Information Package / Course Catalogue - Adnan Menderes University

General Information Unit Staff Academic Information Programme Outcomes Course Structure Diagram Contact Information

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Complex Variables and Applications

Course Code	: MTK570
Course Type	: Area Elective
Couse Group	: Second Cycle (Master's Degree)
Education Language	: Turkish
Work Placement	: N/A

Theory	: 3
Prt.	: 0
Credit	: 3
Lab	: 0
ECTS	: 8

Objectives of the Course

This course aims to acquaint students with the fundamental notions of Complex Variables and Applications including Complex numbers, functions, limits, continuity, complex differentiation, Cauchy- Riemann equations, complex integration, Cauchy’s theorem, Cauchy’s integral formulas, infinite series, Taylor’s and Laurent series, Residue theorem, conformal mapping, physical applications of conformal mapping.

Course Content

Complex numbers, functions, limits, continuity, complex differentiation, Cauchy- Riemann equations, complex integration, Cauchy’s theorem, Cauchy’s integral formulas, infinite series, Taylor’s and Laurent series, Residue theorem, conformal mapping, physical applications of conformal mapping.

Name of Lecturer(s)

Learning Outcomes

1.	To be able to comprehend the basic concept of theory of complex functions
2.	To be able to develop mathematical sense
3.	To be able to develop the capacity of posing and solving problems
4.	To be able to gain the skill of interpreting some interrelations among these concepts
5.	To be able to use mathematical concepts in solving certain types of problems

Recommended or Required Reading

1.	Complex Variables with an introduction to conformal mapping and its applications, M. R. Spiegel, 1991.
2.	Complex Variables and applications, R. V. Churchill

Weekly Detailed Course Contents

Week 1 - Theoretical

Complex numbers

Week 2 - Theoretical

Functions

Week 3 - Theoretical

Limits

Week 4 - Theoretical

Continuity

Week 5 - Theoretical

Complex differentiation

Week 6 - Theoretical

Cauchy- Riemann equations

Week 7 - Theoretical

Complex integration

Week 8 - Theoretical

Cauchy’s theorem

Week 9 - Theoretical

Cauchy’s integral formulas

Week 10 - Theoretical

Infinite series (Midterm)

Week 11 - Theoretical

Taylor’s and Laurent series

Week 12 - Theoretical

Residue theorem

Week 13 - Theoretical

Applications of residue

Week 14 - Theoretical

Conformal mapping and physical applications of conformal mapping

Assessment Methods and Criteria

Type of Assessment	Count	Percent
Midterm Examination	1	%30
Final Examination	1	%70

Workload Calculation

Activities	Count	Preparation	Time	Total Work Load (hours)
Lecture - Theory	14	0	3	42
Individual Work	14	0	6	84
Midterm Examination	1	30	2	32
Final Examination	1	40	2	42
TOTAL WORKLOAD (hours)				200

Contribution of Learning Outcomes to Programme Outcomes

	PÇ-1	PÇ-2	PÇ-3	PÇ-4	PÇ-5	PÇ-6	PÇ-7	PÇ-8	PÇ-9	PÇ-10	PÇ-11	PÇ-12	PÇ-13	PÇ-14	PÇ-15
OÇ-1	5		4				4
OÇ-2	5		4				4						2
OÇ-3	5		4		4								2
OÇ-4	5		4		4		4						2
OÇ-5	5		4		4		4						2

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