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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 5042 PERTURBATION METHODS ELECTIVE 3 0 0 7

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

ASSISTANT PROFESSOR MELDA DUMAN

Offered to

Mathematics Mathematics

Course Objective

The aim of this lecture is to study for the effects of small disturbances in the algebraic equations, integrals, linear and nonlinear differential equations.

Learning Outcomes of the Course Unit

1   Will be able to apply elementerary operations on the asymptotic expansions. 2   Will be able to approach the roots of a regular and singular perturbed algebraic equation. 3   Will be able to apply at least one regular perturbation method for a differential equation near the equlibruim point. 4   Will be able to apply at least one regular perturbation method for a differential equation near the limit cycle points. 5   Will be able to apply the method of matched for a linear differential equation near the boundary layer.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 Dimensional analysis, gauge functions, order symbols. 2 Asymptotic series, elementary operations on asymptotic expansions, uniformity 3 Root finding, methods of determined and undetermined gauge functions. 4 Perturbed second order differential equations 5 Direct error estimation for second order initial value problems 6 Initial value problems for nearly linear systems 7 Periodic solutions and Lindstedt series 8 Midterm exam. 9 The method of multiple scales 10 The method of averaging 11 Initial layers. 12 Van Dyke rules. 13 Matching, overlap domains.Boundary layers 14 Boundary layers

Recomended or Required Reading

Textbook: Perturbations Theory and Methods, J. A. Murdock, John Wiley & Sons, Inc. References: Nonlinear Differential Equations and Dynamical Systems, F. Verhults, Springer. Partial Differential Equations of Applied Mathematics, E. Zauderer, John Wiley&Sons, Inc Supplementary Book: Introduction to Perturbation Techniques, A. H. Nayfeh, John Wiley&Sons, Inc.

Planned Learning Activities and Teaching Methods

Lecture notes, presentiations, solving problems, homeworks.

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 ASG ASSIGNMENT 2 MTE MIDTERM EXAM 3 FIN FINAL EXAM 4 FCG FINAL COURSE GRADE ASG * 0.30 + MTE * 0.30 + FIN * 0.40 5 RST RESIT 6 FCGR FINAL COURSE GRADE (RESIT) ASG * 0.30 + MTE * 0.30 + RST * 0.40 *** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

English

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

melda.duman@deu.edu.tr

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 13 3 39 Preparations before/after weekly lectures 13 3 39 Preparation for midterm exam 1 30 30 Preparing assignments 3 10 30 Preparation for final exam 1 20 20 Final 1 3 3 Midterm 1 3 3 TOTAL WORKLOAD (hours) 164

Contribution of Learning Outcomes to Programme Outcomes

PO/LO PO.1 PO.2 PO.3 PO.4 PO.5 PO.6 PO.7 PO.8 PO.9 PO.10 PO.11 LO.1 5 5 5 4 4 3 3 3 3 LO.2 4 LO.3 4 3 3 3 3 LO.4 LO.5