Partial Differential Equations in Engineering
|Course code MATH2470||Units 10||Level 2000||Faculty of Science and Information TechnologySchool of Mathematical and Physical Sciences|
Differential equations arise in all branches of science and engineering. In Chemical Engineering students encounter problems involving heat transfer, diffusion and vibration which involve functions of 2 variables and their derivatives. The resulting equations are partial differential equations. Usually the solutions must satisfy physical restrictions - the resulting equations are called boundary value problems. Students will apply their knowledge of calculus and ordinary differential equations, as well as learning new techniques. Theoretical methods such as Fourier series are covered in lectures and applied methods such as the finite difference method are studied using specialised computer software.
Math2470 cannot count for credit with MATH2800.
Available in 2015
|Objectives||1. Provide the necessary mathematical knowledge and skills in solving boundary-value problems related to the diffusion of heat, mass and momentum.|
2. Provide the necessary numerical and computing skills for solving boundary-value problems arising in Chemical Engineering applications.
|Content||. Conduction of heat in solids and the heat equation. |
. Types of boundary conditions.
. Steady-state temperature and Laplace's equation.
. Separation of variables.
. Fourier series.
. 1-dimensional heat transfer problems.
. Higher-dimensional problems in cartesian coordinates.
. Higher-dimensional problems in polar, spherical, and cylindrical coordinates.
. Numerical differentiation using finite differences.
. Discretisation of the steady state and transient heat equation.
. Discretisation of various types of boundary conditions.
. Numerical solutions of the steady state and transient heat equation.
|Assumed Knowledge||MATH1120 or MATH1220.|
|Modes of Delivery||Internal Mode|
|Contact Hours||Lecture: for 3 hour(s) per Week for Full Term|
Computer Lab: for 2 hour(s) per Week for Full Term
|Timetables||2015 Course Timetables for MATH2470|