutions.ipynb │ ├── homework1.md │ ├── homework2-solutions.ipynb │ ├── homework2.md │ ├── homework3-solutions.ipynb │ ├── homework3.md │ ├── homework4-solutions.ipynb │ ├── homework4.md │ ├── homework5-solutions.ipynb │ ├── homework5.md │ ├── homework6-solutions.ipynb │ ├── homework6.md │ ├── homework7-solutions.ipynb │ ├── homework7.md │ ├── homework8.md │ ├── ideas.txt │ └── project.md ├── in_class │ ├── in-class-fft.ipynb │ ├── in-class-hilbert-matrix.ipynb │ ├── in-class-ode-projectile.ipynb │ └── signal.txt ├── interpolation │ ├── 56ni-56co_electroncapture.dat │ ├── application-interpolating-reaction-rates.ipynb │ ├── bilinear_ecapture.png │ ├── conservative-interpolation.ipynb │ ├── density_interpolation.png │ ├── going-further.md │ ├── interpolation.md │ ├── lagrange-interpolation.ipynb │ ├── linear-interpolation.ipynb │ ├── linear-interpolation.png │ └── spline_example.png ├── intro.md ├── machine-learning │ ├── README │ ├── application-galaxies-intro.ipynb │ ├── application-galaxies-keras-cnn.ipynb │ ├── application-galaxies-keras.ipynb │ ├── application-galaxies.ipynb │ ├── gradient-descent.ipynb │ ├── ideas.txt │ ├── keras-clustering.ipynb │ ├── keras-last-number.ipynb │ ├── keras-mnist.ipynb │ ├── last-number-hidden.ipynb │ ├── last-number.ipynb │ ├── machine-learning-in-astro.md │ ├── machine-learning-libraries.md │ ├── machine-learning-types.md │ ├── mnist-cxx.md │ ├── mnist_test.csv.zip │ ├── mnist_train.csv.zip │ ├── neural-net-basics.md │ ├── neural-net-derivation.md │ ├── neural-net-hidden.md │ ├── neural-net-improvements.md │ ├── neural-net-mnist.ipynb │ ├── nn_fig.png │ ├── nn_fig.py │ ├── nn_fig_hidden.png │ ├── notes.txt │ ├── sigmoid.png │ └── sigmoid.py ├── overview │ ├── intro.md │ └── using.md ├── projects │ └── projects.md ├── python │ ├── anatomy1.png │ ├── jupyter.ipynb │ ├── matplotlib-basics.ipynb │ ├── numpy-advanced.ipynb │ ├── numpy-basics.ipynb │ ├── numpy.md │ ├── python-advanced-datatypes.ipynb │ ├── python-basics.md │ ├── python-classes.ipynb │ ├── python-control-flow.ipynb │ ├── python-datatypes.ipynb │ ├── python-functions-classes.md │ ├── python-functions.ipynb │ ├── row_column_major.png │ └── slicing.png ├── references.bib ├── rt_small.png └── stars │ ├── lane-emden.ipynb │ ├── le_extrap.png │ └── stars.md ├── examples ├── ODEs │ ├── RK45 │ │ ├── README.md │ │ └── orbit_adaptive.cpp │ ├── adaptive_RK4 │ │ ├── adaptive_rk4_dt.png │ │ ├── adaptive_rk4_orbit.png │ │ ├── orbit.py │ │ ├── orbit_adaptive.cpp │ │ ├── orbit_adaptive.dat │ │ ├── orbit_adaptive.py │ │ └── orbit_verlet_adaptive.py │ └── orbit_fixed │ │ └── orbit_rk4.cpp ├── advection │ ├── second_order │ │ ├── advection_fv.cpp │ │ ├── fvgrid.H │ │ └── initial_conditions.H │ └── upwind │ │ ├── fdgrid.H │ │ ├── initial_conditions.H │ │ └── upwind.cpp ├── few_body │ ├── three_body.cpp │ └── three_body.py ├── fft │ ├── dft.H │ └── dft_test.cpp ├── fitting │ ├── fitting.H │ ├── gauss.H │ ├── inverse.H │ ├── matrix.H │ ├── test_fitting.cpp │ ├── test_inverse.cpp │ └── test_matrix.cpp ├── floating_point │ ├── limits.cpp │ └── simple_roundoff.cpp ├── integration │ ├── blackbody.cpp │ ├── gaussian.cpp │ └── simpsons.cpp ├── interpolation │ ├── lagrange_interp.cpp │ └── linear_interp.cpp ├── linear-algebra │ ├── array.H │ ├── gauss.H │ ├── gauss.py │ ├── gauss_test.cpp │ ├── gauss_test.py │ ├── hilbert.cpp │ ├── lorenz-roots.cpp │ ├── matmul.H │ ├── matmul.py │ └── test_matmul.cpp ├── linear_error │ └── linear_error.py ├── machine_learning │ └── mnist │ │ ├── GNUmakefile │ │ ├── README.md │ │ ├── matrix.H │ │ ├── mnist.H │ │ ├── mnist_test.csv │ │ ├── mnist_train.csv │ │ ├── neural_network.H │ │ ├── neural_network_relu.H │ │ ├── test_matrix.cpp │ │ ├── test_mnist.cpp │ │ ├── test_nn.cpp │ │ └── test_random.cpp ├── mathematical_vectors │ ├── test_vectors.cpp │ └── vector2d.H ├── matrix │ ├── matrix.H │ └── test_matrix.cpp ├── mercury │ └── mercury.ipynb ├── planetary_stability │ ├── orbit_state.H │ ├── planet_positions.dat │ ├── planetary_stability.cpp │ ├── planets-fft.ipynb │ ├── radial_velocity.cpp │ ├── radial_velocity.dat │ └── solar_system.H ├── poisson │ ├── poisson.H │ └── poisson.cpp ├── roots │ ├── degeneracy.cpp │ └── roots.cpp └── tridiagonal │ ├── tridiag.H │ └── tridiag.cpp ├── figures ├── 2dgrid.png ├── 2dgrid.py ├── adaptive_timesteps.py ├── advection-states.png ├── advection_states.py ├── array-labels.png ├── array_labels.py ├── bilinear-eos.py ├── ccfd_ghost.png 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