Courses 7

 

College:

Faculty of Science

Department:

Mathematics

Course Title:

Mathematics and Packages Programs

Course Code:

Math 333

Credit Hours:

3

Prerequisite:

Fundamentals of integral calculus (Math 200) and  General statistics(Stat 201)

Text Books:

1.

Wolform S., The Mathematica book, Wolform Media/Cambridge University press, New York, 2003 (5th ed).

2.

3.

Course Description:

This course is designed to strengthen mathematics computer programs concepts. Topics include a Mathematica program which cover some  areas of mathematics.

Learning Objectives:

1.  Summary of the main learning outcomes for students enrolled in the course.

-          Learn the link between the computer and mathematics.

-          The student knows the importance of using computer software in the various branches of mathematics, statistics, physics, chemistry, engineering and science.

-          The student learn how construct a program from a build in functions to solve different problems.

Grading: 

No.

Assessment

Evaluation

1.

Homework 1 through 14

5%

2.

Quizzes in computer  lab

5%

3.

First mid-term exam

25%

4.

Second mid-term exam

25%

5.

Final Exam

40%

Total

100 %

Methods of Teaching: (Lectures, Laboratory, Individual exercises, In-class discussion, Selection of Readings,…)

1.

Lectures

2.

Computer Laboratory

3.

Homework

4.

Quizzes  in Laboratory

Course Outline:

Week

Lecture Topics

1.

List as ordered set, Some operations on list(Part, Range). Vectors and Matrix  

2.

Some standard Mathematics function.

3.

Application in different branches by using  build in functions in:

       Operations on algebraic expression.

4.

Basic Plotting in 2 dimension with some options .

5.

Basic Plotting in 3 dimension with some options .

6.

Algebraic sets.

7.

Differentiation  and Integration

8.

Solution of algebraic equations.

9.

Sample user function with applications with passing parameters.

10.

Conditionals functions (If, Which, Picewise).

11.

Loop functions (Table, Do, While, For)

12.

User function  by using Module with applications

13.

The concept of the recurrence  (Dynamic programming) with a local function.

14.

More applications with concept of functions

15.

Review

College:

Science

Department:

Mathematics

Course Title:

Integral Equations

Course Code:

MATH 408

Credit Hours:

3

Prerequisite:

Differenial equations : MATH305, Real Analysis 1 (Math311)

Text Books:

1.

Introduction to Integral Equations with Applications, 2nd  ed. Jerri, (1999), Wiely-Interscience.

2.

3.

Course Description:

Relation between linear differential equations and Voltera’s integrals equations. Voltera’s integral equations with analytical kernel. The solution of Voltera’s integral equations with analytical kernel. The method of successive approximations. Finding the analytic kernel using the  successive kernels. Method of Fredholm’s determinants. Integral equations with degenerated kernels- Eigenvalues and Eigenfunctions- the solution of the homogenous integral equations.The solution of integro-differential equation by using Laplace transform.

Learning Objectives:

The course aims to provide the students with the a new concept of equations differ from the well known differential equations,  the integral equations.

Grading: 

No.

Assessment

Evaluation

1.

Mid Term Exam 1

25

2.

Mid Term Exam 2

25

3.

Homework

5

4.

Quiz

5

5.

Final Exam

40

Total

100 %

Methods of Teaching: (Lectures, Laboratory, Individual exercises, In-class discussion, Selection of Readings,…)

1.

Lectures

2.

Individual exercises

3.

In-class discussion

4.

Course Outline:

Week

Lecture Topics

1.

Relation between linear differential equations and Voltera’s integrals equations.

2.

Voltera’s integral equations with analytical kernel.

3.

The solution of Voltera’s integral equations with analytical kernel.

4.

The method of successive approximationsof Voltera’s integral equations.

5.

Series method of Voltera’s integral equations

6.

Laplace transform to solve a Voltera’s integral equations.

7.

Finding the analytic kernel using the  successive kernels.

8.

Method of Fredholm’s determinants.

9.

Laplace transform to solve a Fredholm’s integral equations.

10.

The method of successive approximationsof Fredholm’s integral equations.

11.

Integral equations with degenerated kernels

12.

- Eigenvalues and Eigenfunctions-

13.

The solution of the homogenous integral equations.

14.

The solution of integro-differential equation by using Laplace transform.

15.

Continue

College:

Science

Department:

Mathematics

Course Title:

Complex Analysis 1

Course Code:

MATH 413

Credit Hours:

3

Prerequisite:

Real Analysis1Math 311

Text Books:

1.

Zill D. G. and Shanahan P. D., A First Course in Complex Analysis with Applications, Jones & Bartlett Publishers, New York, 2003.

2.

Brown J. andChurchill R., Complex Variables and Applications, McGraw-Hill, 1996 (6th ed).

3.

Course Description:

The Complex Number System, Geometric Representation of the Complex Number-Polar form, Solving equations of in complex variables, Concept of Functions with Complex Variables, Limits and Continuity, Differentiability, Polar form of the Cauchy-Riemann equations, L’Hospital’s Rule, Complex differential operators, Complex Integration, Cauchy’s Integral formula,  Laurent expansion and Residues

Learning Objectives:

1-Let the students present importance of the complex variables theory.

2- Let the students analyze the Properties of the functions in complex variables

3-  Let the students illustrate some  applications of the complex Theory

Grading: 

No.

Assessment

Evaluation

1.

Mid Term Exam 1

25

2.

Mid Term Exam 2

25

3.

Homework

5

4.

Quiz

5

5.

Final Exam

40

Total

100 %

Methods of Teaching: (Lectures, Laboratory, Individual exercises, In-class discussion, Selection of Readings,…)

1.

Lectures

2.

Individual exercises

3.

In-class discussion

4.

Course Outline:

Week

Lecture Topics

1.

Introduction

2.

Geometric Representation of the Complex Number-Polar form

3.

Solving equations of in complex variables

4.

Concept of Functions with Complex Variables

5.

Limits

6.

Continuity

7.

Review

8.

Differentiability

9.

 Polar form of the Cauchy-Riemann equations

10.

L’Hospital’s Rule

11.

Complex differential operators

12.

Complex Integration

13.

Cauchy’s Integral formula

14.

 Laurent expansion and Residues

15.

Review

College:

Science

Department:

Mathematics

Course Title:

General Topology

Course Code:

MATH 464

Credit Hours:

3

Prerequisite:

Basic of mathematics – Math  251, Real Analysis1Math 311

Text Books:

1.

J. R. Patty, Foundation of Topology, PWS-Kent Publishing Co.,1993.

2.

Paul E. Long. An Introduction to General Topology. Charles E. Merril Publishing Company, 1971.

3.

B. Mendelson. Introduction to Topology. Dover Publications,Inc.,New York,1990.

Course Description:

Definition of a topology: Open sets, closed sets, interior, closure, and boundary of a set. Dense sets and separable spaces. Bases, Subbase and second countable spaces. Finite product of spaces- Subspaces. Continuous functions and Homeomorphisms. Separation axioms- spaces: T0 , T1 , T2 , T3 , , T4  and regular, normal spaces. Metric spaces: Definitions of compact and connected spaces

Learning Objectives:

- To let the student deal with abstract mathematical concepts .

- To let the student develop the skills of writing clear and precise proofs .

- To let the student study topological spaces and metric spaces .

- To let the student study the definitions of continuous, connectedness, compactness.

Grading: 

No.

Assessment

Evaluation

1.

Mid Term Exam 1

25

2.

Mid Term Exam 2

25

3.

Homework

5

4.

Quiz

5

5.

Final Exam

40

Total

100 %

Methods of Teaching: (Lectures, Laboratory, Individual exercises, In-class discussion, Selection of Readings,…)

1.

Lectures

2.

Individual exercises

3.

In-class discussion

4.

Course Outline:

Week

Lecture Topics

1.

Definition of a topology: Open sets, closed sets,

2.

interior, closure, and boundary of a set.

3.

Dense sets and separable spaces. Bases,

4.

Subbase and second countable spaces.

5.

Finite product of spaces

6.

Subspaces.

7.

Continuous functions and Homeomorphisms.

8.

Separation axioms-

9.

spaces: T0 , T1 , T2

10.

spaces: T3 , , T4

11.

regular, normal spaces.

12.

Metric spaces:

13.

Definitions of compact and connected spaces

14.

Continue

15.

College:

Science

Department:

Mathematics

Course Title:

History of mathematics among the Arabs and Muslims

Course Code:

MATH 481

Credit Hours:

3

Prerequisite:

Text Books:

1.

-      Howard Eves. An Introduction to the History of Mathematics, 4th Edition. Holt, Rinehart, and Winston, New York 1998.

2.

Carl B. Boyer. A History of Mathematics. Oxford University Press, 1993.

3.

Course Description:

Historical development of geometry, arithmetic, algebra, and calculus from ancient times to 20th century

Learning Objectives:

-To allow the student understandthe historical development of mathematics

-To allow the student emphasize the role of Arabs and Muslims in development of mathematics. And their role in the transfer and translation of ancient scientific heritage, and whether scientists West.

-To provide the student with Knowledge of systems numbers Babylonian and ancient Egyptian, Greek and Hindi.

-To allow the student learn some calculations on these systems and the conversion from one system to another.

 -To allow the student identify the geniuses of the nations that have contributed to the development of mathematics

Grading: 

No.

Assessment

Evaluation

1.

Mid Term Exam 1

25

2.

Mid Term Exam 2

25

3.

Homework

5

4.

Quiz

5

5.

Final Exam

40

Total

100 %

Methods of Teaching: (Lectures, Laboratory, Individual exercises, In-class discussion, Selection of Readings,…)

1.

Lectures

2.

Individual exercises

3.

In-class discussion

4.

Course Outline:

Week

Lecture Topics

1.

Introduction

2.

Knowledge of systems numbers Babylonian and ancient Egyptian, Greek and Hindi 

3.

Make some calculations on these systems and the conversion from one system to another

4.

To identify the geniuses of the nations that have contributed to the development of mathematics