Courses 6

 

College:

Science

Department:

Mathematics

Course Title:

Partial differential equations

Course Code:

Math 406

Credit Hours:

3

Prerequisite:

Differenial equations : MATH305

Text Books:

1.

Differential Equations, 11thed. (2002), N.M.KAPOOR, Pitambar Pub. Co.  LTD.

2.

3.

Course Description:

Introduction to PDEs and their solutions; existence-uniqueness theorem; derivation of PDEs by elimination of arbitrary constants and arbitrary functions; solution of PDEs: linear PDEs of order one: Lagrange's method; non-linear PDEs of order one; Charpit's method; method of characteristics, linear and quasi-linear PDEs, examples from physics; Second order linear PDEs: classification; d’Alembert’s solution to the wave equation and propagation of discontinuities; Fourier series and their convergence; Separation of Variables: homogeneous equations, examples from the heat, wave, and Laplace equations.

Learning Objectives:

-    Student knows that partial differential equations may be derived by the elimination of arbitrary constants and functions, and   methods for finding the complete and general solutions of linear partial differential equations of order one, also the complete and singular solutions for non-linear PDEs.

-    Student studies some applications in physics , for example, D'Alemberts formula for a string.

-    Student learns how can expand a function by using the Fourier series to use it to find the solutions of some kinds of PDEs by using the method of separation of variables.

-     Training student to acquire the ability to analyze and think logically  to find solutions to the problems and natural phenomena.

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, Eliminate of arbitrary constants.

2.

Eliminate of arbitrary functions, Complete solutions to linear PDEs of order one.

3.

General solutions to linear PDEs of order one, Complete,  Singular , and general solutions to non-linear PDEs of order one.

4.

Complete solution( Charpit's Method).

5.

D'Alembert's formula for a string.

6.

Fourier series

7.

Separation of variables;

8.

Oscillation of a string

9.

Heat equation

10.

Continue

11.

Oscillation of a Membrane

12.

Continue

13.

Continue

14.

Continue

15.

Review

College:

Science

Department:

Mathematics

Course Title:

Abstract Algebra (2)

Course Code:

Math 343

Credit Hours:

3

Prerequisite:

Abstract Algebra (1): Math 342

Text Books:

1.

A first course in abstract algebra, 6th ed. (1998); Fraligh J. B.; Addition-wily publishing co. London,.

2.

3.

Course Description:

Definition and basic properties of a ring - fields - Divisors of zero and cancellation - Integral domain - The characteristic of a ring - Quotient rings and ideals - Definition and elementary properties - Maximal and Prime ideals - Ring of polynomials - The division algorithm in F[x] – Irreducible polynomials - Uniqueness of Factorization in F[x] - Euclidean Domain - Conjugate classes and the class equation – the sylow theorem – Application to p-group.

Learning Objectives:

- Let the student teach the basic definitions in abstract algebra, and to study the algebraic structures with two binary operation(rings and fields).

- Let the student development the ability of the student to abstract and logic thinking, and to development the ability of the  student to dealing with the abstract proofs

- Let the student study the proofs in abstract algebra and methods of solution, and they acquires cognitive skills through thinking and problem solving.

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 and basic properties of rings

2.

Definition and basic properties of fields

3.

Divisors of zero and cancellation

4.

Integral domain

5.

The characteristic of a ring -

6.

Quotient rings and ideals

7.

Definition and elementary properties of homomorphism

8.

Maximal and Prime ideals

9.

Ring of polynomials

10.

The division algorithm in F[x]

11.

Irreducible polynomials

12.

Uniqueness of Factorization in F[x]

13.

Euclidean Domain

14.

The sylow theorem

15.

Application to p-group

College:

Science

Department:

Mathematics

Course Title:

Introduction to numerical analysis

Course Code:

MATH 334

Credit Hours:

3

Prerequisite:

STAT 201; MATH 203

Text Books:

1.

R. Burden, and J. D. Faires. Numerical Analysis. PWS-Kent Publishers, 1993.

2.

V. A. Patel. Numerical Analysis. Harcourt Brace, College Publishers, 1994.

3.

R. Burden, and J. D. Faires. Numerical Analysis. PWS-Kent Publishers, 1993.

Course Description:

Numerical solutions of non-linear equations: Bisection method, Newton-Raphson method, secant method, convergence. Finite difference: Newton ‘s forward and backward formulas. Interpolation: Lagrange, Newton divided difference, Hermite formulas. Numerical differentiation:First derivative, higher derivatives. Numerical integration:Trapezoidal rule, Simpson’s rule, Gaussian integration. Algorithms and programs:

Learning Objectives:

- Let the students know how to differentiate and integrate numerically.

- Let the students study the method of iterations for solving nonlinear equations of one variable.

-Let the students illustrate numerical methods by using the numerical analysis software and computer facilities.

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.

Fundamental theorem of interpolation

3.

Lagrange interpolation- divide difference interpolation

4.

Finite differences –forward differences and backward difference

5.

Forward and backward difference fomulas -

6.

Hermite interpolation

7.

3-point of differentiation

8.

3-point backward fomula of differentiation

9.

Richardson extrapolation

10.

Elements of numerical integration

11.

Composite numerical integration

12.

Fixed points of functions –fixed point iteration method

13.

Newton's method- Quazi-Newton methods

14.

Fundamental theorem of interpolation

15.

Review

College:

Science

Department:

Mathematics

Course Title:

Introduction to Operation Research

Course Code:

Stat 340

Credit Hours:

3

Prerequisite:

Advanced Calculus : Math 203

Text Books:

1.

Operations Research: An Introduction, 8th edn (2007), Hamdy A.T. ;  Prentice Hall.

2.

3.

Course Description:

Modeling with linear programming. The simplex method, M-method and two phase method. Transportation model and iterative computations of the transportation algorithm.

Learning Objectives:

-          Let the student know the importance of the operation research in practical life problems.

-          Let the student acquire knowledge by learning, algorithms, and methods of solution in mathematical programming.

-          Let the student learn the methods of solving linear programming and transportation model.

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.

Modeling with Linear Programming.

2.

Graphical LP solution

3.

Continue

4.

The Simplex method

5.

Continue

6.

M-method 

7.

Tow Phase method 

8.

Special case in the simplex method 

9.

Definition of the dual Problem-Optimal Dual solution

10.

Sensitivity Analysis

11.

Continue

12.

Transportation Model 

13.

Continue

14.

Iterative computations of the Transportation Algorithm

15.

Review