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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 4008 PERTURBATION TECHNIQUES ELECTIVE 4 0 0 7

Offered By

Mathematics

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

PROFESSOR DOCTOR HALIL ORUÇ

Offered to

Mathematics (Evening) 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   Wil be able to apply elementerary operations on the asymptotic expansions. 2   Wil be able to approach the roots of a regular and singular perturbed algebraic equation. 3   Wil be able to give an asymptotic expansion for some integrals depend on small or large positive paremeter. 4   Wil be able to apply at least one regular perturbation method for a second order differential equation near the equlibruim point. 5   Wil be able to apply at least one regular perturbation method for a second order differential equation near the limit cycle points. 6   Wil 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. 3 Asymptotic solutions of perturbed algebraic equations, the methods of determined and undetermined gauge functions. 4 Asymptotic approximations to integrals. Integration by parts, Laplace method. 5 The method of stationary phase, the method of steepest descent to integrals. 6 Applications for some special functions given by integrals. 7 The Duffing equation (unforced), the straight forward method, the Lindstedt-Poincaré method. 8 Problems and Solutions 9 The method of renormalization, the method of multiple scales, the method of averaging for the Duffing equation. 10 The linear and weakly nonlinear damped oscillator. 11 Self-excited oscillators, the Van Der Pol equation 12 General weakly nonlinear systems, Fourier series. 13 The second order linear boundary-layer problems. 14 The method of matching by Van Dyke s rules.

Recomended or Required Reading

Textbook(s): Introduction to Perturbation Techniques, A. H. Nayfeh, John Wiley&Sons, Inc. Supplementary Book(s): References: Perturbations Theory and Methods, J. A. Murdock, John Wiley & Sons, Inc. Materials:Presentiations

Planned Learning Activities and Teaching Methods

Lecture notes, presentiations, solving problems, homeworks.

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 VZ Vize 2 FN Final 3 BNS BNS VZ * 0.40 + FN * 0.60 4 BUT Bütünleme Notu 5 BBN Bütünleme Sonu Başarı Notu VZ * 0.40 + BUT * 0.60

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)

e-posta: halil.oruc@deu.edu.tr Tel : (232) 3018577 Ofis B205

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 14 4 56 Preparations before/after weekly lectures 13 3 39 Preparation for midterm exam 1 32 32 Preparation for final exam 1 40 40 Final 1 2 2 Midterm 1 2 2 TOTAL WORKLOAD (hours) 171

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 PO.12 PO.13 LO.1 5 3 5 LO.2 5 4 3 5 LO.3 5 4 3 5 LO.4 5 4 3 4 3 3 LO.5 5 4 3 4 3 3 LO.6 4 4 3 4 3 3