TOPICS IN ANALYSIS

MTE731

Course Code: MTE731
Semester: -
Theory+Practice: 3 + 0
ECTS: 10

Course Type

Elective Course

Course Level

Doctorate Of Science

Year of Study

Semester

ECTS

Name of Lecturer(s)

Learning Outcomes

At the end of this course, the students;

know the concepts of Vector and Fourier Analysis
can apply Cauchy?s theorem.
can make the series expansion of analytic functions
can make the applications of Residue?s theorem

Mode of Delivery

Face to face

Prerequisites

Recommended Optional Programme Components

Course Description

Vectoranalysıs, Fourieranalysis, Cauchy?sTheorem, Series representation of analytic functions, Calculus of residues, Conformal mappings, The Laplace transformand applications.

Course Contents

WEEK	TOPICS
1^st Week	Fundamenbtaş Concepts of Real and Complex Analysis
2^nd Week	Vector Analysis
3^rd Week	Vector Analysis
4^th Week	Fourier Analysis
5^th Week	Fourier Analysis
6^th Week	Cauchy?s Theorem
7^th Week	Applications of Cauchy?s Theorem
8^th Week	Midterm
9^th Week	Series representation of analyticfunctions-Power series
10^th Week	Taylor and Laurent Series
11^th Week	Calculus of residues-Residue Theorem
12^th Week	Calculus of residues
13^th Week	Conformal mappings
14^th Week	The Laplace transform and applications
15^th Week	The Laplace transform and applications.

Recommended or Required Reading

Lars V. Alfhors, Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable, McGraw-Hill, 1996.

James Ward Brown, Ruel V. Churchill, Complex Variables and Applications, Mc Graw Hill Science, 1995.

Real and Complex Analysis, Walter Rudin.

Planned Learning Activities and Teaching Methods

Lecture
Questions/Answers

Assessment Methods and Criteria

	Quantity	Percentage (%)
Mid-term	1	40
Total(%)		40
Contribution of In-term Studies to Overall Grade(%)		40
Contribution of Final Examination to Overall Grade(%)		60
Total(%)		100

ECTS Allocated Based on Student Workload

Activities	Quantity	Duration (Hour)	Total Workload (Hour)
Midterm exam	1	2	2
Preparation for Quiz
Individual or group work	13	15	195
Preparation for Final exam	1	35	35
Course hours	13	3	39
Preparation for Midterm exam	1	27	27
Laboratory (including preparation)
Final exam	1	2	2
Homework
Total Work Load			300
Total Work Load / 30 (h)			10
ECTS Credit of the Course			10

Language of Instruction

Turkish

Work Placement(s)

Programme Qualifications / Learning Outcomes

	LO1	LO2	LO3	LO4
K1	X	X	X	X
K2	X	X	X	X
K3
K4	X	X	X	X
K5	X	X	X	X
K6	X	X	X	X
K7
K8
K9
K10
K11
K12