MATH202-12S2 (C) Semester Two 2012
Differential Equations and Vector Calculus

Description

This course is a core part of 200 level maths (along with MATH201 and
MATH203) and is strongly recommended to anyone who is considering majoring in mathematics or another subject that involves a high level of numeracy. It covers more advanced techniques in differential equations and vector calculus with  interesting applications to many areas of science, commerce and engineering.

Topics covered:
Differential equations: Review of second order linear differential equations. Reduction of order. Variation of Parameters. Laplace Transforms: Initial Value Problems, Shift Theorems, step functions and impulses, convolution, resonance. Fourier Series. Introduction to Fourier Transforms.

Vector Calculus: Multiple integration, change of variables and Jacobian determinant.
Surface integrals, flux through a surface. Div, grad, curl. Stokes'
Theorem and the Divergence Theorem.

Learning Outcomes

At the end of the course, students will:

• be proficient in the standard techniques of differential equations: Laplace transforms, convolutions and Fourier series
• be proficient in the standard techniques of multivariate calculus: surface integrals, flux, Stokes theorem and divergence theorem
• understand why these techniques work
• be able to use these techniques in a variety of applications, using appropriate software
• have developed problem solving skills both as part of a team and as an individual
• have developed written and oral communication skills, emphasizing the ability to explain what the mathematics means

Pre-requisites

Restrictions

For further information see Mathematics and Statistics.