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Introduction
Computational Physics:
An introductory course
Richard Fitzpatrick
Associate Professor of Physics
The University of Texas at Austin
Introduction
Intended audience
Major sources
Purpose of course
Course philosophy
Programming methodologies
Scientific programming languages
Scientific programming in C
Introduction
Variables
Expressions and statements
Operators
Library functions
Data input and output
Structure of a C program
Control statements
Functions
Pointers
Global variables
Arrays
Character strings
Multi-file programs
Command line parameters
Timing
Random numbers
C++ extensions to C
Complex numbers
Variable size multi-dimensional arrays
The CAM graphics class
Integration of ODEs
Introduction
Euler's method
Numerical errors
Numerical instabilities
Runge-Kutta methods
An example fixed-step RK4 routine
An example calculation
Adaptive integration methods
An example adaptive-step RK4 routine
Advanced integration methods
The physics of baseball pitching
Air drag
The Magnus force
Simulations of baseball pitches
The knuckleball
The chaotic pendulum
Introduction
Analytic solution
Numerical solution
Validation of numerical solutions
The Poincaré section
Spatial symmetry breaking
Basins of attraction
Period-doubling bifurcations
The route to chaos
Sensitivity to initial conditions
The definition of chaos
Periodic windows
Further investigation
Poisson's equation
Introduction
1-d problem with Dirichlet boundary conditions
An example tridiagonal matrix solving routine
1-d problem with mixed boundary conditions
An example 1-d Poisson solving routine
An example solution of Poisson's equation in 1-d
2-d problem with Dirichlet boundary conditions
2-d problem with Neumann boundary conditions
The fast Fourier transform
An example 2-d Poisson solving routine
An example solution of Poisson's equation in 2-d
Example 2-d electrostatic calculation
3-d problems
The diffusion equation
Introduction
1-d problem with mixed boundary conditions
An example 1-d diffusion equation solver
An example 1-d solution of the diffusion equation
von Neumann stability analysis
The Crank-Nicholson scheme
An improved 1-d diffusion equation solver
An improved 1-d solution of the diffusion equation
2-d problem with Dirichlet boundary conditions
2-d problem with Neumann boundary conditions
An example 2-d diffusion equation solver
An example 2-d solution of the diffusion equation
3-d problems
The wave equation
Introduction
The 1-d advection equation
The Lax scheme
The Crank-Nicholson scheme
Upwind differencing
The 1-d wave equation
The 2-d resonant cavity
Particle-in-cell codes
Introduction
Normalization scheme
Solution of electron equations of motion
Evaluation of electron number density
Solution of Poisson's equation
An example 1D PIC code
Results
Discussion
Monte-Carlo methods
Introduction
Random numbers
Distribution functions
Monte-Carlo integration
The Ising model
About this document ...
Richard Fitzpatrick 2006-03-29
