PDF Program: Department: College: Institution: Umm Al-Qura University

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Course Title:

Complex Analysis

Course Code:

^MTH3142-3

Program:

BSc. in Mathematics

Department:

Mathematics

College:

Jamoum University College

Institution:

Umm Al-Qura University

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2

3 A. Course Identification

1. Credit hours: 3 2. Course type

a. ^University College Department ✔ Others

b. Required ✔ Elective

3. Level/year at which this course is offered: Seventh level/second year 4. Pre-requisites for this course (if any):

Introduction to Complex Analysis (MTH3142-3) 5. Co-requisites for this course (if any):

6. Mode of Instruction (mark all that apply)

No Mode of Instruction Contact Hours Percentage

1 Traditional classroom Three hours/week %100

2 Blended 0 0

3 E-learning 0 0

4 Distance learning 0 0

5 Other 0 0

7. Contact Hours (based on academic semester)

No Activity Contact Hours

1 Lecture 30

2 Laboratory/Studio 0

3 Tutorial 0

4 Others (specify) 0

Total 30

B. Course Objectives and Learning Outcomes

1. Course Description

Topics covered are: Complex line integrals; Cauchy's theorem and the Cauchy integral formula; zeros of holomorphic functions; the Residue Theorem; calculation of definite integrals and evaluation of infinite series using residues.

2. Course Main Objective

The objectives of this course are to:

•Introduce students to the Complex line integral and its applications

3. Course Learning Outcomes

CLOs Aligned

PLOs 1 Knowledge and Understanding: by the end of this course, the

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4

CLOs Aligned

PLOs student is expected to be able to

1.1 Apply the methods of complex analysis to evaluate definite integrals and infinite series.

1.2 Demonstrate understanding and appreciation of deeper aspects of complex analysis.

Demonstrate skills in communicating mathematics orally and in writing..

2 Skills: by the end of this course, the student is expected to be able to 2.1 Develop connections of complex analysis with other disciplines

show the ability to work independently and within groups.

C. Course Content

No List of Topics Contact

Hours

1

Chapter 1:

• Complex Integration 1.1 Contours

1.2 Contour Integrals 1.3Independence of Path

1 1.4 Cauchy's Integral Theorem

1.5 Cauchy's Integral Formul1 and Its Consequences o

10

2

Chapter 2: Series Representations for Analytic Functions 2.1 Sequences and Series

2.2 Taylor Series 2.3 Power Series

2.4 zeros and Singularities 2.7 The Point at Infinity

10

3

Chapter 3: Residue Theory 3.1 The Residue Theorem

3.2 Improper Integrals of Certain Functions

10

Total 30

D. Teaching and Assessment

1. Alignment of Course Learning Outcomes with Teaching Strategies and Assessment Methods

Code Course Learning Outcomes Teaching Strategies Assessment Methods 1.0 Knowledge and Understanding

1.1 Recognize basic knowledge of complex line integral.

Lecture and

Tutorials

Exams, quizes

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5

Code Course Learning Outcomes Teaching Strategies Assessment Methods 1.2 Residues Theorem. Zero of

holomorphic functions

Lecture and

Tutorials

Exams, quizes

2.0 Skills

2.1 define singularities of a function, know the different types of singularities, and be able to determine the points of singularities of a function.

Introduce Line integral of complex function. Define integral and contours on the complex plan Compute the series and Laurent series of complex function and the residue of a function

Lecture/ Individual or group work

Exams, quizzes

2.2 Application of Laurent Series Zeros and Singularities 2.7 The Point at Infinity

Lecture/ Individual or group work

Exams, quizzes

3.0 Values

2. Assessment Tasks for Students

# Assessment task* Week Due Percentage of Total

Assessment Score

1 Midterm Exam 6th %25

2 Quizes and homeworks During semester %25

3 Final exam End of semester %50

*Assessment task (i.e., written test, oral test, oral presentation, group project, essay, etc.)

E. Student Academic Counseling and Support

Arrangements for availability of faculty and teaching staff for individual student consultations and academic advice : -

Each group of students is assigned to a particular faculty where he or she will provide academic advising during specific academic hours. Each staff will provide at least one session/week. –

There will be an academic advisor how will be a responsible for helping the student by doing the general supervision. –

The people in the library will support the students during the time of the course.

F. Learning Resources and Facilities

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6

1.Learning Resources Required Textbooks

1 Churchhill & Brown: Complex Variables and Applications;

517.53 C563

Essential References Materials

2. -Complex variables and its application (Eighth Edition) BY James Ward Brown and Ruel V. Churchill

3. Marsden & Hoffman: Basic Complex Analysis; 517.54 M363b 4. Conway: Functions of One Complex Variable; 517.53 C767f 5. Ahlfors: An Introduction to the Theory of Analytic Functions of One Complex Variable; 517.53 A28A Patrick D. Shanahan.

Electronic Materials None Other Learning

Materials None

2. Facilities Required

Item Resources

Accommodation

(Classrooms, laboratories, demonstration rooms/labs, etc.)

Classrooms Technology Resources

(AV, data show, Smart Board, software, etc.)

Data Show, Smart Board Other Resources

(Specify, e.g. if specific laboratory equipment is required, list requirements or

attach a list)

None

G. Course Quality Evaluation

Evaluation

Areas/Issues Evaluators Evaluation Methods

Effectiveness of teaching and assessment 

Students Direct

Quality of learning resources Students Direct

Extent of achievement of course learning outcomes

Faculty Member Direct

Evaluation areas (e.g., Effectiveness of teaching and assessment, Extent of achievement of course learning outcomes, Quality of learning resources, etc.)

Evaluators (Students, Faculty, Program Leaders, Peer Reviewer, Others (specify) Assessment Methods (Direct, Indirect)

H. Specification Approval Data

Council / Committee Council of the Mathematics Department

Reference No.

Date