1.1 Computational modeling and visualization
1.2 The science and art of numerics
1.3 Fundamentals of programming and visualization
1.A Floating point representation
1.C The Matplotlib plot function
1.D Basic NumPy array operations
2 Free fall and ordinary differential equations
2.1 Free fall with Euler's method
2.3 System of first order ODEs
2.A Area preservation of the leapfrog method
2.B Program listings and descriptions
3 Realistic projectile motion with air resistance
3.1 Visualization of ideal projectile motion
3.5 Quadratic air resistance and spin
3.A Bisection and Newton's root finders
3.B Program listings and descriptions
4 Planetary motion and few-body problems
4.2 Properties of planetary motion
4.4 Star wobbles and exoplanets
4.5 Planar three-body problems
4.6 The restricted three-body problem
4.A Rotating frames and rate of change of vectors
4.C Radial velocity transformation
4.D Program listings and descriptions
5 Nonlinear dynamics and chaos
5.1 A first model: the logistic map
5.3 A nonlinear driven oscillator
5.5 Power spectrum and Fourier transform
5.A Program listings and descriptions
6.1 A damped harmonic oscillator
6.2 Vibrations of triatomic molecules
6.3 Displacement of a string under a load
6.4 Point source and finite element method
6.8 A falling tablecloth toward equilibrium
6.A Program listings and descriptions
7.1 The game of electric field hockey
7.2 Electric potentials and fields
7.3 Laplace equation and finite element method
7.4 Boundary value problems with FEM
7.5 Meshfree methods for potentials and fields
7.6 Visualization of electromagnetic fields
7.A Program listings and descriptions
8 Time-dependent quantum mechanics
8.1 Time-dependent Schrödinger equation
8.3 Free fall, the quantum way
8.4 Two-state systems and Rabi flopping
8.B Program listings and descriptions
9 Time-independent quantum mechanics
9.1 Bound states by shooting methods
9.2 Periodic potentials and energy bands
9.3 Eigenenergies by FDM and FEM methods
9.B The linear potential and Airy function
9.C Program listings and descriptions
10.1 Random numbers and radioactive decay
10.4 Potential energy by Monte Carlo integration
10.A Statistical theory of Brownian motion
10.C Program listings and descriptions
11.1 Thermodynamics of equilibrium
11.3 Thermal relaxation by simulated annealing
11.A Boltzmann factor and entropy
11.B Exact solutions of the 2D Ising model
11.C Program listings and descriptions
12 Classical and quantum scattering
12.1 Scattering and cross sections
12.2 Rainbow and glory scattering
12.3 Quantum scattering amplitude
12.A Derivation of the deflection function