MM305 : Complex Analysis 1

Department

Department of Mathematics

Academic Program

Bachelor in mathematics

Type

Compulsory

Credits

03

Prerequisite

MM211

Overview

This course introduces students to the basic concepts of complex numbers. It also deals with the trigonometric inequality and its generalization to (n) numbers, equality conditions, and complex level topology. This course aims at developing the student's ability to identify functions in a complex variable, elementary functions, and transformations.

Intended learning outcomes

At the end of the course, the student should be able to

1- Explain the algebraic concepts and operations of complex numbers

2- Explain how to find the roots of complex numbers

3- Define groups in the complex plane

4- Distinguish the geometric concept of the complex function

5- Mention the concepts, principles and laws of limits and continuity of complex functions

6- Recognize complex differentiation, Cauchy-Riemann equations, and analytical functions

7- Analyze the exercises related to algebraic operations with complex numbers

8-Analyze and explain how to find the roots of complex numbers

9- Distinguish the drawing of groups in the complex plane (level) .

10- Discover the geometric concept of the complex function

11- Deduce the continuity of complex functions

12- Analyze and evaluate his knowledge of Cauchy-Riemann terms

13- Explain the concepts and properties of simple complex functions and simple transformations

14- Know the concepts and properties of simple complex functions and simple transformations .

15- Use algebraic concepts and operations to solve single- and multiple-idea problems

16- There are tables of complex numbers, the students should know.

17- Graph the groups in the complex plane (level).

18- Apply the geometric concept of the complex function

19- There is an end, continuity, and derivative of complex functions, the students should know.

20- Use the Cauchy-Riemann equations to find out whether the functions are analytic or not

21- Employ the concepts of complex functions in order to carry out the simple complex transformations.

Teaching and learning methods

1- Practical and theoretical lectures .

2- Discussion and dialogue .

3- Brain storming .

4- Working papers, case study .

5- Presentations .

6- Videos and e-learning

7- Use of software and computer applications such as (MATLAB, GeoGebra, Geometer,)

8- Intensifying applications, solving problems, and linking ideas with reality and life situations

Methods of assessments

1- A written exam (essay + objective) = 25 marks, or its assessment is left to the course instructor

2- Short tests (written or oral), demonstration tasks, applications, exercises, and presentation = 15 marks, or the assessment is left to the course instructor .

3- Written final exam (essay + objective) = 60 marks

Course content:

Week	Scientific subject	Number of Hours	Lecture	exercises	discussion
1-2	Complex numbers and complex plane	6	ü	ü	ü
2-3	Absolute value of a complex number and operations on it / trigonometric inequality and its generalization	6	ü	ü	ü
4	The polar form of a complex number	4	ü	ü	ü
5	First Midterm 2 hours
5-6	De Moivre's Formula / Root of a Complex Number / Euler's Formula	4	ü	ü	ü
6-7	The regions in the complex plane and the point of infinity	4	ü	ü	ü
7-8	The compound function/end and connection of the compound function	6	ü	ü	ü
9-10	Complex differentiation and the two Cauchy-Riemann equations / analytical functions / harmonic functions	6	ü	ü	ü
10	Second Midterm 2 hours
11-12-13	Simple complex functions (polynomials, exponential functions, trigonometric functions, hyperbolic functions, logarithmic functions, inverse trigonometric functions, and inverse hyperbolic functions) and their properties	12	ü	ü	ü
14	Some simple compound conversions	4	ü	ü	ü
	Final Exam
	Total	56

Reference

References Title	publisher	Release Copy	Author
Composite analysis	New Book Almotaheda	First Copy 2013	Dr.. Ramadan Mohamed Juhayma Dr.. Salem Ibrahim Al-Qawi

Arabic language 1 (AR103)
Linear Algebra 1 (MM105)
Planar and Analytical Geometry (MM103)
Quranic Studies 1 (AR101)
computer 1 (CS100)
General Mathematics 1 (MM101)
General English1 (EN100)
Fundamentals of Education (EPSY101)
General Psychology (EPSY 100)
Introduction to Statistics (ST101)
Quranic studies2 (AR102)
Aerospace Engineering (MM114)
General Mathematics 2 (MM102)
Linear Algebra (2) (MM215)
Developmental Psychology (EPSY 203)
General Teaching Methods (EPSY 201)
General English2 (EN101)
Computer 2 (CS101)
Introduction to the science of Probabilities (ST102)
Arabic language 2 (AR104)
Basics Of Curriculums (EPSY 202)
Mathematical Logic (MM317)
Educational Psychology (EPSY 200)
Arabic language 3 (AR105)
Ordinary Differential Equations 1 (MM202)
Static (MM206)
General Mathematics3 (MM211)
Ordinary Differential Equations 2 (MM311)
Vector analysis (MM214)
Mathematical statistics (ST202)
Set Theory (MM213)
Arabic language 4 (AR106)
Research Methods (EPSY301)
Measurements and Evaluation (EPSY 302)
Methods of teaching mathematics (MM208)
Teaching learning Aids (EPSY 303)
Word processing (CS 202)
Psychological Health (EPSY 401)
School mathematics 1 (MM309)
Complex Analysis 1 (MM305)
Real Analysis 1 (MM303)
Dynamics (MM207)
Abstract Algebra 1 (MM302)
Complex Analysis 2 (MM306)
School mathematics2 (MM310)
Real Analysis 2 (MM304)
Abstract Algebra 2 (MM403)
Numerical Analysis (MM308)
measurement theory (MM410E)
Integral equations (MM409E)
Operations Research (MM408E)
History of Mathematics (MM407E)
Functional Analysis (MM406E)
linear programming (MM405E)
Partial Differential Equations (MM401)
Teaching applications (MM400)
Graduation project (MM404)
Teaching Practice (EPSY 402)