COURSE UNIT TITLE

: ASYMPTOTIC ANALYSIS

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 4019 ASYMPTOTIC ANALYSIS 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 learn the basic of asymtotics (order relations, asymptotic equivalence), asymptotic sequences, asymptotic series and asymptotic behavior of solutions of differential equations.

Learning Outcomes of the Course Unit

1   Wil be able to apply order relations.
2   Wil be able to make operations with order relations.
3   Wil be able to discuss asymptotic relations.
4   Wil be able to use asymptotic sequences to find. expansions of a function.
5   Will be able to apply operations on asymptotic series.
6   Will be able to find solutions of equations near regular singular points.
7   Will be able to find solutions of equations near irregular singular points.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Asymptotic approximation, asymptotic behaviour of a function.
2 Order relations and operations with order relations, order of a function.
3 Asymptotic relations, Stokes phenomenon and subdominance in domains.
4 Asymptotic expansions, divergent asymptotic expansions.
5 Asymptotic expansions, divergent asymptotic expansions.
6 Asymptotic series, asymptotic power series.
7 Operations on asymptotic series.
8 Steltjes series, general Steltjes series and integrals. Properties of asymptotic series.
9 Problems and Solutions
10 Linear first and second order differentiable equations.
11 Series expansion of solutions at regular singular point.
12 The Euler equation, singularity at infinity.
13 Asymptotic series expansion of solutions at irregular singular points.
14 Applications on solutions near irregular singular points.

Recomended or Required Reading

Textbook(s): 1. Asymptotic Treatment of Differential Equations, A. Georgescu, Chapman.
2. Asymptotic Methods in Analysis, N.G. De Brujin, Dover Publ.
Supplementary Book(s):
1. Asymptotic Analysis, J.O. Murry, Springer.
2.Perturbation Methods for Differential Equations, K.B. Shivamoggi, Birkhauser.
3. Introduction to Perturbation Techniques, A. H. Nayfeh, Jon Willey.
4. Advanced Mathematical Methods for Scientists and Engineers, C. M. Bender, S. A. Orsag, McGarww Hill.
References:
Materials: Presentiations

Planned Learning Activities and Teaching Methods

Lecture notes, presentiations, solving problems, hometask

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE MIDTERM EXAM
2 FIN FINAL EXAM
3 FCG FINAL COURSE GRADE MTE * 0.50 + FIN * 0.50
4 RST RESIT
5 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.50 + RST * 0.50


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 30 30
Preparation for final exam 1 40 40
Final 1 2 2
Midterm 1 2 2
TOTAL WORKLOAD (hours) 169

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13
LO.154544
LO.25455
LO.344343
LO.435344
LO.544445
LO.6343343
LO.7343333

CONTACT INFORMATION
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Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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