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Computational Physics
Introduction
1. Plotting basics
2. Machine precision
3. Interpolation
4. Linear algebra
5. Non-linear equations
Solving a non-linear equation
Polynomials and their roots
Systems of non-linear equations
Function minimization
6. Numerical integration
Basic methods
Adaptive methods
Improper integrals
High-order and Gaussian quadratures
7. Numerical differentiation
Finite differences
Automatic differentiation
Example: Susceptibility and Bose-Einstein condensation
8. Ordinary differential equations (ODEs)
Basic methods
Systems of ODEs
Time-reversal methods
Boundary value problems
9. Classical mechanics
Classical mechanics problems
Molecular dynamics simulations
10. Partial differential equations (PDEs)
Boundary value problems
Initial value problem: Heat equation
Initial value problem: Wave equation
11. Random numbers and Monte Carlo methods
Uniform random numbers
Computing integrals
Nonuniform random numbers
12. Statistical Physics
Markov chains and Metropolis algorithm
Ising model
Simulated annealing
Percolation threshold
13. Quantum Mechanics
Matrix methods for quantum mechanics
Time dependent Schrödinger equation
Variational Monte Carlo
14. Fourier transform
Index