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PYU44C01 Computer Simulation II

Hilary Term – 24 lectures/tutorials – 5 credits (C Patterson, M Möbius)

Part I: High Performance Computing
Part II: Numerical Methods

Learning Outcomes
On successful completion of this module, students should be able to:

  •  Be able to formulate and solve physical problems which require linear algebra techniques
  •  Be familiar with scientific computing libraries such as SciPy and Gnu Scientific Library
  •  Be familiar with Fourier methods for signal processing.
  •  Be able to solve partial differential equations numerically using finite difference methods.
  •  Be able to implement these methods in Python.


Part I:
Introduction to scientific computing libraries (Gnu Scientific Libray, LAPACK, SciPy), Review of vector spaces and linear algebra, Solution of systems of linear equations, Eigenvalue and eigenvector problems, Matrix decompositions (LU, Cholesky, QR, SVD), Python labs to illustrate algorithms using physical examples.

Part II: Numerical Methods
Review of Fourier series and transforms, Correlation and convolution in Fourier space, Aliasing and spectral leakage in FFT, Signal filtering, Windowing, Solving PDE’s analytically and numerically using finite difference methods, Numerical stability and accuracy of finite difference methods, Python labs to implement algorithms discussed in the course.