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Course Code: 
MATH 357
Semester: 
Fall
Course Type: 
Core
P: 
3
Lab: 
2
Laboratuvar Saati: 
0
Credits: 
4
ECTS: 
7
Prerequisite Courses: 
Course Language: 
English
Course Objectives: 
Getting know about complex numbers, complex variabled 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

Teaching Methods

Assessment Methods

1) Can do calculations with functions of complex variables and sequences of complex numbers.

1,2,3

A,B

2) Can use Cauchy Riemann equations

1,2,3

A,B

3) Knows the concepts of analytic functions and harmonic functions

1,2,3

A,B

4) Knows how to evaluate contour integrals and knows Cauchy Integral Teorem.

1,2,3

A,B

5) Can evaluate integrals using residues.

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

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

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

5

70

Mid-terms (Including self study)

1

10

10

Quizzes

 

 

 

Assignments

 

 

 

Final examination (Including self study)

1

13

13

Total Work Load

 

 

163

Total Work Load / 25 (h)

 

 

6.52

ECTS Credit of the Course

 

 

7