COMPLEX ANALYSIS

Course Code:

MATH 357

Semester:

Fall

Course Type:

Core

P:

3

Lab:

2

Laboratuvar Saati:

0

Credits:

4

ECTS:

7

Prerequisite Courses:

Calculus II

ANALYSIS II

Course Language:

English

Course Objectives:

Getting know about complex numbers, complex variable functions, complex sequences and series, being able to do calculations with them. Information about contour integral and residue and getting know how to evaluate some integral with such techniques.

Course Content:

Algebra of complex numbers. Sequences and series with complex terms. Power series and convergence radius. Some elementary functions and mappings. Riemann surfaces. Regular functions and Cauchy - Riemann equations. Harmonic functions. Contour integrals and Cauchy theorem. Cauchy's integral formula and some of its direct rusults. Residue concept. Taylor and Laurent expansions.

Course Methodology:

1: Lecture, 2: Problem Solving ,3: Question-Answer

Course Evaluation Methods:

A: Written examination, B: Homework

Vertical Tabs

Course Learning Outcomes

Learning Outcomes	Program Learning Outcomes	Teaching Methods	Assessment Methods
1) Can do calculations with functions of complex variables and sequences of complex numbers.	1,2	1,2,3	A,B
2) Can use Cauchy Riemann equations	1,2,4	1,2,3	A,B
3) Knows the concepts of analytic functions and harmonic functions	1,2,4	1,2,3	A,B
4) Knows how to evaluate contour integrals and knows Cauchy Integral Teorem.	1,2,3,4,7,9	1,2,3	A,B
5) Can evaluate integrals using residues.	2,3,4,7,9	1,2,3	A,B

Course Flow

Week	Topics	Study Materials
1	Introduction, Definitions and importance of the subject, Complex numbers and complex plane. Algebraic operations	Course Book 1.1, 1.2,1.3
2	Complex Exponential, powers, roots	1.4,1.5,1.6
3	Functions, Limit and continuity, analyticity	2.1,2.2,2.3
4	Derivative, Cauchy Riemann equations, harmonic functions	2.4,2.5
5	Elementary Functions and Inverses	3.1,3.2,3.3
6	Sequences, Series.	5.1,5.2,5.3
7	Introduction to complex Integration, contours	4.1,4.2
8	Cauchy theorem, Cauchy`s formula and its consequences	4.3,4.4,4.5
9	Midterm
10	Integral Theorems, Laurent Series	4.5,5.5
11	Singularities, Residue Theorem	5.6,5.7,6.1
12	Residue theorem	6.1
13	Trigonometric Integrals	6.2
14	Improper Integrals	6.3,6.4

Recommended Sources

Textbook	Fundamentals of Complex Analysis with Applications to Engineering, Science, and Mathematics (3rd Edition), E. Saff, A. Snider, Pearson Education, 2003.
Additional Resources	Complex variables and applications, R.V. Churchill and J.W. Brown, McGraw-Hill, 1996 Complex analysis, J. Back and D.J. Newman, Springer-Verlag, 1991

Material Sharing

Documents
Assignments
Exams

Assessment

IN-TERM STUDIES	NUMBER	PERCENTAGE
Mid-terms	1	100
Quizzes
Assignments
Total		100
CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE		50
CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE		50
Total		100

COURSE CATEGORY

Expertise/Field Courses

Course’s Contribution to Program

No	Program Learning Outcomes	Contribution
No	Program Learning Outcomes	1	2	3	4	5
1	The ability to make computation on the basic topics of mathematics such as limit, derivative, integral, logic, linear algebra and discrete mathematics which provide a basis for the fundamenral research fields in mathematics (i.e., analysis, algebra, differential equations and geometry)					X
2	Acquiring fundamental knowledge on fundamental research fields in mathematics					X
3	Ability form and interpret the relations between research topics in mathematics			X
4	Ability to define, formulate and solve mathematical problems				X
5	Consciousness of professional ethics and responsibilty			X
6	Ability to communicate actively		X
7	Ability of self-development in fields of interest			X
8	Ability to learn, choose and use necessary information technologies	X
9	Lifelong education		X

ECTS

ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION
Activities	Quantity	Duration (Hour)	Total Workload (Hour)
Course Duration (14x Total course hours)	14	5	70
Hours for off-the-classroom study (Pre-study, practice)	14	6	84
Mid-terms (Including self study)	1	10	10
Quizzes
Assignments
Final examination (Including self study)	1	11	11
Total Work Load			175
Total Work Load / 25 (h)			7
ECTS Credit of the Course			7

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