Semester Two 2012
Differential Equations and Vector Calculus
This course deals with techniques for solving differential equations, and develops further tools for multivariable calculus, building on the material in MATH201.
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.
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.
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
MATH262, MATH264, EMTH202, EMTH204
Course Coordinator / Lecturer
Internal Assessment - TBA
Examination and Formal Tests
There is no required text for this course.
Recommended reading: Boyce and DiPrima, Elementary Dierential Equations and Boundary Value Problems, Wiley,
7th Ed or 8th Ed.
For further information see
Mathematics and Statistics.
All MATH202 Occurrences
Semester Two 2012