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Computational Physics Course Description
Computational Physics -- 3rd/4th Year Option
Angus MacKinnon
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Computational Physics
Course Description
Ordinary Differential Equations
Types of Differential Equation
Euler Method
Order of Accuracy
Stability
The Growth Equation
Application to Non-Linear Differential Equations
Application to Vector Equations
The Leap-Frog Method
The Runge-Kutta Method
The Predictor-Corrector Method
The Intrinsic Method
Summary
Problems
Project -- Classical Electrons in a Magnetic Field
A Uniform Field
Units
The Analytical Solution
Choosing an Algorithm
Crossed Electric and Magnetic Fields
Oscillating Electric Field
Your Report
Partial Differential Equations
Types of Equations
Elliptic Equations -- Laplace's equation
Hyperbolic Equations -- Wave equations
A Simple Algorithm
An Improved Algorithm -- the Lax method
Non-Linear Equations
Other methods for Hyperbolic Equations
Eulerian and Lagrangian Methods
Parabolic Equations -- Diffusion
A Simple Method
The Dufort-Frankel Method
Other Methods
Conservative Methods
The Equation of Continuity
The Diffusion Equation
Maxwell's Equations
Dispersion
Problems
Project -- Lagrangian Fluid Code
The Difference Equations
Boundary Conditions
Initial Conditions
The Physics
An Improvement?
The Report
Project -- Solitons
Introduction
Discretisation
Physics
Matrix Algebra
Introduction
Types of Matrices
Simple Matrix Problems
Addition and Subtraction
Multiplication of Matrices
Elliptic Equations -- Poisson's Equation
One Dimension
2 or more Dimensions
Systems of Equations and Matrix Inversion
Exact Methods
Iterative Methods
The Jacobi Method
The Gauss-Seidel Method
Matrix Eigenvalue Problems
Schrödinger's equation
General Principles
Full Diagonalisation
The Generalised Eigenvalue Problem
Partial Diagonalisation
Sturm Sequence
Sparse Matrices and the Lanczos Algorithm
Problems
Project -- Oscillations of a Crane
Analysis
Project -- Phonons in a Quasicrystal
Introduction
The Fibonacci Lattice
The Model
The Physics
Monte Carlo Methods and Simulation
Monte Carlo
Random Number Generators
Monte-Carlo Integration
The Metropolis Algorithm
The Ising model
Thermodynamic Averages
Quantum Monte-Carlo
Molecular Dynamics
General Principles
Problems
Project -- The Ising Model
Introduction
The Model and Method
The Physics
Project -- Quantum Monte Carlo Calculation
Introduction
The Method
The Physics
Computer Algebra
Introduction
Basic Principles
Solving Equations
Differential Equations
Other Features
Final Example
Project -- The Thomas-Fermi Approximation
Introduction
Some Ideas
Bibliography
