MATH414-12S2 (C) Semester Two 2012

# Computational Methods

 0.1250 EFTS09 Jul 2012 - 11 Nov 2012

## Description

Computational Methods

This course looks at a variety of algorithms for solving important computational problems that arise in
science, engineering, and commerce. Topics covered include an introduction to the numerical solution of partial differential equations, and numerical methods for the solution of nonlinear algebriac and optimisation problem. Other topics include the Fast Fourier Transform, and numerical approximation techniques.

Topics will be selected from the following:
• Rootfinding for non-linear equations
• Approximation methods. Numerical integration and quadrature.
• Fixed-point iterations and modified Newton’s method
• Solution of Nonlinear systems of Equations
• Unconstrained Optimization
• Approximation methods. Polynomial Interpolation. Numerical integration and quadrature.
• Introduction to numerical methods for solving partial differential equations. Finite difference methods for elliptic, hyperbolic, and parabolic PDEs. Marching schemes and stability issues.
• The discrete and Fast Fourier Transforms. Spectral applications.

Course Goals
• To encourage and enable students to use numerical methods to solve applied mathematical problems in science, engineering and elsewhere.
• To be able to know what type of numerical method to apply to a particular problem.
• To know how to solve these computational problems in MATLAB.
• To understand the theoretical basis of these methods.
• To understand the characteristics, strengths, and limitations of the various methods discussed.
• To have an understanding of errors, stability properties and convergence of numerical methods.

Note carefully, that to obtain a clear pass in this course (i.e., a C grade or better), you must obtain at least 40% of the semester final examination.

## Learning Outcomes

To gain understanding of the principles and applications of numerical methods.

• To be able to implement and use such methods.
• To have an appreciation of error build-up, and stability issues.

This course will provide students with an opportunity to develop the Graduate Attributes specified below:

## Pre-requisites

Subject to the approval of the Head of School.

## Assessment

Assessment Due Date Percentage
Internal Assessment - TBA 50%
Final Examination 50%