Advanced Mathematical Techniques in Ordinary Differential Equations for Engineers

Code

MATH3032

School

Mathematical Sciences

Level

3

Credits

10

Semesters

Autumn Malaysia

Summary

This module covers advanced analytic mathematical techniques used to provide exact or approximate solutions to common classes of ordinary differential equations (ODES) typical in Engineering. Techniques covered include

• Method of variation of parameters
• Laplace transform methods
• Taylor series method
• Frobenius method
• Asymptotic regular perturbations
• Strained coordinates and multiple scales
• Singular perturbations; matched asymptotic expansions.

Target Students

BEng and MEng students in the Faculty of Engineering

Classes

• One 1-hour tutorial each week for 12 weeks
• One 2-hour lecture each week for 12 weeks

Assessment

• 100% Exam 1 (2-hour): 2-hour written examination

Educational Aims

Learning Outcomes

Knowledge and understanding of mathematics necessary to support application of key engineering principles. To apply mathematical methods, tools and notations proficiently in the analysis and solution of engineering problems.

On successful completion of this module students will be able to:

• L01 – develop and apply exact solution methods for linear, non-constant coefficient, ODEs
• L02 – develop and apply series methods for linear, non-constant coefficient ODEs
• L03 – develop and apply perturbation methods for nonlinear ODES.
• L04 – classify and solve common classes of ordinary differential equations (ODES) typical in Engineering.

Conveners

• Dr Yee Jiun Yap