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Module MA346F: Practical Numerical Simulations

Credit weighting (ECTS)
5 credits
Semester/term taught
Hilary term 2017-18
Contact Hours
11 weeks, 3 lectures including tutorials per week
Lecturer
Professor Mike Peardon

Learning Outcomes
On successful completion of this module, students will be able to:
  • Write and compile numerical software in C++
  • Find an appropriate numerical technique to solve common problems in applied mathematics and theoretical physics and to recognise its limitations.
  • Construct numerical solutions to mathematical and physical problems in C++
  • Describe the output of their numerical software and interpret results reliably.
Module Content
The module aims to introduce the C++ programming language and object-oriented software concepts by getting students to construct numerical solutions to common problems in applied mathematics and theoretical physics.
C++:
  • Language basics: the compiler, variables, functions.
  • Conditions and loops.
  • Arrays, pointers and references
  • C++ classes
Numerical analysis:
  • Ordinary differential equations - solving initial-value problems with Euler and Runge-Kutta methods.
  • Ordinary differential equations - boundary-value problems and the shooting method.
  • Hamiltonian dynamics - symplectic integrators and the leap-frog method.
  • Partial differential equations - solving the 2d Laplace equation using simple iterative schemes (Jacobi, Gauss-Seidel and SOR) with Dirichlet and Von Neumann boundary data.
  • Introduction to Monte Carlo methods in statistical physics.

Module Prerequisite
MA1241 and one of MA2327, MA2332
Assessment Detail
This module will be examined in a 2 hour examination in Trinity term (60%). Four continuous assessment assignments will contribute 40% to the final grade for the module at the annual examination session. Supplemental if required will consist of 100% exam.