Courses 4

 

College:

Faculty of Science

Department:

Mathematics

Course Title:

Advanced Calculus

Course Code:

Math 203

Credit Hours:

3

Prerequisite:

Fundamentals of integral calculus (Math 200)

Text Books:

1.

Calculus III, 2nd. Edit. (1985):  Jerrold Mrsden and Alan Weinstein Springer-Verlag New York Inc

2.

3.

Course Description:

Cylinderical and Spherical Polar  Coordinates. Functions of several variables: partial derivatives, chain rules. Tangent planes. The gradient and directional derivatives. Extreme of Functions of several variables. Lagrange Multipliers. Multiple Integrals.  Double Integrals. Area, Volume and Surface Area. Double Integrals in Polar Coordinates. Triple Integrals. Change of variables in Multiple Integrals. Vector Calculus. Vector Field. Line Integrals. Green’s Theorem. Curl and Divergence. Surface Integrals. The  Divergence Theorem. Stoke’s Theorem. Applications of vector calculus.

Learning Objectives:

1- Let the student present the importance and applications of the advanced differential  and integration in Physics, Chemistry and Engineering Science

2- Let the student study the Double Integrals. Area, Volume and Surface Area. Double Integrals in Polar Coordinates. Triple Integrals.

3- Let the student acquire the concept of  line Integrals. Green’s Theorem. Curl and Divergence. Surface Integrals. The  Divergence Theorem. Stoke’s Theorem..

Grading: 

No.

Assessment

Evaluation

1.

Med semester exam 1

25%

2.

Med Semester exam 2

25%

3.

Home works

5%

4.

Quizzes

5%

5.

Final Exam

40%

Total

100 %

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

1.

Lectures

2.

Tutorials

3.

Homework

4.

Quizzes

Course Outline:

Week

Lecture Topics

1.

Cylindrical coordinates, Spherical coordinates

2.

Partial derivatives

3.

Chain Rule , Matrix Multiplucation,

4.

Gradients, Level surfaces and Implicit Differentiation

5.

Maxima and Minima

6.

Lagrange Multipliers

7.

Line integrals

8.

Double integrals

9.

Triple integrals

10.

Vector analysis, Curl of a vector field, Laplacian operator

11.

Flux and Divergence

12.

Gauss's divergence theorem

13.

Green's theorem

14.

Stokes's Theorem

15.

Applications in Physics and Engineering

College:

Faculty of Science

Department:

Mathematics

Course Title:

Differential Equations 1

Course Code:

Math 204

Credit Hours:

3

Prerequisite:

Fundamentals of integral calculus (Math 200)

Text Books:

1.

Elementaty Differential Equations  6th ed. (1981) ; Author ; Earl D. Rainville and Phillipe E. Bedient

2.

D. Rainville and P. E. Bedient: Elementary Differential Equations, (1995) MacMillan Pub. Co. Inc. N.Y.

3.

Shepley L. Ross: Differential Equations:3rd. Edit. (1998): John Wiley & Sons, Inc.

Course Description:

Introduction to ordinary differential equations. Solution methods of first order  differential equations. Solution method of second order homogeneous and non homogeneous   of linear ordinary differential equations. Variational Method.

Learning Objectives:

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

-    To know Student the importance of the differential equations in Physics, Chemistry and Engineering Science.

-    To allow Student acquires  knowledge by learning new theories, concepts, and methods of solution in differential equations.

-    To study Student  the linear differential equations of the first order with some applications.

-    To learn Student  studies  the differential equations of higher order and methods of solution.

-    To  acquire Student cognitive skills through thinking and problem solving.

-    To become Student responsible for their own learning through solutions of assignments and time management. 

Grading: 

No.

Assessment

Evaluation

1.

Med semester exam 1

25%

2.

Med Semester exam 2

25%

3.

Home works

5%

4.

Quizzes

5%

5.

Final Exam

40%

Total

100 %

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

1.

Lectures

2.

Tutorials

3.

Homework

4.

Quizzes

Course Outline:

Week

Lecture Topics

1.

Introduction to differential equations.

2.

Classification of Differential Equations.

3.

First-Order Differential Equations,  Separable equations.

4.

Homogeneous equations. 

5.

Equations tends to Homogeneous

6.

Exact equations.

7.

Equations tends to Exact

8.

Linear equations,  Bernoulli's equation

9.

Introduction to Second and Higher-Order Equations.

Linear independence and dependence (Wronskian)

10.

Homogeneous Second-Order linear differential equations with constant coefficients;

the auxiliary equation

11.

Non-homogeneous Second-Order Linear differential Equations with Constant Coefficients. Method of Undetermined coefficients

12.

Operator's Method

13.

Method of Variation of Parameters, Second-Order linear differential equations with variable coefficients(Euler's equation and Cauchy's equation)

14.

Higher-Order Linear Differential Equations with Constant Coefficients

15.

Review

College:

Science

Department:

Mathematics

Course Title:

Linear Algebra

Course Code:

Math 241

Credit Hours:

3

Prerequisite:

Basics of Mathematics Math 251

Text Books:

1.

Anton H., Elementary Linear Algebra, John Wiley, 2001.

2.

3.

Course Description:

Introduction to systems of linear equations: Gaussian elimination and Gauss-Jordan elimination for solving Equations; Matrices: Operations on matrices, properties of matrix operations, inverse of a matrix; Determinant of a matrix: Elementary row operations, properties of determinants, Cramer’s rule; Vector spaces: Subspaces, linear combinations, linear independence, bases and dimensions; Rank of a matrix: The coordinates, change of bases; Linear transformations: Kernel, range, nullity of a linear transformation, linear transformations and matrices; symmetric matrices; Eigenvectors: Introduction to eigen values, eigenvectors and eigen spaces.

Learning Objectives:

-Let the student know the basic topics of linear algebra such as matrices, vector spaces.

-Let the student acquire solution linear equations in variables

-Let the student learn how to find eigen values and eigenvectors

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.

Tutorials

3.

Homework

4.

Quizzes

Course Outline:

Week

Lecture Topics

1.

Introduction

2.

Introduction to systems of linear equations: Gaussian elimination

3.

Gauss-Jordan elimination for solving Equations

4.

Matrices: Operations on matrices

5.

inverse of a matrix; Determinant of a matrix

6.

Elementary row operations.

7.

properties of determinants, Cramer’s rule;

8.

Vector spaces: Subspaces

9.

linear combinations, linear independence

10.

bases and dimensions; Rank of a matrix

11.

Linear transformations

12.

symmetric matrices

13.

Eigenvectors: Introduction to eigen values

14.

eigenvectors and eigen spaces.

15.

Review

College:

Faculty of Science

Department:

Mathematics

Course Title:

General Statistics

Course Code:

Stat 201

Credit Hours:

4

Prerequisite:

Text Books:

1.

Sheldon M. Ross: Introductory Statistics  3th ed. (2010)

2.

David Freedman, Robert Pisani and Roger Purves Hardcover (2007)" Statistics" , W. W. Norton, 4th Edition

3.

Dennis Wackerly, William Mendenhall, Richard L. Scheaffer Hardcover, (2007) Mathematical Statistics with Applications (7th Edition) Duxbury Press

Course Description:

Methods of  collection and Presentation Of Statistical Data by different ways, calculate some Measures of Central Tendency, measures of dispersion, Correlation and Regression.   The main Principles of Probability, random variables and some Statistical Distributions.

Learning Objectives:

Student knows the importance of  Statistics in all Sciences.

Student acquires  knowledge by learning new theories, concepts and methods of  collection and Presentation Of Statistical Data by different ways, calculate some Measures of Central Tendency, measures of dispersion, Correlation and Regression. 

Student studies The main Principles of Probability, random variables and some Statistical Distributions.

Student becomes responsible for their own learning through solutions of assignments and time management

Grading: 

No.

Assessment

Evaluation

1.

1st midterm exam

25 %

2.

2nd midterm exam

25%

3.

Homework

5 %

4.

Quizzes

5 %

5.

Final exam

40 %

Total

100 %

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

1.

Lectures

2.

Tutorials

3.

Homework

4.

Quizzes

Course Outline:

Week

Lecture Topics

1.

Collection and Presentation Of Statistical Data

2.

Frequency distributions, Cumulative Frequency distributions

3.

Measures of Central Tendency: Arithmetic mean, The Median and The Mode

4.

Measures of Central Tendency: The Geometric Mean, Quartiles, Deciles and Percentiles

5.

Measures of dispersion: The Range, The Mean Deviation,The Variance and the  Standard  Deviation

6.

Measures of dispersion: The Coefficient of Variation, The  Standard variable

7.

Correlation and Regression

8.

Principles of Probability: Random experiments, kind of Sample Space, Events and definitions of Probability

9.

Disjoint events, Independent events and conditional Probabilities

10.

The Total Probability law, Baye's theory

11.

Discrete Random Variables

12.

Continuous Random Variables

13.

Properties of Random Variables

14.

Some of discrete Probability distributions

15.

Some of Continuous Probability distributions