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PHYS 512 Computational Physics with Applications - Home PHYS 512 Computational Physics with Applications - Home

About the course

  • Course outline

Getting started

  • Getting set up
  • Programming best practices
  • Floating point arithmetic

Manipulating functions

  • Derivatives
  • Interpolation
  • Integration
  • Solutions to exercises
    • Derivatives exercises
    • Interpolation exercises
    • Integration exercises

Random numbers

  • Random numbers
  • Linear Congruential Generators
  • Probability distributions
  • Monte Carlo integration
  • Metropolis-Hastings algorithm
  • Solutions to exercises
    • Probability distributions Exercise 1
    • Probability distributions Part 2
    • Monte Carlo Integration
    • Metropolis-Hastings

Solving systems of equations

  • Matrices in numpy
  • Linear least squares
  • Polynomial fitting
  • Non-linear least squares
  • Solutions to exercises
    • Orthogonal polynomials
    • Lorentzian fit

Machine Learning

  • Machine Learning
  • ChatGPT ‘Real-Life Example’
  • Example : Higgs Boson

Differential equations

  • Initial value problems
  • Boundary value problems
  • Symplectic integrators
  • Poisson’s equation
  • Sparse matrices
  • Boundary conditions and numerical stability
  • Diffusion in multi-dimensions
  • Solutions to exercises
    • Initial value problems
    • Boundary value problems
    • Symplectic integrators
    • Conjugate gradient solutions
    • Boundary conditions and numerical stability solutions
    • Alternating-direction implicit

Spectral methods

  • Discrete Fourier transform
  • Advection-diffusion
  • Amplitude and phase errors
  • Burgers’ equation
  • Signal processing
  • Solutions to exercises
    • Discrete Fourier Transform
    • More on the 1D DFT
    • Advection-diffusion with Fourier
    • Advection-diffusion with finite differences
    • LIGO tutorial: find an inspiral

Performance

  • Timing, profiling and compiling

Summary

  • Summary

Homework

  • Homework 1
  • Homework 2
  • Homework 3
  • Homework 4
  • Homework 5
  • Homework 6
  • Homework 7
  • Exam questions and solutions
  • Project Instructions
  • Homework solutions
    • Homework 1 solutions
    • Homework 2 solutions
    • Homework 2: Common Issues
    • Homework 3 solutions
    • Homework 4 solutions
    • Homework 5 solutions
    • Homework 6 solutions
    • Homework 7 solutions
  • Repository
  • Open issue

Index

By Andrew Cumming

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