MATH3712 Partial Differential Equations

2016

4.5

1 x 1-hour lecture-1 weekly
1 x 2-hour lecture-2 weekly
1 x 1.5-hour tutorial weekly

1 of MATH2711, ENGR2711

1 of MATH8712, MATH9712 has been successfully completed

This topic includes: The one dimensional wave equation, vibrating string, characteristics, reflection and the free boundary problem, non-homogeneous wave equation; Linear Second Order Partial Differential Equations, linearity and superposition, Uniqueness of solution, classification of second order equations; Elliptic and Parabolic Equations, Laplace's equation, Green's theorem and uniqueness for Laplace's equation, the maximum principle, the Heat equation; Separation of variables and Fourier Series, orthogonality and least square approximation, completeness and Parseval theorem, sine and cosine series, solution of Heat and Laplace's equation in one and two dimensions, non-homogeneous problems; the Fourier Transform, the Heat equation in three dimensions.

This topic equips the students with the skills needed to solve mathematical

problems in the partial differential equations. These provide the mathematical pre-requisites that the student needs for the third and higher year Mathematics topics. The focus is on the application of the mathematical ideas to practical problems

At the completion of the topic, students are expected to be able to:

1. Understand and be able to solve the wave equation
2. Understand and be able to solve the heat equation
3. Understand and be able to solve Laplace's equation
4. Understand and be able use Fourier series and transforms to solve partial differential equations