Overview
This course introduces the student to the theoretical study of series
with complex terms, complex integration, regular convergence, application to
power series and residuals calculation. It also deals with isolated points, the
sediment theorem, and the integration of Laurent series in its region of
convergence by calculating the real improper integral using the sediment
theorem
Intended learning outcomes
By
the end of the course, the student should be able to:
1- Indicate the type of group in terms of
interdependent or non-interdependent, simple-associated or multi-associated
2- Determine the type of path, as it is
closed, open, simple, or multiple
3- Explain path integration, its path
independence, Cauchy-Jorsah theorem and Cauchy's integral formula
4- Distinguish sequences and series of
complex numbers and complex functions
5- Compare power series with Taylor,
Maclaurin and Laurent series
6- State the type of isolated anomalous points
using the Laurent series
7- Recognize the remainder theorem and use it
to find the value of integration
8- Link path types and group types
9- Deduce the independence of the integration
on the path
10-
Explore the use of Cauchy's theorem to find the value of integration
11- Deduce sequences and series of complex
numbers and complex functions
12- Analyze how to
find the Taylor and Maclaurin series
13- Explain the
Laurentian series relationship in the classification of anomalous points
14- use the residual theorem in finding the
value of integration
15- The concept of interconnected or not,
simple interconnected, or multiple interconnected groups is used to determine
their type
16- Apply the concept of the path to
determine its type
17- Apply Cauchy's theorem to find the complex
integral values
18- There are
sequences and sequences of complex numbers and complex functions
19- There is a Taylor and Maclaurin series
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, tests, 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
|
Tracks and link
|
3
|
1
|
1
|
1
|
|
2
|
Linear integral with a
complex variable
|
3
|
1
|
1
|
1
|
|
3
|
path integration
|
3
|
1
|
1
|
1
|
|
4
|
Path independence and Cauchy's theorem
|
3
|
1
|
1
|
1
|
|
5
|
First Midterm ( 2 hours)
|
|
5-6
|
Cauchy-Jorsa theory
|
4
|
2
|
1
|
1
|
|
7
|
Cauchy's integral formula
|
3
|
1
|
1
|
1
|
|
8-9-10
|
Complex number sequences and series
|
7
|
4
|
2
|
1
|
|
10
|
Second Midterm ( 2 hours)
|
|
11
|
Power series - Taylor and Maclaurin series
|
3
|
1
|
1
|
1
|
|
12-13
|
Laurent series
|
4
|
2
|
1
|
1
|
|
13
|
Zeros and points
|
2
|
ü
|
ü
|
ü
|
|
14
|
Remainder
Math
|
3
|
1
|
1
|
1
|
|
15
|
Final Exam
|
|
|
Total
|
42
|
|
|
|
References
|
Reference Title
|
Publisher
|
Copy
|
Author
|
|
Composite analysis
|
United New Book
|
The First
2013
|
Dr. Ramadan Mohamed Juhayma
Dr. Salem Ibrahim
Al-Qawi
|
