Syllabus

Course Title: Calculus Basics  
Course Code: Math 200  
Credit Hours: 4  
Prerequisite: Calculus l Math-101  
Text Books:  
1. -  H. Anton, I. Bivens and S. Davis; "Calculus ",  John Wiley and Sons. (2005).  
2. -Robert T. Smith & Roland B. Minton; Calculus: Mc-Graw Hill(2007).  
3. -  G. B. Thomas  "Calculus ", Addison Wesley Pub. Co. (2005).  
Course Description:  
Definiteandindefinite integralsoffunctionsof a single variable.  Applications of the definite integral to area, volume, arc length and surface of revolution Fundamental Theorem of Calculus. Techniques of integration including integration by substitutions, by parts, by partial fractions and by reduction. Mean value theorems and L'Hopital's rule. Definition of Hyperbolic and Inverse Hyperbolic functions and its differentiations and integrations. Improper integrals. Sequences and series: convergence tests, integral, comparison, ratio and root tests. Alternating series. Absolute and conditional convergence. Power series. Taylor and Maclaurin series.  
Learning Objectives:  

-   To let the student know the definiteandindefinite integralsoffunctionsof a single variable.

-   To let the student identify the fundamental theorem of calculus, mean value theorems and L'Hopital's rule for undetermined limits.Provide the definiteandindefinite integralsoffunctionsof a single variable.

-   To let the student acquire different techniques of integration.

-   To let the student enumerate integration and its applications in parametric and polar coordinates.

- To let the student recognize the notion of improper integrals and their kinds.

-   To let the student understand alternating series, absolute and conditional convergence, power series. Taylor & Maclaurin series

  
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.  Indefinite integrals,  Integration by substitution  
2.  Definite integral,  The fundamental Theorem of calculus, Definite integral by Substitution  
3.  Hyperbolic Functions  
4.  Area Between Two Curves, Volumes By Slicing ; Disks And Washers  
5.  Volumes By Cylindrical Shells, Length of a plane Curve,  Area of a Surface of Revolution  
6. Integration By parts,  Trigonometric Integrals  
7. Trigonometric Substitutions, Integrating Rational fractions  
8. Improper Integrals, Sequences  
9. Monotone Sequences, Infinite Series  
10. Convergence Tests, The Comparison ,Ratio, and Root  tests  
11. Alternating Series; Conditional convergence  
12. Maclaurian and Taylor polynomials  
13. Maclaurian And Taylor series; Power Series  
14. REVIEW FOR FINAL EXAM  
15.    
             

 

Course Title: Basic Mathematics
Course Code: Math 251
Credit Hours: 3
Prerequisite: Calculus l Math-101
Text Books:
1. Robert Wolf, Proof, Logic and Conjecture: The mathematician Toolbox, W. H. Freeman (1997).
2. Seymour Lipschutz, Schaum, Outline of Theory & Problems of Set Theory and Related Topics, (1994), Int. Pub. & Dist. House, Cairo, Egypt.
3.  
Course Description:
Set theory-symbols and expressions-union-intersection- difference- complement- Ven's diagram - sets. Numbers - natural numbers - integers numbers - rational numbers-real numbers. Relations and functions- cartesian product- binary relations-.operations on relations- composition of relations- equivalence relations and partitions. Maps- injective, surjective and bijective. Equivalence and countable sets- finite and infinite sets- power of a set- countable and uncountable sets.
Learning Objectives:

- Let the student present Basic concepts of mathematical logic.

- Let the student study of mathematical induction.

- Let the student acquire and development of skills on theory of sets.
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. Set theory- symbols and expressions- union- intersection- difference- complement- Ven's diagram- sets.
2. Operations on Sets.
3. Finite Sets, Power Sets. Mathematical Induction
4. Product Sets
5. Relations, Composition of Relations, Partition
6. Functions, Composition of Functions, One to one, Onto.
7. Propositions and Compound Propositions
8. Propositions and Truth Tables
9. Logical Equivalence, Algebra of Propositions, Logical Implication
10. Propositional functions
11. Boolean Algebra as Lattices, sum of products form for Sets
12. Representation theorem
13. Sum of products form for Boolean Algebra
14. Binary operations
15. Review
           
Course Title: Analytic Geometry
Course Code: Math 261
Credit Hours: 3
Prerequisite: Calculus l Math-101
Text Books:
1. Calculus and Analytical Geometry", 9th Ed, Addison-Wesley 1998, George B. Thomas, Ross L. Finney, Publishing Company,     
2.  
3.  
Course Description:
Cartesian and polar coordinates-Vectors in plane-  algebra of vectors- angle between two vectors- dot product- vector product- triple product- area of triangle-Vectors in three dimensions-.Straight lines in plane-  Straight lines in space- parametric representation of straight line-Conic sections- circle- parabola- ellipse- hyperbola-Polar form of conic sections-Applications of conic sections in Astronomy, Cylindrical coordinates- Spherical coordinates
Learning Objectives:
Present the importance of the analytical geometry in Physics and Engineering Science, study the equations of the conic sections and its polar form with some applications in orbital Mechanics and introduce new coordinate systems, cylindrical and spherical coordinates.
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. Cartesian and polar coordinates
2. Vectors in plane-  algebra of vectors- angle between two vectors- dot product .
3. vector product- triple product- area of triangle.Vectors in three dimensions.
4. Straight lines in plane-  Straight lines in space - parametric representation of straight line.
5. Equation for planes in space .
6. Conic sections:  circle- parabola.
7. Conic sections : ellipse- hyperbola.
8. Translation of Axes .
9. Rotation of Axes.
10. Polar form of conic sections : circle- parabola.
11. Polar form of conic sections: ellipse- hyperbola
12. Cylindrical coordinates
13. Spherical coordinates
14. Revision

توصيف المقرر

Syllabus

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

​ 


 

​

Syllabus

College: Faculty of science
Department: Mathematics

 

Course Title: Differential Equations(2)
Course Code: Math 305
Credit Hours: 3
Prerequisite: Differential Equations 1 Math 204
Text Books:
1. Shepley L. Ross: Differential Equations:3rd. Edit. (1998): John Wiley & Sons. , Inc
2. D. Rainville and P. E. Bedient: Elementary Differential Equations, (1995) MacMillan Pub. Co. Inc. N. Y.
3.  
Course Description:
System of linear ordinary differential equations with an emphasis on applications on initial value problems. Topics include power series solutions, Laplace transform, solution of initial value problems, and nonlinear differential equations.
Learning Objectives:

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

2- Let the student study the methods for solving ODE, series solution, solutions by Laplace transform.

3- Let the student acquire the concept of nonlinear differential equations.
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. System of first-order equations- Introductory remarks
2. Homogenous linear system with constants coefficients
3. Introduction and review of power series
4. Series solutions of first-order DE
5. Second order differential equations – ordinary points
6. Laplace transform, introduction
7. First Term Exam,  
8. Derivatives and integrals of Laplace transform
9. Convolutions,
10. Applications to Differential Equations
11. Nonlinear differential equations- Introduction
12. The Unit step function ,TheImpulse function ,Second Term Exam
13. Solution of equations with discontinuous forcing terms
14. Revision
15. Final Exam
           

 

College: Faculty of Science
Department: Mathematics
Course Title: Real Analysis1
Course Code: Math 311
Credit Hours: 3
Prerequisite: Fundamentals of integral calculus (Math 200), Basics of Mathematics Math 251
Text Books:
1. Elements of Real Analysis,2nd Edition. John Wiley and Sons,Inc. New York, 1976- R. G. Bartle
2. Basic  elements of Real Analysis - Murrary H.Protter
3. Introduction to Real Analysis, 2nd edition, by Manfred Stoll
Course Description:
This course concerns itself with the concepts of limit and continuity, which are the basis of mathematical analysis and the calculus from which it evolved.  We focus on limits of sequences and of functions, and continuity of functions and the the concept of differentiability.  While the main context is the real numbers, i.e. limits of sequences of real numbers, continuity of functions from the real numbers to the real numbers,... Existence of global extrema and the Intermediate Value Theorem are studied…
Learning Objectives:

To develop and generalize techniques studied in Calculus 1 in IR and to master theoretical subtleties such as uniform convergence and uniform continuity…

At the completion of this course, the successful student will have demonstrated these abilities:

·         The ability to understand both abstract and concrete mathematical reasoning.

·         The ability to differentiate between sound mathematical reasoning, flawed reasoning, and non-rigorous reasoning.

·         The ability to use the basic tools and methods of proof seen in analysis, in particular set theory and epsilon-delta and epsilon-n arguments.

·         The ability to formulate and prove theorems that arise from the definitions and concepts of the course content, and the ability to apply those theorems to specific examples.

·         The ability to write up, and occasionally present orally, one’s mathematical proofs and arguments in a clear and compelling manner.
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. Real numbers – Algebraic properties
2. Completeness- arrangement properties
3. Open sets- closed sets
4. limit points–  Compact sets
5. Heine-Borel Theorem and Weirstrass Theorem
6. Continuity
7. Uniform Continuity
8. Differentiation
9. Mean value Theorem –L’Hˆopital’s rule 
10. Convergent sequences
11. Limits - Theorem of limits
12. upper and lower of limit sequences , Cauchy sequence
13. Tests of convergence : Comparison test – root test ratio – Abel's Test – Alternating series test…
14. REVIEW FOR FINAL EXAM
15.  
             

 

College: Faculty of Science 
Department: Statistics
Course Title: Probability Theory
Course Code: Stat. 311
Credit Hours: 3 hrs
Prerequisite: General Statistics (Stat 201)
Text Books:
1.

Introduction to Probability and Mathematical Statistics, Second Edition

Author : Bain and Engelhardt
2.

Mathematical Statistics with Applications  (7th Edition)

Author : Dennis Wackerly, William Mendenhall, Richard L. Scheaffer
3. Recommended Books and Reference Material (Journals, Reports, etc)
Course Description:
The course focuses on the importance and the efficiency of the random variables idea in statistical mechanism. The several types of discrete and continuous random variables in addition to Some applications of random variables beside the mathematical illustration of several issues related to random variables and statistical distributions.
Learning Objectives:

-The course aims to enable students to apply the fundamentals of probability theory.

-The course Provide students with the required knowledge of random variables (Discrete and continuous), bivariate and multivariate random variables in addition to the applications of moment generating function and its use

  - The course aims to teach  students the meaning of the continuous probability distributions and their applications as well as derivations of their means and variances
Grading: 
No. Assessment Evaluation
1. Quiz 1 05
2. First midterm 25
3. Quiz 2 05
4. Second midterm 25
5. Final Examination 40
Total 100 %
Methods of Teaching: (Lectures, Laboratory, Individual exercises, In-class discussion, Selection of Readings…)
1. Lectures
2. Tutorials
3. Exercises
4. Discussions
Course Outline:
Week Lecture Topics
1. Revision on Discrete and continuous random variables and Probability.
2. Moment generating function method.
3. Geometric distribution, Gamma distribution.
4. Exponential distribution, Normal distribution, Mean.
5. Joint discrete distributions, Multinomial distribution.
6. Joint continuous distributions.
7. Independent Random Variables, Conditional Distributions.
8. Properties of the expected values.
9. Correlation, Conditional expectation.
10. Bivariate normal distribution
11. Joint moment generating function
12. The CDF technique
13. Transformation methods
14. Sum of random variables
15. Moment generating function method
             

 

 

 

College: Science
Department: Mathematics
Course Title: Abstract Algebra 1  
Course Code: Math 342  
Credit Hours: 3  
Prerequisite: Basic of mathematics – Math  251  
Text Books:  
1. A First Course in Abstract Algebra. 5th ed. 1999 John B. Fraleigh,  Addison-Wesly Pub. Co.  
2. Topics in Algebra, I. N.  Herstein, John wily & sons 1975  
3. Abstract Algebra: A first Course By Dan Saracino. 1980.  
Course Description:  
Sets, relations and Binary operation - Definition and basic properties of group - Solutions of equations in any group - power of element in a group The order of a group and the order of element - Definition of Cyclic group – generators of a Cyclic group – Definition, elementary properties and Theorems of a subgroups - Definition of function – one to one and onto function – definition of permutation–composition of permutation – cyclic notation – even and odd permutation Cosets of a subgroup - Lagrange's theorem and its corollaries – multiplication of two subgroups - Normal subgroup and Quotient group – Homomorphsim and The fundamental theorem of homomorphisms  
Learning Objectives:  

1- Let the student present the basic definitions in abstract algebra, Let the student study the algebraic structures with one binary operation (groups).

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

3- 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. 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. Individual exercises  
3. In-class discussion  
4. Home works, Quizzes  
Course Outline:  
Week Lecture Topics  
1. Sets  and Relations – Binary operation -  
2. Definition and basic properties of group - Examples - Theorems  
3. Solutions of equations in any group - power of element in a group - Quizzes 1  
4. The order of a group and the order of element – Examples  
5. Definition of Cyclic group – generators of a Cyclic group  
6. Midterm 1 - Definition and elementary properties – Theorems of a subgroups  
7. Definition of function–one to one and onto function – definition of permutation - Composition of permutation – cyclic notation – even and odd permutation  
8. Cosets of a subgroup – Examples  
9. Lagrange's theorem and its corollaries- multiplication of two subgroups  
10. Continue - Normal subgroup  
11. Midterm 2 -Quotient group  
12. Continue Homomorphsims  
13. The fundamental theorem of homomorphism- Quizzes 2  
14. Continue  
15. Review and Final exam  

 



 

Syllabus

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

 

 


 

Syllabus

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
               

 

Syllabus

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

 


 

Syllabus

College: Science  
Department: Mathematics  
Course Title: Discreet Mathematics
Course Code: MATH 462
Credit Hours: 3
Prerequisite: Basics of Mathematics Math 251
Text Books:
1. Introduction to Integral Equations with Applications, 2nd  ed. Jerri, (1999), Wiely-Interscience.
2.  
3.  
Course Description:

Basic of discrete mathematics- Formal logic -Theorem sets. Algebraic basic rules- semigroups- Identities-Sets-Linear code. Graph theory: Graphs- Directed graphs-Paths- Walks - Eulerian and Hamiltonian graphs- Shortest  path - Planar graphs –Path colouring – Trees- Spanning trees –Different algorithms.

Viability of the account :Table of transition- Planning graphs- Homomorphisms, Isomorphism -The partial regression functions- Languages and rules- The regular expressions.
Learning Objectives:

-       To provide the student with knowledge of logical thinking

-       To provide the student with the basic concepts discrete mathematics

-       To teach student how to apply software on these topics
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. Basic of discrete mathematics
2. Formal logic -Theorem sets.
3. Algebraic basic rules- semigroups
4. Identities-Sets-Linear code.
5. Graph theory: Graphs- Directed graphs-Paths- Walks -
6. Eulerian and Hamiltonian graphs
7. Shortest  path - Planar graphs –Path colouring
8. Trees
9. Spanning trees
10. Different algorithms.
11. Viability of the account :Table of transition- Planning graphs-
12. Homomorphisms
13. Isomorphism
14. The partial regression functions- Languages and rules-
15. The regular expressions.
               

 

College: Faculty of science
Department: Mathematics
Course Title: Differential Geometry
Course Code: Math 463
Credit Hours: 3
Prerequisite: Math 204, Math 305
Text Books:
1. P. Petersen, Riemannian Geometry, Springer, New York, 1998.
2. Geodesics: Christoffel symbols, "straight lines," more geodesics
3.

 

 
Course Description:
Study the Geometry of Curves and Surfaces in three dimensional space using calculus techniques. Topics include Curves: arclength, tangent vector, curvaturebinormal vector, torsion Gauss Curvature: normal section, principal curvature Surfaces in E3: surfaces of revolution, parallelsFirst Fundamental Form: metric form, intrinsic propertySecond Fundamental Form: Frenet Frame, normal curvature Gauss Curvature in Detail: principal curvature. .
Learning Objectives:

Students who are successful in this course will improve in the following general education areas:

 - differential geometry (with an emphasis on curvature),

-  Surfaces in E3

- Geodesics: Christoffel symbols. We will spend about half of our time on the theories of curves and surfaces in E3.
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. Curves:  Arclength, Tangent vector, curvature.
2. Curvature, binormal vector
3. Torsion, Gauss Curvature
4. normal section, principal curvature
5. Theories of curves
6. Surfaces in E3: surfaces of revolution, parallels
7. First Term Exam  ,  
8. Theories of surfaces
9. First Fundamental Form: metric form, intrinsic property
10. Second Fundamental Form: Frenet Frame, normal curvature
11. Gauss Curvature in Detail: principal curvature
12. Second Term Exam  ,  
13. Introduction to Christoffel symbols
14. Revision
15.  
             

 

College: Science  
Department: Mathematics  
Course Title: Functional Analysis
Course Code: MATH 462
Credit Hours: 3
Prerequisite: Linear Algebra 1: MATH241, Real Analysis 1 (Math311)
Text Books:
1. Lax. P. ''Functional analysis'', Wiley- inter science, 2002.
2. Akhiezer, N. I. and Glazman, I. M. '' Theory of linear operators in Hilbert space'' Frederrich Ugar publishing Co. New York Vol I (1961), Vol II (1963).
3.  Kolmogorov A.N., Fomin S.V. ''Elements of the theory of functions and functional analysis'' Dover publications, (1999)
Course Description:
Vector spaces:linear subspace - linear dependence and linear combination- dimension and basis- spanning- direct sum decomposion for V(F). Inner product spaces:Cauchy Schwarz  inequality- Minkowski inequality- polarization identity – orthogonality and orthogonal sets of vectors - orthogonalization (Gram-Schmidt). Normed spaces and metric spaces:Holder inequality- general Minkowski inequality- metric and metric spaces- some topological notion in metric spaces- convergent and completeness – Cauchy sequence – complete metric –continuity and uniform continuity on metric spaces- contraction mappings. Banach spaces and Hilbert spaces:Linear manifold – orthogonal system – Fourier coefficient. Linear operators:bounded operators –continuous – linear functional in Hilbert H- adjoint operator- self adjoint operator – normal operator- unitary and isometric operators – projection operators- closed operator- graph of an operator- eigenvalues and eigenvector – symmetric operators- positive operators- the formal differential operator ( - spectrum of self adjoint operator.
Learning Objectives:

-       To allow the student study the theoretical spaces.

-       To allow the student acquire some properties of sequences that are defined on the theoretical spaces.
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. Vector spaces: linear subspace - linear dependence and linear combination- dimension and basis
2. Spanning- direct sum decomposion for V(F).
3. Inner product spaces: Cauchy Schwarz  inequality- Minkowski inequality- polarization identity.
4. Orthogonality and orthogonal sets of vectors - orthogonalization (Gram-Schmidt).
5. Normed spaces and metric spaces: Holder inequality- general Minkowski inequality.
6. Metric and metric spaces- some topological notion in metric spaces.
7. Convergent and completeness – Cauchy sequence – complete metric.
8. Continuity and uniform continuity on metric spaces- contraction mappings.
9. Banach spaces and Hilbert spaces: Linear manifold – orthogonal system – Fourier coefficient.
10. Linear operators: bounded operators –continuous – linear functional in Hilbert H.
11. Adjoint operator- self adjoint operator – normal operator- unitary and isometric operators.
12. Projection operators- closed operator- graph of an operator.
13. Eigenvalues and Eigenvector.
14. Symmetric operators- positive operators.
15. The formal differential operator- spectrum of self adjoint operator.