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Next: Introduction Up: Computational physics Previous: Computational physics

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• 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 ...

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Richard Fitzpatrick 2006年03月29日