MA603 : Complex Analysis

Department

Department of Mathematics

Academic Program

Master in Applied Mathematics

Type

Compulsory

Credits

03

Prerequisite

Overview

The general objectives of the course in the form of outputs that the student is supposed to acquire after successful completion of the course are:

  • · Acquire basic concepts in complex analysis that can be used in theory and to solve practical problems in fields such as physics, statistics, and engineering.

· Learn about deep concepts of analytic functions

  • · Familiarity with complex integrals - Cauchy's theorem - Cauchy's integral formulas and their functions - and the Taylor and Laurent series
  • · The possibility of determining the analytic function in a large area by knowing the values of its derivatives at a single point or by knowing its values in a small neighborhood and gaining knowledge of the point and regular convergence of sequences and series and what results from that.

Intended learning outcomes

The targeted learning outcomes of the course are:

A. Knowledge & (Understand)

The basic information and key concepts that a student must acquire after successfully studying the course in the fields of knowledge and understanding are:

1

The student remembers the most basic concepts of complex analysis

2

The student is introduced to analytic functions and what distinguishes them from real functions

3

The student interprets the theory of remainder and the concepts of point and regular convergence

4

The student is introduced to the concepts and principles of integration and complex convergence, their results and applications

B. Mental (skills)

The mental skills that the student acquires on analysis after studying the course successfully are:

1

The student distinguishes the most important properties of complex and analytical functions

2

The student compares common and generalized concepts from real analysis to complex

3

The student analyzes theoretical problems related to practical applications, using analysis tools, which increases his ability to understand and visualize

4

The student should suggest how to solve problems, especially with regard to dealing with convergence of all kinds.

C. Practical & Professional (Skills)

The skills that a student must acquire when studying the course successfully are:

1

The student uses complex analysis tools to solve scientific problems related to physics, statistics and engineering

2

The student uses complex analysis theories to find real integrals and complex practical theory in simple ways

3

The student should design ways to familiarize himself with analytical functions and how to use them in applied journals

4

The student should distinguish between convergence and uniform convergence and how to use it in the convergence of sequences and series

D. Generic (and transferable skills)

The general skills or skills that can be used in the fields of work that the student must acquire when successfully studying the course are:

1

Ability to discuss precise concepts in mathematics and explain deep concepts in communication with colleagues and professors.

2

Using books and electronic libraries and writing, explaining and deriving scientific concepts

3

Ability to write reports, scientific articles and oral presentations,

4

The student should be able to communicate and communicate in writing and orally and in group work

Teaching and learning methods

The methods and methods used in teaching the course are:

  • · Lectures, Solving Exercises and Discussion
  • · Assign the student to collect and formulate information and share it with the class
  • · Supervising the student's self-reliance and independent study by reading books from electronic libraries related to the course

Methods of assessments

The types of assessment used in the process of teaching and learning the course are:

Rating No.

Evaluation methods

Evaluation Duration

Evaluation weight

Percentage

Rating Date (Week)

First Assessment

First midterm exam

3 hours

25 scheduled

20%

Sixth

Second Assessment

Second Midterm Exam

3 hours

25 scheduled

20%

Eleventh

Third Assessment

Assignments, exercises and discussion

Determined by the professor

Determined by the professor

10%

Determined by the professor

Final Evaluation

Final Exam

4 hours

All Course

50%

End of Semester

Total

100 degree

100%

(References)

Bibliography

Publisher

Version

Author

Where it is located

Textbooks

Complex Variables and Applications

McGraw-Hill Book Company, New York.

Recent edition

CHURCHILL, R . V.

U.S.A

Help Books

Complex Variables

Holden-Day, Inc., San Francisco

Recent edition

LEVINSON, NORMAN, and REDHEFFER, RAYMOND M.

U.S.A

Help Books

Complex Analysis

McGraw-Hill Book Company, New York

Recent edition

AHLFFORS, L. V.

U.S.A

Scientific Journals

Analytic Function Theory

Vol. I. Ginn /Blaisdell, Waltham, Mass.

-

Hille, E.

-

Internet Sites

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elective

elective

elective

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