MTH409 Computational Methods

Topic outline

• General
  

  General

  • News forum
• Introduction
  

  Introduction

  We examine what computational mathematics is about and introduce the basic objects that we will be dealing with.

  • Intro Page

    Notes (in HTML) of the first lecture.
  • Intro File
  • IEEE 754 page on Wikipedia URL
  • Chapter 1 of Chasnov's book URL
  • Assignment 1 File
  • Some Algorithmic Techniques Page
• Summing Series
  

  Summing Series

  Some techniques to sum series.

  • Power series Page
  • Assignment 2 File
  • Power Series Unit Test 1 File
• Matrix operations and decompositions
  

  Matrix operations and decompositions

  Algorithmic techniques to optimise row-reduction and inversion of matrices. Based on the problem an appropriate decomposition theorem from Group theory becomes applicable.

  • Read Chapter 7 of Epperson's book (or any other equivalent resource)
  • Assignment 3 File
  • Problems with row reduction Page
  • Problems with row reduction (PDF) File
  • Row Reduction Using Python File
• Solving non-linear Equations
  

  Solving non-linear Equations

  Bisection, interpolation and Newton methods for solving equations.

  • Assignment 4 File
• Interpolation
  

  Interpolation

  We use polynomials to interpolate various classes of functions and examine the accuracy and efficiency of such representations.

  • Notes on interpolation File
  • Assignment 5 File
• Integration
  

  Integration

  Numerical Integration

  • Notes on Integration File
  • Assignment 6 File
• Differential Equations
  

  Differential Equations

  Numerical Solutions of Ordinary Differential Equations

  • Deriving equations for Runge Kutta Heun Parameters File
  • Assignment 7 File
• Left overs
  

  Left overs

  Montel Carlo Methods, Best fit

  • Assignment 8 File
  • Notes on Curve Fitting File
• Topic 9
  

  Topic 9
• Topic 10
  

  Topic 10