Module Code - Title:

MS4407 - PERTURBATION TECHNIQUES AND ASYMPTOTICS

Year Last Offered:

2025/6

Hours Per Week:

Lecture

2

Lab

1

Tutorial

1

Other

0

Private

6

Credits

6

Grading Type:

N

Prerequisite Modules:

MS4403

MS4404

Rationale and Purpose of the Module:

To learn the basic concepts and techniques of asymptotic and perturbation methods.

Syllabus:

Non-dimensionalisation, scaling, ordering, definition of asymptotic series, algebraic equations, integrals, LaplaceÆs method, method of steepest descent, regular and singular perturbations, multiple scales, strained coordinates, boundary layer techniques.

Learning Outcomes:

Cognitive (Knowledge, Understanding, Application, Analysis, Evaluation, Synthesis)

1. Demonstrate an understanding of scaling asymptotic scaling of differential equations and the principles of asymptotic approximations. 2. Solve a regular perturbation differential or algebraic equation. 3. Demonstrate an understanding of the concept of a singular perturbation in algebraic equations and boundary layers (matched asymptotic expansions) in differential equations. 4. Demonstrate an understanding of multiple scale techniques for differential equations. 5. Demonstrate an understanding of WKB techniques. 6. Demonstrate an understanding of asymptotic techniques for approximation of integrals (LaplaceÆs method, steepest descent).

Affective (Attitudes and Values)

N/A

Psychomotor (Physical Skills)

N/A

How the Module will be Taught and what will be the Learning Experiences of the Students:

Normal mathematics lectures. Students will have homework (not for credit), a mid-term text worth 5%, 5% for participation in tutorial problem solving sessions and a final exam worth 90%.

Research Findings Incorporated in to the Syllabus (If Relevant):

Prime Texts:

M.H. Holmes (1995) Introdcution to perturbation methods , Springer

J. Hinch (1991) Perturbation methods , CUP

A.H. Nayfeh (1981) Introduction to perturbatio techniques , Wiley

J. Kevorkian, J.D. Cole (1981) Perturbation methods in applied mathematics , Springer-Verlag

Other Relevant Texts:

C.A. Bender, S.A. Orszag (1987) Advanced mathematical methods for scientists and engineers , Mcgraw-Hill

J. Murdock (1991) Perturbations , Wiley

J. David Logan (1996) Applied mathematics , Wiley

J. Keener (1995) Principles of applied mathematics , Addison-Wesley

Programme(s) in which this Module is Offered:

Semester(s) Module is Offered:

Module Leader:

doireann.okiely@ul.ie