Advanced Mathematical Techniques in Ordinary Differential Equations for Engineers

Code

MTHS3002

School

Mathematical Sciences

Level

3

Credits

10

Semesters

Autumn UK

Summary

This course 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

Available to BEng and MEng students in the Faculty of Engineering.

Classes

• One 1-hour workshop each week for 13 weeks
• One 2-hour lecture each week for 13 weeks

Each week there will normally be 2 lectures to introduce key mathematical knowledge/ideas/techniques on module topics. Alternate weeks 1 hour of worked examples to facilitate solving of problems/tutorial/problem class or provide students with the opportunity to gain individual help understanding module topics, clarification of lecture notes or support in developing problem solving skills.

Assessment

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

Assessed by end of autumn semester

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 course students will be able to:

develop and apply exact solution methods for linear, non-constant coefficient, ODEs

develop and apply series methods for linear, non-constant coefficient ODEs

develop and apply perturbation methods for nonlinear ODES.

classify and solve common classes of ordinary differential equations (ODES) typical in Engineering.
 

Conveners

• Dr Tom Ward