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Dedication
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Dedication
by Jay Wang
Computational Modeling and Visualization of Physical Systems with Python
Cover Page
Title Page
Dedication
Preface
Contents
Chapter 1: Introduction
1.1 Computational modeling and visualization
1.2 The science and art of numerics
1.3 Fundamentals of programming and visualization
1.4 Exercises and Projects
1.A Floating point representation
1.B Python installation
1.C The Matplotlib plot function
1.D Basic NumPy array operations
Chapter 2: Free fall and ordinary differential equations
2.1 Free fall with Euler’s method
2.2 The Runge-Kutta (RK) methods
2.3 System of first order ODEs
2.4 The leapfrog method
2.5 Exercises and Projects
2.A Area preservation of the leapfrog method
2.B Program listings and descriptions
Chapter 3: Realistic projectile motion with air resistance
3.1 Visualization of ideal projectile motion
3.2 Modeling air resistance
3.3 Linear air resistance
3.4 The Lambert W function
3.5 Quadratic air resistance and spin
3.6 Physics of ball sports
3.7 Shooting methods
3.8 Exercises and Projects
3.A Bisection and Newton's root finders
3.B Program listings and descriptions
Chapter 4: Planetary motion and few-body problems
4.1 Motion of a planet
4.2 Properties of planetary motion
4.3 Precession of Mercury
4.4 Star wobbles and exoplanets
4.5 Planar three-body problems
4.6 The restricted three-body problem
4.7 Exercises and Projects
4.A Rotating frames and rate of change of vectors
4.B Rotation matrices
4.C Radial velocity transformation
4.D Program listings and descriptions
Chapter 5: Nonlinear dynamics and chaos
5.1 A first model: the logistic map
5.2 Chaos
5.3 A nonlinear driven oscillator
5.4 The Lorenz flow
5.5 Power spectrum and Fourier transform
5.6 Fractals
5.7 Exercises and Projects
5.A Program listings and descriptions
Chapter 6: Oscillations and waves
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
6.5 Waves on a string
6.6 Standing waves
6.7 Waves on a membrane
6.8 A falling tablecloth toward equilibrium
6.9 Exercises and Projects
6.A Program listings and descriptions
Chapter 7: Electromagnetic fields
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
7.7 Exercises and Projects
7.A Program listings and descriptions
Chapter 8: Time-dependent quantum mechanics
8.1 Time-dependent Schrödinger equation
8.2 Direct simulation
8.3 Free fall, the quantum way
8.4 Two-state systems and Rabi flopping
8.5 Quantum waves in 2D
8.6 Exercises and Projects
8.A Numerical integration
8.B Program listings and descriptions
Chapter 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
9.4 Basis expansion method
9.5 Central field potentials
9.6 Quantum dot
9.7 Exercises and Projects
9.A Numerov's method
9.B The linear potential and Airy function
9.C Program listings and descriptions
Chapter 10: Simple random problems
10.1 Random numbers and radioactive decay
10.2 Random walk
10.3 Brownian motion
10.4 Potential energy by Monte Carlo integration
10.5 Exercises and Projects
10.A Statistical theory of Brownian motion
10.B Nonuniform distributions
10.C Program listings and descriptions
Chapter 11: Thermal systems
11.1 Thermodynamics of equilibrium
11.2 The Ising model
11.3 Thermal relaxation by simulated annealing
11.4 Molecular dynamics
11.5 Exercises and Projects
11.A Boltzmann factor and entropy
11.B Exact solutions of the 2D Ising model
11.C Program listings and descriptions
Chapter 12: Classical and quantum scattering
12.1 Scattering and cross sections
12.2 Rainbow and glory scattering
12.3 Quantum scattering amplitude
12.4 Partial waves
12.5 Exercises and Projects
12.A Derivation of the deflection function
12.B Partial wave analysis
12.C Program listings and descriptions
List of programs
Bibliography
Index
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Title Page
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Preface
To my Father and Mother
who taught me that knowledge is to be revered
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