Department of Mathematics - Jazan Ucolleges.jazanu.edu.sa/sites/en/sci/math/Documents/Math Bsc program... · Faculty of Science Department of Mathematics 1 PDF created with pdf Factory

____________________________________________________________________________________________________

Faculty of Science Department of Mathematics

1

PDF created with pdf Factory Pro trial version www.pdffactory.com

المملكـة العربيـة السعوديـة وزارة التعليم العالي

جامعة جازان

كليــــــة العلـــــوم

Kingdom of Saudi Arabia

Ministry of Higher Education

Jazan University

Faculty of Science

Department of Mathematics

____________________________________________________________________________________________________


2







Jazan University

Faculty of Science

Introduction The Department of Mathematics is considered to one of the most important departments of the faculty of Science; it offers bachelor's degree in mathematics. The department is responsible for teaching courses of mathematics in various university faculties: Faculty of Science, Faculty of Engineering, Faculty of Computer and Many Others.

Date of Establishment: The departments of College of Science is established in 1426 and the department of Mathematics was one of them.

Vision: Our vision is that of a department which is recognized nationally and internationally for excellence in teaching, research and training.

Mission: Our mission is to provide high quality undergraduate, graduate and professional programs of study which attract the best students, to produce significant research and to attend to the mathematical needs of the University and the community, in a congenial and stimulating environment for learning and research ,

Objectives: 1. Prepare specialists in mathematics participating in the overall development. 2. Meet the needs of educational institutions with cadres of high scientific efficiency. 3. To encourage scientific research and publication in scientific journals locally and internationally 4. To support the student's ability to link the scientific theory with practical applications 5. Develop the capacity of students in scientific research and stay informed. 6. Prepare a generation of academic researchers with high scientific qualifications that give them the ability to

make scientific research in various fields of mathematics. 7. To achieve scientific communication with specialists in different fields of mathematics locally and

globally. 8. To achieve quality and academic accreditation locally and globally

Degrees conferred by section: Department of Mathematics gives the degree of Bachelor of Science in mathematics.

____________________________________________________________________________________________________


3







Jazan University

Faculty of Science

The syllabus of the department: For a bachelor's degree in Mathematics, the study requires completion of 130 Credit Hours with level not less than Satisfactory, and average of at least 2 of 5 in courses taught in the Department of Mathematics, ranked as follows:

Requirements Contact Hours CreditHours

Lectures Sec/Lab

University Requirements 14 2 15

College Requirement 27 9 24

Section Requirements 89 4 91

Total 130 15 130

____________________________________________________________________________________________________


4







Jazan University

Faculty of Science

First – University Requirements: University Requirements is studied by all students of the University and involved 15 credit units contribute to prepare students academically and provide them with multiple skills such as English language needed for study in Coming years, and principles for dealing with the computer.

Course Name Course Code

Contact Hours Credit hours

Prerequisite lectures Sec/Lab Islamic culture 1 101 Islm 2 - 2 -

Islamic culture 2 102 Islm 2 - 2 -



Language Skills 101 Arab 2 - 2 -

Liberalization Arab 102 Arab 2 - -

Introduction to Computer

101 Comp 2 2 3 -

Total 14 2 15

Second - College Requirements: College Requirements is studied by all college students in the first year of preparations and goes to 24 credit hours, contribute to prepare students academically and providing them with basic skills of natural sciences (Mathematics, Physics, Chemistry and Biology).

Course Name Course Code

Contact Hours Credit Hours Prerequisite lectures Sec/Lab

General Mathematics 101 Math 3 - 3 - General Physics 101 Phys 3 2 4 - General Biology 101 Biol 3 2 4 -

General Chemistry 101Chem 3 2 4 - English language 105 Engl 12 3 6 -

Scientific English language

106 Engl 3 - 3 -

Total 27 9 24

____________________________________________________________________________________________________


5







Jazan University

Faculty of Science

Third- Mathematics Section Requirements: Section requirements is studied by students during the years of study, all compulsory courses, and involved 91 credit hours contribute to prepare student scientifically and academically.

# Course Name Course Code Contact Hours Credit Hours Prerequisite lectures Sec/Lab

1 Calculus 1 211 Math 3 - 3 101 Math 2 Calculus 2 212 Math 3 - 3 211 Math 3 Foundation of Mathematics 221 Math 3 - 3 101 Math 4 Abstract Algebra 1 222 Math 3 3 221 Math 5 Geometry Analysis 241 Math 3 3 - 6 Mathematical Statistics 251 STAT 3 3 - 7 Statics 261 Math 3 3 -

8 Algorithms & programming

271 Comp 2 2 3 101 Comp

9 Calculus 3 313 Math 3 3 212 Math 10 Complex Analysis 314 Math 3 - 3 313 Math 11 Real Analysis 1 315 Math 3 3 313 Math 12 Numerical Analysis 1 316 Math 3 3 212 Math 13 Abstract Algebra 2 323 Math 3 3 222 Math 14 Linear Algebra 324 Math 3 3 323 Math 15 Differential Equations 1 331 Math 3 3 212 Math 16 Differential Equations 2 332 Math 3 3 331 Math 17 Probability Theory 352 STAT 3 3 251 STAT 18 Dynamics 362 Math 3 3 212 Math 19 Analytical Mechanics 363 Math 3 3 362 Math 20 Real Analysis 2 417 Math 2 2 315 Math 21 Functional Analysis 418 Math 2 2 417 Math 22 Numerical Analysis 2 419 Math 3 3 434 Math 23 Discrete Mathematics 425 Math 3 3 313 Math 24 Mathematical Methods 433 Math 3 3 212 Math 25 Partial Differential

Equations 434Math 3 3 332 Math

26 Topology 442Math 3 3 315 Math 27 Differential Geometry 443Math 3 3 331 Math 28 Applied Statistics 453 STAT 2 2 3 215 STAT 29 Fluid Mechanics 464Math 3 3 434 Math 30 Mathematical Modeling 472 Math 3 3 332 Math 31 Operations Research 473 Math 3 3 324 Math

Total 89 4 91

____________________________________________________________________________________________________


6







Jazan University

Faculty of Science

Fourth - Classification of section requirements:

Group Number

Group Specialized Credit Hours

1 Set of analysis: (Calculus (1) - Calculus (2) - Calculus (3) - Real Analysis (1) - Real Analysis (2) - Complex Analysis - Functional Analysis - Numerical Analysis (1) - Numerical Analysis (2)

25

2 Group of algebra: (Foundation of Mathematics - Abstract Algebra (1) - Abstract Algebra (2) - Linear Algebra - Discrete Mathematics)

15

3 differential equations (Differential Equations (1) - Differential Equations (2) - Mathematical Methods -Partial Differential Equations)

12

4 Group Geometry and topologies: (Geometry Analytical - topology - Differential Geometry

9

5 Group of statistics and probabilities: (Mathematical Statistics - Probability Theory - Applied Statistics).

9

6 Group of Applied Mathematics (Statics - Dynamics - Analytical Mechanics - Fluid Mechanics)

12

7 Computer Science and Operations Research: (Algorithms and Programming - Operations Research - Mathematical Modeling)

9

Fifth - The interpretation of the requirements of section numbers: Course number consists of three digits interpreted as follows*:

First Digit Second Digit Third Digit

The course order in its specialized sets

Number of specialized sets Year in which the course is given

• Courses of University Requirements and College Requirement are not subject to the above number system.

____________________________________________________________________________________________________


7







Jazan University

Faculty of Science

Details of the syllabus

First level

# Course Name

Course Code Number of hours of study Credit Hours

Prerequisite lectures Sec/Lab 1 Islamic Culture 1 101 Islm 2 - 2 -

2 General Mathematics 101 Math 3 - 3 -

3 General Biology 101 Biol 3 2 4 -

4 Introduction to Computer

101 Comp 2 2 3 -

5 English language 105 Engl 12 3 7 -

Total 22 7 18

Second level

# Course Name

Course Code

Contact Hours Credit Hours

Prerequisite lectures Sec/Lab 1 Islamic Culture 2 102 Islm 2 - 2 - 2 General Chemistry 101Chem 3 2 4 - 3 General Physics 101 Phys 3 2 4 - 4 Language skills 101 Arab 2 2 - 5 Scientific English

Language 106 Engl 3 3 -

Total 13 4 15

____________________________________________________________________________________________________


8







Jazan University

Faculty of Science

Third level

# Course Name

Course Code


Prerequisite lectures Sec/Lab 1 Islamic Culture 3 103 Islm 2 - 2 - 2 Arabic Editing 102 Arab 2 - 2 - 3 Calculus 1 211 Math 3 - 3 101 Math 4 Static 101 Math 3 3 -

5 Analytical Geometry 105 Math 3 - 3 -

6 Foundation of Mathematics

221 Math 3 3 101 Math

Total 16 - 16

Fourth level

# Course Name

Course Code


Prerequisite lectures Sec/Lab 1 Islamic Culture 4 104 Islm 2 - 2 -

2 Mathematical statistics 251 STAT 3 3 101 Math

3 Abstract Algebra 1 222 Math 3 3 221 Math

4 Calculus 2 212Math 3 3 211 Math

5 Algorithms and programming

271 Comp 2 2 3 101 Comp

Total 13 2 14

____________________________________________________________________________________________________


9







Jazan University

Faculty of Science

Fifth level

# Course Name

Course Code Contact Hours Credit Hours Prerequisite lectures Sec/Lab

1 Calculus 3 313Math 3 - 3 212 Math

2 Abstract Algebra 2 323 Math 3 - 3 222 Math

3 Probability Theory 352 STAT 3 - 3 251STAT

4 Differential Equations 1 331 Math 3 - 3 212 Math

5 Dynamics 362 Math 3 - 3 212 Math

Total 15 - 15

Sixth Level

# Course Name

Course Code


Prerequisite lectures Sec/Lab 1 Analytical Mechanics 363 Math 3 - 3 362 Math

2 Complex Analysis 314 Math 3 - 3 313 Math

3 Linear Algebra 324 Math 3 - 3 323 Math

4 Real Analysis 1 315 Math 3 - 3 313 Math

5 Numerical Analysis 1 316 Math 3 - 3 212 Math

6 Differential Equations 2 332 Math 3 - 3 331 Math

Total 18 - 18

____________________________________________________________________________________________________


10







Jazan University

Faculty of Science

Seventh Level

# Course Name


1 Topology 442 Math 3 3 315 Math 2 Discrete Mathematics 425 Math 3 3 313Math 3 Partial Differential

Equations 434 Math 3 3 332 Math

4 Applied Statistics 453 STAT 2 2 3 215 STAT 5 Real Analysis 2 417 Math 2 2 315Math

6 Mathematical Methods 433 Math 3 3 212Math

Total 16 - 17

Eighth level

# Course Name


1 Differential Geometry 443 Math 3 3 331 Math 2 Mathematical Modeling 472 Math 3 3 332 Math 3 Functional Analysis 418 Math 2 2 417 Math 4 Operations Research 473 Math 3 3 324Math 5 Fluid Mechanics 464 Math 3 3 434Math

6 Numerical Analysis 2 419Math 3 3 434 Math

Total 17 - 17

____________________________________________________________________________________________________


11







Jazan University

Faculty of Science

Summary of the Study Plan of Mathematics Department

First Year

First Level Second Level

Course

code course name

Contact hours credit

hour prerequisite

Course

code course name


hour prerequisite

lectures Sec/Lab lectures Sec/Lab

101 Islm Islamic Culture (1) 2 - 2 - 102 Islm Islamic Culture (2) 2 - 2 -

101Math General Mathematics 3 - 3 - 101Chem General Chemistry 3 2 4 -

101 Biol General Biology 3 2 4 - 101 Phys General Physics 3 2 4 -

101Comp Introduction to

Computer Science 2 2 3 - 101 Arab Language Skills 2 - 2 -

105 Engl English Language 12 3 6 - 106 Engl Scientific English

Language 3 - 3 -

Total 22 7 18 Total 13 4 15

Fourth Year

Seventh Level Eighth Level

Course

code Course name


hour prerequisite

Course

code Course name


hour prerequisite


442Math Topology 3 - 3 315 Math 443Math Differential Geometry 3 - 3 331 Math

425Math Discrete Mathematic 3 - 3 221 Math 472Math Mathematical modeling 3 - 3 332Math

434Math Partial Differential Equations 3 - 3 332 Math 418Math Functional Analysis 2 - 2 417 Math

453 Stat Applied statistics 2 2 3 251 Stat 473Math Operation research 3 - 3 324 Math

417Math Real Analysis(2) 2 - 2 315 Math 464Math Fluid Mechanics 3 - 3 434 Math

433Math Mathematical Methods 3 - 3 313 Math 419Math Numerical Analysis (2) 3 - 3 434 Math

Total 16 2 17 Total 17 - 17

Total Number of Credit Units Is 130

Second Year

Third Level Fourth Level

Course

code course name


hour prerequisite

Course

code course name


hour prerequisite


103 Islm Islamic Culture (3) 2 - 2 - 104 Islm Islamic Culture (4) 2 - 2 -

211 Math Calculus (1) 3 - 3 101 Math 251 Stat Mathematical statistics 3 - 3 101 Math

261Math Static 3 - 3 - 222Math Abstract algebra (1) 3 - 3 221 Math

241 Math Analytic Geometry 3 - 3 - 212Math Calculus (2) 3 - 3 211Math

221 Math Foundation of

Mathematics 3 - 3 101 Math 271

Comp

Algorithmic and

programming 2 2 3 102 Comp

102 Arab Arabic Editing 2 - 2 -

Total 16 - 16 Total 13 2 14

Third Year

Fifth Level Sixth Level

Course

code course name


hour prerequisite

Course

code course name


hour prerequisite


313 Math Calculus (3) 3 - 3 212 Math 363Math Analytical Mechanics 3 - 3 362 Math

323 Math Abstract algebra (2) 3 - 3 222 Math 314Math Complex Analysis 3 - 3 313 Math

362 Math Dynamics 3 - 3 212 Math 324Math Linear Algebra 3 - 3 323 Math

313 Math Differential Equations (1) 3 - 3 212 Math 315Math Real Analysis(1) 3 - 3 212 Math

352 Stat Probability theory 3 - 3 251 Stat 316Math Numerical Analysis (1) 3 - 3 212 Math

332Math Differential Equations (2) 3 - 3 331 Math

Total 15 - 15 Total 18 - 18

____________________________________________________________________________________________________


12







Jazan University

Faculty of Science

Description of the Courses of the Department of Mathematics

____________________________________________________________________________________________________


13







Jazan University

Faculty of Science

Course summary: General Mathematics course contents are the basic algebraic operations, equations, inequalities, functions, topics in analytical Geometry, system of equations, system of inequalities, and matrices. General Course Objectives: After finishing the course, the student is expected to be familiar with the following:

• Basic algebraic operations • Equations and Inequalities • Functions • Topics in Analytical Geometry • System of equations and inequalities • Matrices

Course Description: • Basic Algebraic Operations • Equations and Inequalities • Functions • Topics in Analytical Geometry • System of equations and inequalities • Matrices

Course Assessments: - First Exam 20% - Second Exam 20% - Quizzes and homework 10% - Final Exam 50%

Methods of teaching the course: - Academic lectures - Scientific discussions - Homework - The use of mini-model of education - Assign students to prepare scientific projects

The Textbook: - Precalculus, Custon Edition, Barnett, Ziegler and Bylenn, Complied by Samir H. Saker, McGraw Hill,(2009).

Scientific References: -Algebra and Trigonometry, R. E. Larson, R. P. Hostetler,6thEdition, Houghton Mifflin Company,(2004) - College Algebra and Trigonometry,R. Aufmann, V. Barker, and R. Nation, 4thEdition, Houghton Mifflin Company,(2003)

Prerequisite level year Contact hours

Course Code

Course Name Credit Hours Sec/Lab Lectures

- 1 1 3 - 3 101 Math General Mathematics

____________________________________________________________________________________________________


14







Jazan University

Faculty of Science

Course summary: Calculus (1) is an important course in mathematics, because it is the basis in studying other courses. General Course Objectives: After finishing the course, the student is expected to be familiar with the followings:

• Show the importance of differentiation and integration in branches of science and Geometry and recognize the relationship between them

• Understand the basic rules of differentiation, integration and their applications. • Develop the student’s logical thinking and providing students with skills necessary to solve problems.

Course Description: • The functions: Definition, Types of functions, domain of the functions, graph of functions, composite

functions, properties of functions, Inverse functions. • The Limits and continuity: limit by definition, theorems, limits and continuity of trigonometric functions. • Derivatives of functions: Techniques of differentiation, derivation rules, chain rule, implicit and

parametric differentiation, higher derivatives. • Applications of differentiation: The absolute and local maximum and minimum values of a function,

Roll’s Theorem, The Mean Value Theorem, critical points, increasing and decreasing, concavity, Infliction point, vertical and horizontal Asymptotes and graph of curves.



The Textbook: - Calculus, H. Anton, 8thEdition, John Wiley and Sons, (2005).

Scientific References: - Calculus, J. Stewart, 5thEdition, Brooks/ Cle Publishing Company, (2003). - Calculus, R. E. Larson, R. P. Hostetler, and B. H. Edwards, 7thEdition, Houghton Mifflin Company, (2002) - Calculus, G. B. Thomas, Early Transcendentals, 11thEdition, Addition-Wesley, New York (2006) - Calculus,E. Swokowski, M. Olinic, and D. Pence, 6thEdition, PWS Publishing Company, (1994)

Prerequisite level year Contact Hours Course

Code Course Name Credit Hours Sec/Lab Lectures

101 Math 3 2 3 - 3 211 Math Calculus 1

____________________________________________________________________________________________________


15







Jazan University

Faculty of Science

Course summary: Calculus (2) is an important course in mathematics, because it enables students to study other courses

General Course Objectives: After finishing the course, the student is expected to be familiar with the following:

• Show the importance of differentiation and integration in branches of science and Geometry and recognize the relationship between them.

• View more rules of differentiation and integration methods and their applications, numerical series, geometric series.

• Develop the student’s logical thinking and providing them with skills necessary to solve problems.

Course Description: • Indefinite Integration : (Properties of Indefinite Integration, Brief Table of Indefinite Integration, some

theorems of integration) • Methods of integration: (integration by substitution, Integration by Parts, Integration by Partial Fractions,

integration in other ways) • Definite Integration: Fundamental theorem of calculus, change of variables, properties of definite integral • Application of Integration : (Area calculations, Solids of Revolution, Arc Length and surfaces of

Revolution) • Improper Integrals : (types of Improper Integrals, examples, applications)


Methods of teaching the course: - Academic lectures - Scientific discussions - Homework. - The use of mini-model of education. - Assign students to prepare scientific projects.

The Textbook: - Calculus, H. Anton, 8thEdition, John Wiley and Sons, (2005).

Scientific References: - Calculus, J. Stewart , 5thEdition, Brooks/ Cle Publishing Company, (2003). - Calculus, R. E. Larson, R. P. Hostetler, and B. H. Edwards. 7th Edition, Houghton Mifflin Company, (2002). - Calculus, G. B. Thomas, Early Transcendentals, 11thEdition, Addition-Wesley, New York (2006) - Calculus, E. Swokowski, M. Olinic, and D. Pence, 6thEdition, PWS Publishing Company (1994)

Prerequisite level year Contact Hours

Course Code


211 Math 4 2 3 - 3 212 Math Calculus 2

____________________________________________________________________________________________________


16







Jazan University

Faculty of Science

Course summary: Foundation of Mathematics gives the opportunity for understanding the primary concepts in mathematics(Mathematical Logic, Set Theory, Relations, Applications, Binary process and Algebraic systems), which considered to be the basic for studying mathematics. General Course Objectives: After finishing the course, the student is expected to be familiar with the following:

• Identify the basic concepts in mathematics • Development of skills necessary for understand ding the logical and abstract mathematics • Development of methods of understanding hypotheses, theories, and proofs • Training students to solve exercises and applications

Course Description: • Mathematical logic: Statements, Open statements, Truth values, Simple and Compound statements, Negation,

Logical connectives and their T-F values, Implications, Logical Equivalence, Tautologies, Methods of giving proofs. • Sets: Representation of sets, subsets, Power set, Partitions of set, Algebraic operations on sets and their properties. • Relations: Cartesian product of Sets and properties, Binary relations and properties, Domain, Rang and

inverse of a set, Partially and totally order relations, Equivalence relations, Equivalence classes, Partitions and equivalence relations on a set, congruent modulo n.

• Mappings: Definition of mapping and its properties, Types of mapping, Composition of mappings • Binary operations on Set: Definition, examples and Properties of Binary operations, Semi-group, Monoid


Methods of teaching the course: - Academic lectures - Scientific discussions. - Homework. - The use of mini-model of education. - Assign students to prepare scientific projects. ·

The Textbook: - Foundations of Discrete Mathematics, P. Fletcher, H. Hoyle and C. W. Batfy, PWS-Cant Pub. Co, (1991) Scientific References:

- Introduction to Abstract Algebra, W. K. Nicholson, PWS-Kent publishing Co Boston, 1993 - Discrete Mathematics and Applications, K. H. Rosen, McGraw-Hill, 5thEdition (2004) - Elements of Logic and Moderen Algebra, M. V. shat and M.L. Bhave, Published by S.Chond and Company

Ltd. H. O. Ram Nagar, New Delhi, (1986).


Course Code Course Name Credit

Hours Sec/Lab Lectures

- 3 2 3 - 3 221 Math Foundation of Mathematics

____________________________________________________________________________________________________


17







Jazan University

Faculty of Science

Course summary: The student will recognize many of algebraic systems such as semi Group and Group and study a variety of examples for them. General Course Objectives: After finishing the course, the student is expected to be familiar with the following:

• Identify the basic concepts in abstract algebra. • Development of student logical and abstract thinking • Development of the student's ability to deal with abstract proofs • Training students to solve exercises and applications

Course Description: • Group: Definition of group and Abelian group substitution, Varies Examples, General properties of group,

cyclic groups, subgroups (Theories and examples) • Permutations:(Sn, o) Symmetric group of order n for any natural number n, cyclic permutation of length n • Transpositions: Even and odd permutations, Alternative group, An subgroup of Even permutations of

group Sn • Normal subgroups: Cosets, Factor Group G / N for any N ⊲G • Homomorphism of groups, symmetry, Basic homomorphism theorems, Isomorphism.

Course Assessments - First Exam 20% - Second Exam 20% - Quizzes and homework 10% - Final Exam50%


The Textbook: - A First Course in Abstract Algebra, J. B. Fraleigh, 6thEd. Addison - Wesley Publishing Co. London, 1998. Scientific References: - Introduction to Abstract Algebra, W. K. Nicholson, PWS-Kent publishing Co Boston, 1993. - Topics in Algebra, I. N. Herstein, John Wiley and Sons, 1975. - Elements of logic and Moderen algebra, M. V. Shat and M. L. Bhave, Published by S. Chond and Company Ltd HO: Ram Nagar, New Delhi - 110055 (1986).

Prerequisite Level year Contact Hours



221 Math 4 2 3 - 3 222 Math Abstract Algebra (1)

____________________________________________________________________________________________________


18







Jazan University

Faculty of Science

Course summary: Analytic Geometry course is one of the most important Mathematics courses. Through the algebraic equation of the second degree in two or three variables, you can plot the Geometric shape which representing the equation through which you can study the properties of this Geometric shape. General Course Objectives: After finishing the course, the student is expected to be familiar with the following:

• Identify the type of Conic Section throughout its equation. • Convert the general equation for the Conic Section to the standard formula. • Classifying the general equation of the second degree in two variables, three variables • To identify the linear surfaces. • Identify the different coordinate systems • Identify the Geometric methods to convert from one coordinate system to another.

Course Description: • Plane: Cartesian orthogonal coordinate system and polar coordinates system and relations of the

conversion from one to other, Conic Section that represented by general equation of the second degree in two variables (a pair of lines, Circle, a parabola, Ellipse, hyperbolic), Conic Section in polar coordinates

• Space: coordinate systems and relations of the conversion from one to the other, different type equations of the straight line, different type plane equations, regular surfaces, Quadratic surfaces (for example a ball).

Course Assessments - First Exam 20% - Second Exam. 20% - Quizzes and homework 10% - Final Exam. 50%

Methods of teaching the course: - Academic lectures - Scientific discussions. - Homework. - The use of mini-model of education. - Assign students to prepare scientific projects. ·

The Textbook: - Analytic Geometry, 6thEdition, Brooks Douglas R. Riddle, / Cole Publ. Co., (1995) Scientific References: - Calculus with analytic geometry,C.H. Edwards and D.E. Penney, 6thEdition, Prentice Hall, (2002). - Geometric Analysis planar and spatial. A. D. Abd-Alshafi Obada. Dr. Hassan Mustafa Alawade. Dar AlfekerAlarabe 1425


code Course name Credit hours Sec/Lab Lectures

- 3 2 3 - 3 241 Math Analytic Geometry

____________________________________________________________________________________________________


19







Jazan University

Faculty of Science

Course summary: Mathematical Statistics is an important course in mathematics, studying this course enables the student using Statistics to organize, describe and represent data graphically, and find the relationship between statistics and different fields of life such as industry, economy, agricultures and many others. General Course Objectives: After finishing the course, the student is expected to be familiar with the following:

• The use of statistics in solving different types of problems. • Application of statistical methods to describe and analyze the data. • Identify the methods of data collection, organizing and analysis. • Use some software in Mathematical Statistics. (SSPS, MATLAB – Excel)

Course Description: • Introduction to Statistics: Definition of Statistics science and its functions, data types, methods and data

collection techniques. • Methods of representing data: representing descriptive data in frequency table and graphically,

representing quantitative data in frequency table and graphically, frequency distributions, graphical representation of the frequencytables

• Measure of central tendency: arithmetic mean and its properties, mode, median, geometric and harmonic mean.

• Measure of dispersion: Range, quartiles, quartile variation, deciles, percentiles, mean deviation, variance, standard deviation, standard error, coefficient of variations, moments, measure of skewness, measure of kurtosis

• Correlation and Regression: definition of correlation, discovering the relation through scatter plots, coefficient of correlation properties, Spearman correlation coefficient, Pearson correlation coefficient, definition of regression, model of simple linear regression, estimating simple linear regression coefficients using Least Square Method



The Textbook: - Elementary Statistics: Picturing the World, Larson, R. C.& Farber, E. 3rdEdition, Prentice Hall. (2006). Scientific References: - Introduction to the Statistics. Mood, A. M. & al 3rdEdition, McGraw-Hill, (1974) - Principles of statistics and probability, Dr. Adnan Albarre, & others, Alnasher &Almatabe, 3rd Edition, 1997

Prerequisite level Year Contact Hours

Course Code


- 4 2 3 - 3 251 Stat Mathematical statistics

____________________________________________________________________________________________________


20







Jazan University

Faculty of Science

Course summary: The course gives an idea about types of Vector product (Scalar product, Cross product), forces analysis in two or three dimensions, and give the student information about moments, friction laws and the virtual work. General Course Objectives: After finishing the course, the student is expected to be familiar with the following:

• Show the importance of statics in branches of science and engineering. • Identify statics rules and its application in various branches of science and life. • Development of the student's ability to use statics in solving problems

Course Description: • Introduction in Vectors algebra graphically and algebraically, Types of Vector product (Scalar product,

Cross product). • Analysis of Structures to Centroids and Centers • Force and moment vectors, Moments of Inertia for Areas, Equivalent Systems of Forces, trilateral and

conditions of Equilibrium of Rigid Bodies • Centers of Gravity of objects of simple and complex shapes • Laws of Friction, Coefficient Friction between the body and Plan, Study of Coup and Sliding Friction and

Stability of equilibrium • Virtual work

Course Assessments - First Exam 20% - Second Exam 20% - Quizzes and homework 10% - Final Exam 50%


The Textbook: - Vector Mechanics for Engineers, Statics, Beer and Johnston, 8thed., McGraw-Hill, 2007 Scientific References: -Statics, A. Ramsay, London, 1972. - A text book on Statics, M. Ray, New Delhi (India), 1984. - Fundamental of statics, Adel Younis, Alrashed Library,Riyadh, 2005




- 3 2 3 - 3 261 Math Statics

____________________________________________________________________________________________________


21







Jazan University

Faculty of Science

Course summary: Calculus (3) is an important course in mathematics, it enables students to study other courses General Course Objectives: After finishing the course, the student is expected to be familiar with the following:

• Show the importance of differentiation and integration in branches of science and Geometry and recognize the relationship between them.

• View basis of differentiation and integration of functions with multiple variables and their applications, and vector calculation.

• Developing the student’s logical thinking and providing students with skills necessary to solve problems.

Course Description: • Multivariate functions : Definition of the function of several variables, limit function of several variables,

continuous function of several variables, partial derivation, exact differentiation, upper and lower limits, directional derivatives, Tangent planes.

• Multiple integrals : Double integrals, Geometric meaning of Double integration, properties of double integration, calculation of double integration, Areas and Volume using double integrals, Double integration in polar coordinates, Triple integrals, Triple integrals in the Cylindrical coordinates, and spherical, Calculate volumes using triple integrals.

• Linear integrals: definition, theorems Course Assessments:

- First Exam 20% - Second Exam 20% - Quizzes and homework 10% - Final Exam 50%


The Textbook: - Calculus, H. Anton, 8thEdition, John Wiley and Sons, (2005). Scientific References: - Calculus, J. Stewart, 5thEdition, Brooks/ Cle Publishing Company, (2003). - Calculus, R. E. Larson, R. P. Hostetler, and B. H. Edwards. 7thEdition, Houghton Mifflin Company, (2002). - Calculus, G. B. Thomas, Early Transcendentals, 11thEdition,Addition-Wesley, New York (2006) - Calculus, E. Swokowski, M. Olinic, and D. Pence, 6thEdition, PWS Publishing Company (1994)




212 Math 5 3 3 - 3 313 Math Calculus (3)

____________________________________________________________________________________________________


22







Jazan University

Faculty of Science

Course summary: Complex Analysis is an important course in mathematics, the student will be able to understand real and complex numbers and solve some issues that do not have solution in the field of real numbers, and will be able to apply rules of field of real numbers on field of complex numbers.


• Definition of complex numbers and operations on them • Apply rules of field of real numbers on field of complex numbers. • The differences between the real and complex numbers • To distinguish between analytical characteristics and function differentiability • Make simple conversion then plot regions. • To use residue theory in the calculation of complex integrals

Course Description: • System of Complex Numbers: Structure of Complex Numbers, Algebraic Properties, Polar and Exponential formula, Powers

and Roots, De Moivre's theorem, Geometric Representation. • Complex variable functions: Curves and Regions in the Complex plan, Single-valued functions and Multi-values, limits and

continuous • Derivation: Possibility of Derivation, Cauchy and Riemann Equations, Analytic Functions and Harmonic Functions, Simple

Functions (Exponential, Logarithmic Functions, Trigonometric and Hyperbolic), Derivation Rules with applications. • Simple Transfers: Shift Convert, Rotation Convert, Restricted Dimension Convert, linear Convert, Inverse Convert. • Integration of Complex Variable Functions: Liner Integration of Complex Functions, orbit, Simple and Multiple connected

region, Cauchy- Coursat theorem, Cauchy formula of integration and applications • Series: Series and sequences, converge, Taylor series, Laurent series, power series, Zeros, Singularity points. • Residue Theory: Residue Theory, the expense of the rest, Integration of trigonometric functions, Improper integrals



The Textbook: - Complex Variables and Applications, J.W. Brown and R.V. Churchill, 7thEdition McGraw-Hill Company, New york,2000

Scientific References: -Basic Complex Analysis, J. E. Marsden and M. J. Hoffman, 2ndEdition, W.H. Freeman and Company, New york, 1987 - Invitation to Complex Analysis, R .P. Boas.Dar Random, New York, 1987 - Complex Analysis, Dr. Ramadan Sabra. Dar Almanahej, 2007. - Principles of complex analysis. D. Mahmoud Kutkut, Dar Alshorooq 1990.


Course Code


313 Math 6 3 3 - 3 314 Math Complex Analysis

____________________________________________________________________________________________________


23







Jazan University

Faculty of Science

Course summary: Real analysis is an important course in mathematics studying this course enables the student to use Logical methods and mathematical theorems to solve mathematical problems and applications, and will be expert in using mathematical methods of proving. General Course Objectives: After finishing the course, the student is expected to be familiar with the following:

• Know algebraic and non-algebraic properties of R. • Using different mathematical proof methods to prove some basic theorems in analysis • Using theorems to evaluate limits of sequences and functions • Distinguish between different types of continuity of functions • Using theorems to find derivative of some functions • Know the geometric meaning of important mathematical concepts; limit, continuity and derivative.

Course Description: • Real Numbers: Algebraic Properties, Bernoulli’s inequality, Cauchy’s inequality, Triangle inequality, Topology of

Real Number • Sequences: convergence, algebraic operations, theorems, subsequences, Bolzano-Weierstrass theorem, Cauchy

criterion, Cauchy sequences • Limits : the precise definition, convergence criterion, divergence criteria, theorems, infinite limits, limits at infinity • Continuity : The precise definition of continuity, discontinuity criterion, continuity on intervals, combination of

continuous functions, composition of continuous functions, Bolzano's Theorem(Intermediate Value), uniform continuity, relation between continuity and uniform continuity, uniform continuity criteria, Lipschitz functions.

• Differentiation : Theorems of differentiation, rules of differentiation, chain rule, derivative of inverse function, Fermat’s theorem, Rolle's Theorem, Mean Value Theorem with its applications, Darboux's Theorem, L'Hopital's Rule, Taylor's Theorem.



The Textbook: - Introduction to Real Analysis, R.G. Bartle and D.G. Sherbert, 3rdEdition.John Wiley and Sons, New York, 2000

Scientific References: - Introduction to Real Analysis, M. Stoll, 2ndEdition, Addison-Wesley Longman, Boston, 2001 - Elementary Analysis: Theory of Calculus K. A. Ross, Springer-Verlag New York, 1980 - Principles of Real Analysis, D. Mahmoud Kutkut, Dar almarekh.1990


Course code

Course name Credit hours

Sec/Lab Lectures

Math313 6 3 3 - 3 Math315 Real Analysis(1)

____________________________________________________________________________________________________


24







Jazan University

Faculty of Science

Course summary: Numerical analysis is an important course in mathematics, studying this course enables the student to use Numerical methods to solve mathematical problems and applications, and using computers or software to solve numerical problems. General Course Objectives: After finishing the course, the student is expected to be familiar with the following:

• The use of numerical methods to solve algebraic equations • The use of different numerical methods to solve systems of linear equations • The use of interpolation methods in the approximation of functions • The use of numerical methods to find numerical derivatives and integrals of functions • The use of numerical methods in solving ordinary differential equations of first order • The use of some Software (Matlab - Mathematical) in numerical solutions

Course Description: • Errors (classification errors, approximation of numbers, theorems of errors) • Solving equations (bisection method, secant method, Newton's method, method of convergence approximations, and

calculate the errors in each method). • Numerical solution of systems of linear algebraic equations (Gauss method, Gauss _Jordan method, LU-

factorization method, Gauss _ Jacoby method, Gauss _ Seidel method, Method of Eigenvalues). • Numerical solution of systems of nonlinear algebraic equations (Newton's method, method of convergence

approximations). • Interpolation (function approximations): (Lagrange’s method, Newton’s divided difference, forward-difference and

backward-difference formulae), interpolation opposite. • Numerical derivatives and integrals (numerical derivatives, numerical methods in the calculation of integration,

trapezoidal rule, Simpson's method, method Quadratic Gaussian). • Numerical solution of differential equations of first order (Euler's method, Euler method (Hoen) improved,

Runge-Kutta method)



The Textbook: - Numerical Methods with Applications by Autar Kaw and Egwu Eric Kalu, Publisher: Lulu.com 2008 Scientific References: - Numerical Analysis, V. A. Patel, Harcourt Brace, College Publishers, (1994) - Numerical Mathematics and Computing, W. Cheney and D. Kincaid, Brooks / Cole Publishing Company, (2003).


code Course Name Credit


212 Math 6 3 3 - 3 316 Math Numerical Analysis 1

____________________________________________________________________________________________________


25







Jazan University

Faculty of Science


Code Course Name Credit


222 Math 5 3 3 - 3 323 Math Abstract Algebra (2)

Course summary: Abstract Algebra (2)is an extension of Abstract Algebra(1), which depends on group theory while Abstract algebra(2) depends on Ring theory(extension of group theory) and depends on fields and their extensions, this course focus on some types of rings and knowledge of Isomorphism of Ring.


• Understanding the Ring which is an extension of the Group • Understanding the subring which is an extension of the Subgroup, Ideal which is an extension of the Normal

subgroup, and Factor Ring which is an extension of the Factor Group. • Understanding the Homomorphism of rings as an extension of Homomorphism of groups • Understanding some types of Rings, Fields and their extensions

Course Description: • Ring: Definition and Theorems, Commutative Ring, Zero divisors, Ring and its group of units, Integral

domain, Field • Subrings and Ideals: Subrings, ideals and relationship between them, factor ring. • Homomorphism and Isomorphism of Ring: Definition, Theorem and examples, kernel and image of

Homomorphism, First_ Second and Third Isomorphism theorems and its applications. • Euclidean rings and Ring of polynomials: Euclidean Rings, Unique factorization theorem, Construct

Ring of polynomials - Roots of Ring of polynomials over a Field, Polynomial Ring on Field rational numbers.

• Field Extension: Simple algebraic extension and simple transcendental extension, Finite extension, Algebraic closure, Splitting Fields, Finite Field



The Textbook: - Topics in Algebra. Herstein, I.N. New York: John Wily and sons, 1977. - A First course in Abstract Algebra, J. B. Fraleigh, 7thEdition, Addison-Wesley Publishing Co. London, 2003

Scientific References: - A survey of modern Algebra. Maclane, S. and Birkhoff, G. New York: Macmillan, 1977. -Algebra, S. Lang, 3rdEdition, Addison-Wesley, 1993. - Basic Algebra, Paul, M. Cohn, Springer-Verlag N.y. 2002.

____________________________________________________________________________________________________


26







Jazan University

Faculty of Science

Course summary: Linear Algebra is an important course in Algebra and has wide applications not only in Mathematics but also in other branches. Knowing Vector space, subspace, Basis and Dimension and Linear transformations General Course Objectives: After finishing the course, the student is expected to be familiar with the following:

• Knowing the basic topics of Linear Algebra such as Matrices and Vectors • Knowing Spaces, Linear Transformations, Basis and Dimension • Promoting Students' skills for solving linear equations in n variables • Knowing methods of solving systems of linear equations and algebraic properties of Matrices and Determinants. • Knowing how to find Eigenvalues and Eigenvectors

Course Description: • Vector spaces over a field: Definition, Theorem and Examples of definition of vector space. • Linear combinations of vectors and spanning set. • Sub-spaces: Definition and Theorem, Examples of sub-space, subset generate vector space, sub-space generated by

subset from vector space, Sum and direct sum of two subspaces- Intersection of two subspaces. • Linear independence and correlation: Definition and examples, Basis and Dimension of vector space, Linear

dependence. • Coordinate matrices and Change of Basis • Inner product space: Definition and examples, Orthogonality, Angle and Distance between two vectors in Inner

product space • Linear Transformations: definition and examples, and theorems, Kernel and Range of Linear transformations,

Matrices of general Linear transformations • Eigenvalues, Eigenvectors and diagonalization.



The Textbook: -Elementary Linear Algebra, H. Anton, John Wiley (2001). - Elementary Linear Algebra, R. E. Larson and B. E. Edwards, Edition Heath 5th, D.H. and Company, (2004)

Scientific References: - Theory and problems of Linear Algebra, S. Lipschutz, Schaum's Outline Series (2000) - Linear Algebra and its Applications, David C. Lay, Addisson Wesley (2003).



323 Math 6 3 3 - 3 324 Math Linear Algebra

____________________________________________________________________________________________________


27







Jazan University

Faculty of Science

Course summary: Differential Equations is an important course in mathematics, studying this course enables the student to use different methods to solve differential equations then use them in some applications.


• Demonstrate concepts and understanding topics of the course. • Demonstrate the use of proper mathematical notation. • Use deductive methods and critical thinking to solve problems

Course Description: • Some definitions • First-order differential equations and their applications • Higher-order differential equations with constant coefficients .and their applications • Laplace transformations, and their applications



The Textbook: - A First Course in Differential Equations, 8thedition, Dennis G. Zill. Copyright 2005 Scientific References:

- Differential Equations, 3rded., P. Blanchard, R. Devaney and G. Hall, Thomson Brooks / Cole, Boston University, 2006.

- Ordinary Differential Equations (Chapman Hall / CRC Mathematics), D. K. Arrowsmith, C. M. Place, Chapman & Hall. (1982).




212 Math 5 3 3 - 3 331 Math Differential Equations 1

____________________________________________________________________________________________________


28







Jazan University

Faculty of Science

Course summary: Differential Equations is an important course in applied mathematics, studying this course enables the student to use different methods to solve differential equations with variable coefficients and solve some boundary value problems. General Course Objectives: After finishing the course, the student is expected to be familiar with the following:

• Demonstrate concepts and understanding in the topics of the course . • Demonstrate the use of proper mathematical notation • Use deductive methods and critical thinking to solve problems

Course Description: • higher order differential equations with variables coefficients • system of differential equations • use variation of parameters to solve differential equations • use the method of undetermined coefficients to solve differential equations • use power series to solve differential equations • boundary value problems • Stability of solution



The Textbook: - A First Course in Differential Equations, 8thedition, Dennis G. Zill. Copyright 2005 Scientific References:

- Differential Equations, 3rded., P. Blanchard, R. Devaney and G. Hall, Thomson Brooks / Cole, Boston University, 2006.

- Ordinary Differential Equations (Chapman Hall / CRC Mathematics), D. K. Arrowsmith, C. M. Place, Chapman & Hall. (1982).


code Course name Credit

hours Sec/Lab Lectures

331 Math 6 3 3 - 3 332 Math Differential Equations 2

____________________________________________________________________________________________________


29







Jazan University

Faculty of Science

Course summary: Probability Theory is an important course in mathematics, studying this course enables the student to use probability principles to solve random problems, and apply it in different fields (statistical applications, industry, economy). General Course Objectives: After finishing the course, the student is expected to be familiar with the following:

• Use probability in random experiment. • Use probability distributions in problems with an outcome that can’t be predicted. • Follow-up course of random operations in the future • Use some software (MATLAB - FORTRAN - Java) in probabilities.

Course Description: • Introduction to Sets: subset, union, intersection, differences, classes of sets, permutation, combinations

• Principles of probability : random experiment, sample space, events, methods of calculating probability, definition and axioms of probability, conditional probability, independent events, dependent events, methods of counting, overall probability theory, Conditional probability, Bayer's theorem, simply with replacement and without replacement.

• Random variable: definition of random variable, types of random variables, probability density function, probability mass function, cumulative distribution function, relation between distribution function and density function, probability distribution function for two variables and its properties, conditional probability functions, independent variables, mathematical expectation, variance, standard deviation,

• Probability Distributions , discrete probability distributions and its properties, binomial distribution, Poisson distribution, continuous probability distributions and properties, normal distribution, standard normal distribution.

• Sampling distribution : sampling distribution of means and its properties, central limit theorem, sampling distribution of sample variance and proportion, probability distribution of different means of samples, probability distribution of sample variance, probability distribution of ratio in sample, sampling distribution of samples Selected together, Tchebytchev theorem.



The Textbook: -First course in probability: Sheldon Ross Scientific References: - Probability, Random Variables and Stochastic Processes A. Papoulis & S.U. Pillai. 4thEdition, Tata McGraw-Hill. (2005). - Principles of statistics and probability, Dr. Adnan al-Barre, & others, Alnasher &Almatabea, 3rd Edition, 1997 - Introduction to statistics and probability by Dr. Fair valleys and others, Alrashed Library,2nd edition, 2005



251 Stat 5 3 3 - 3 352 Stat Probability Theory

____________________________________________________________________________________________________


30







Jazan University

Faculty of Science

Course summary: Dynamics enables the student to describe Phenomena and try to model them to mathematical expression identical to mathematical, physical and geometric rules. General Course Objectives:

• Ability to describe and model the movement of particle in a straight line and plane, to study the causes of motion, study equations of motion

• Identify the moments of inertia of some forms and study the motion of elastomeric particle in plane • Show the importance of dynamics in branches of science and engineering. • To accustom the student to think logically and to gain proper skills necessary to resolve issues.

Course Description: • Dynamics: the basic principles of the motion, motion in straight line, speed and acceleration, motion of

variable particle mass in a straight line, some applications. • Laws of motion: Newton’s laws, law of payment, Work, Energy, principle of conversation the momentum

and the energy, collision particles • The motion of particle in the plane: using Cartesian coordinates and polar, circular motion, the central

pathways, Design Space using three Cartesian coordinates and cylindrical • Motion of projectiles: in non-resistant, the path of the projectile • Moments of inertia of some simple objects • Study the rigid body motion in plan: (transitional motion and rotational motion).



The Textbook: - Vector Mechanics for Engineers: Dynamics, Beer & Johnston, 8th edition, McGraw-Hill, 2007 Scientific References:

- Classical Mechanics, Chow, John Wiley, 1995 - "Dynamics of particle and coherent body," Abu al-Nur Abdullah, Ismail Hassanein, Alrashed Library,

Riyadh, Saudi Arabia, 2006 - "General Mechanics (2) dynamics,"Fouad Zein Arab, Dar Alrateb Aljameaea, Lebanon.



212 Math 5 3 3 - 3 362 Math Dynamics

____________________________________________________________________________________________________


31







Jazan University

Faculty of Science

Course summary: Analytical Mechanics is an important course in mathematics, studying this course enables the student to study motion of particles and rigid bodies, chosen coordinates, cyclic coordinates, Canonical transformations, and study applications depending on Hamilton’s principle. General Course Objectives

• Show the importance of analytical mechanics in branches of science and engineering. • Ability to describe, study motion of particles and rigid bodies, chosen coordinates and cyclic coordinates,

Canonical transformations, and study applications depending on Hamilton’s principle • To accustom the student to think logically and to gain proper skills necessary to resolve issues

Course Description: • Generalized coordinates: conservative groups and non-conservative, and the constraints of power,

employment and the amount of motion in generalized coordinates - the principle of Drop (the amount of linear motion, angular momentum, total energy).

• Lagrange’s method and applications. • Hamilton’s method, Hamilton’s principle, principle equation/ Jacoby and using in solving the harmonic

oscillator, Variability of the principles and the principle of minimum action. • Canonical transformations generated functions, Poisson brackets and using moments in relationships.



The Textbook: - Lidstrm P.: Lecture Notes on Analytical Mechanics. Div. of Mechanics. Lund University.2007 Scientific References: -Goldstein, Poole & Sa o: Classical Mechanics. 3rded. Addison Wesley. 2002 - "Analytical Dynamics" HaimBaruh, Pub. Mc. Graw-Hill 1998. - "Analytical Mechanics" Grant R. Fowles. Pub, Brace Publisher Harcount 1995 - Analytical Mechanics, Ismail Hassanein, Abu al-Nur Abdullah, Alrashed Library, 2005


code Course name Credit Hours Sec/Lab Lectures

362 Math 6 3 3 - 3 363 Math Analytical Mechanics

____________________________________________________________________________________________________


32







Jazan University

Faculty of Science

Course summary: Real analysis is an important course in mathematics, the student will be able to use Logical methods and mathematical theorems to solve mathematical problems and applications, and will be expert in using mathematical methods of proving. General Course Objectives: After finishing the course, the student is expected to be familiar with the following:

• Evaluation of the area using Riemann sums. • Using the difference mathematical proof methods to prove some fundamental theorems in analysis • Using the fundamental theorems to evaluate Riemann integrals • Distinction between the uniform and pointwise convergence of sequence of functions • Using the convergent tests of numerical series and series of functions

Course Description: • Riemann Integral: Definition of Riemann integral, Riemann criterion for integrability, the integrability of

monotone and continuous functions, properties of Riemann integral, First-second Fundamental Theorem, Integration by Parts, first-second substitution theorems, Mean value theorem, Tailor theorem, Improper Integrals, Liner Integrals.

• Infinite Series: Convergence of infinite series, tests for Convergence, Cauchy criterion for series, absolute convergence, rearrangement of Series, tests for absolute convergence, alternating series, Abel’s test, Dirichlet's test.

• Sequences and Series of Functions: Pointwise and uniform convergences, Cauchy criterion, Weierstrass theorem, series of functions, differentiation and integration of series of functions, Uniqueness theorem, Tailor Series, Fourier Series.



The Textbook: - Introduction to Real Analysis, R.G. Bartle and D.G. Sherbert, 3rdEdition. John Wiley and Sons, New York,(2000) Scientific References: - Introduction to Real Analysis, M.Stoll 2ndEdition, Addison –Wesley Longman, Boston, (2001) - Elementary Analysis: Theory of Calculus, K.A. Ross Springer-Verlag NewYork, (1980) - Principles of complex analysis, D. Mahmoud Kutkut, House Sunrise 1990

Prerequisite level Year Contact Hours Course


315 Math 7 4 3 - 3 417 Math Real Analysis 2

____________________________________________________________________________________________________


33







Jazan University

Faculty of Science

Course summary: Functional Analysis is an important course in mathematics, studying this course enables the student to generalize mathematical concepts, and theorems to more generalized spaces. General Course Objectives: After finishing the course, the student is expected to be familiar with the following:

• Generalize mathematical concepts on more general Spaces. • Using concepts of metric spaces and normed spaces to study convergence and divergence of sequences • Know the linear operators and functions in different spaces. • Know definition of Hilbert spaces.

Course Description: • Metric Space: Metric Space, examples, Continuous functions and Convergence in metric space, Complete

Metric Space, topology Generated by Metric • Normed Space: Linear Space, Linear subspace, Normed Spaces, Relationship Between Metric and

Normed Spaces, Banach Space, Continuity and Convergence in Normed Spaces, Topology Generated By Normed.

• Operators: Linear Operators, Continuous Linear Operators, Linear Operators in Normed Spaces. • Functionals: Linear Functionals, Continuous Linear Functionals, Dual Space, Generalized Functions.



The Textbook: - Introductory Functional Analysis with Applications, E. Kreyszig, John Wiley and Sons, New York (1978 ). Scientific References: - A Course in Functional Analysis J.B. Conway, 2nd ed., Springer, Berlin,(1990). - A First Course in Functional Analysis, C. Goffman and G. Pedrick. Prentice-Hall, (1974) - Functional Analysis, E. B. V. Limaye, 2nded., New Age International, New Delhi,(1996). - Introduction to Functional Analysis, A. Taylor and Delay, Wiley, New York, (1980) - Principles of the theory of functions and mathematical analysis Dali, Translated by Dr.Ibrahem Mahmoud Shousha, Dar Al-Mir, 1989.



317 Math 8 4 2 - 2 418 Math Functional Analysis

____________________________________________________________________________________________________


34







Jazan University

Faculty of Science

Course summary: Numerical analysis is an important course in mathematics, studying this course enables the student use numerical methods to solve mathematical problems and different applications, and use computers and some software to solve numerical problems. General Course Objectives: After finishing the course, the student is expected to be familiar with the following:

• The use of numerical methods to solve ordinary differential equations. • The use of numerical methods in solving ordinary differential equations of higher order. • The use of numerical methods in solving Partial differential equations. • Introducing the Differential equations and numerical solutions. • The use of some Software (Matlab – Mathematica, and others) in solving ordinary and partial differential

equations Course Description:

• Numerical solution of systems of differential equations (numerical solution of systems of differential equations of first order, numerical solution of differential equations with higher-order, Reduction in rank translate to equations of first order, use the software in numerical solutions of differential equations).

• Numerical solution of partial differential equations (Fourier method to separable variables, Dalimber method of Changing variables, open manner, Crank-Nicholson method, numerical solution of partial differential equations (elliptic and hyperbolic and parabola), Methods of solve of partial differential equations of first and second order , the general situation (Fourier method and Dalimber method, use the software to find the solution).

• Systems of partial differential equations • Difference equations



The Textbook: - Numerical Methods with Applications by Autar Kaw and Egwu Eric Kalu, Publisher: Lulu.com 2008 Scientific References: - Numerical Analysis, Harcourt Brace, V. A. Patel College Publishers, (1994) - Numerical Methods for Ordinary Differential Systems, John Denholm Lambert, John Wiley & Sons, Chichester,(1991).




434 Math 8 3 3 - 3 419 Math Numerical Analysis 2

____________________________________________________________________________________________________


35







Jazan University

Faculty of Science

Course summary: Discrete Mathematics is one of mathematical branches that contains different problems of discrete variables not continuous variables such as algebra set, combination theory, logic algebra, Boolean algebra and forms theorem. Discrete mathematics has different applications in information theory, computer science and artificial intelligence. General Course Objectives: After finishing the course, the student is expected to be familiar with the following:

• Know the basics of discrete mathematics. • Understanding the Combination theorem and its applications. • Understanding the Boolean algebra and its application in designing the logic circuits. • Understanding and knowing the concepts and applications of graph theory.

Course Description: • Counting: Basics of counting, permutations, combinations, the binomial theorem. • Boolean algebra: Definition, properties, Boolean functions, logic gates, logic circuits • Graphs: Graphs and graph models, graph terminology and special types of graphs, connectivity, paths,

cycles, Hamiltonian graphs, Hamiltonian paths, Hamiltonian cycles, Euler graphs, Euler paths, shortest- path problems, planar graphs, graph coloring.

• Trees: Definitions, properties, spanning trees, minimum spanning trees, binary search trees, trees applications, Huffman coding, different algorithms



The Textbook: - Discrete mathematics and its applications, K.H. Rosen, McGraw-Hill.( 2000). Scientific References: - Discrete and combinatorial mathematics: an applied introduction, R.P. Grimaldi,(1998), Addison-Wesley. - Principles of Discrete Mathematics, D. Marof Abed Al Rahman Samhan, D. Ahmed Humaid Charar. Dar Khuraiji toAlnasher &Altaozea, Riyadh 1426.



221 Math 7 4 3 - 3 425 Math Discrete Mathematical

____________________________________________________________________________________________________


36







Jazan University

Faculty of Science

Course summary: Mathematical Methods is an important course in mathematics, studying this course enables the student to use Fourier series and its physics application and to derive function for its differential equations. General Course Objectives: After finishing the course, the student is expected to be familiar with the following:

• Show the importance of mathematical methods in different branches of science, and engineering. • Use method of Fourier series and integral transforms (Fourier and Laplace). • Understand its importance in basic physical applications. • Learn how to derive special functions (Gamma, Beta, Bissell, Legendre, Laguerre and Hermit) from

different physical equations. • Developing the student’s logical thinking and providing them with skills necessary to solve problems.

Course Description: • Fourier Series and Fourier Integration • Laplace transformation and applications • Special Functions (Gamma, Beta, Bissell, Legendre, Laguerre and Hermit functions )



The Textbook: - Special Functions for Scientists and Engineers, W. Bell, D. Van Nostrand Company,London Scientific References: - Advanced Mathematics for Engineers and Scientists. Murray R. Spiegel, McGraw Hill Book Company.




313 Math 7 4 3 - 3 433 Math Mathematical Methods

____________________________________________________________________________________________________


37







Jazan University

Faculty of Science

Course summary: Partial differential equations is an important course in mathematical applications of various scientific fields, the student will be able to solve partial differential equations of first and second order, and solve Boundary -value problems. General Course Objectives: After finishing the course, the student is expected to be familiar with the following:

• Where and how Partial Differential Equations are used in applications • Conclude fundamental ideas in Partial Differential Equations theory • Learn methods for solving Partial Differential Equations • Know some applications in physics and mathematic

Course Description: • Solve of first order linear Partial Differential Equations. • Solve of Second order linear Partial Differential Equations. • Boundary -value problems for linear second order Partial Differential Equations of hyperbolic type (wave

equation), parabolic type (heat equation), and elliptic type (Laplace equation)



The Textbook: - A First Course in Differential Equations, 8th edition. Dennis G. Zill. Copyright 2005, Scientific References: - Partial Differential Equations, 4thed., by Fritz John. Springer, 1991 - Partial differential equations. Evans, L.C. AMS, 1991. - Partial differential equations, methods and applications. Mcowen, R. Prentice-Hall, 1996




331 Math 7 4 3 - 3 434 Math Partial Differential Equations

____________________________________________________________________________________________________


38







Jazan University

Faculty of Science

Course summary: Knowing topological space, Subspace Topology and relative Topology, and knowing basis of topological space, Homeomorphism, Topological properties, Connected and Compact space General Course Objectives: After finishing the course, the student is expected to be familiar with the following:

• Generalize the concepts of Euclidean and metric spaces. • Develop student’s ability in conclusion and imagination • Deepen the concept of continuity. • Identify the topological properties using the concept of equivalence topology. • Understand the relationship between metric spaces and topological spaces • Study concepts of compactness and connectedness needed for the study of algebraic topology.

Course Description: • Topological space: Definition and Examples- The usual topology on the real line • Accumulation points (Limit points) and the derived set • Closed sets and Closure of set • Interior, Exterior and Boundary set. • Neighborhood’s and Neighborhood’s systems • Subspace Topology and relative Topology. • Bases and sub bases. • Continuity and Topological Equivalent • Open and Closed functions • Homeomorphism and Topological properties • Connected and Compact space



The Textbook: - A Introduction to General Topology, Paul E.long, Charles E Menil Publishing Company, (1971). Scientific References: - A Introduction to Topology, B. Mendelson, Dover Publications, Inc., New York, (1990). - General Topology, S. Lipschutz, Schaum's Outline Series, (1965). - Topology: A first Course , J. R. Munkres, Prentice-Hall, (1977). - Foundation of Topology , C. W. Patt y, PWS-Kent Publishing Co., (1993). - Introduction to General Topology, D. Ahmed Mohammed Zhran, Library AlkhbetaAlthqafeea, Bisha, 1420 - Foundations of General Topology, A.D.Ahmed Abdel MonsefAllam, Library Dar Alzaman for publication and distribution, Medina .1426. - General Topology, A. D. Ahmed Abdel-Kader Ramadan, , Dr.Taha Merse Aladoe, Alrashed Library, 2ndedition 1426/2005.


code Course name Credit

hours Sec/Lab Lectures

315 Math 7 3 3 - 3 442 Math Topology

____________________________________________________________________________________________________


39







Jazan University

Faculty of Science

Course summary: Differential Geometry is an important course in mathematics, which enables student to understand concept of curvature and torsion curve, concepts of normal torsion of surface, and Gaussian torsion of curves, calculate area of surface and classify its points.


• Know the curvature and the torsion of curves and how a regular curve can be completely determined by its curvature and torsion.

• Demonstrate the surface area using the coefficients of the 1st fundamental form. • Classifying the points of surfaces using the coefficients of the 2ndfundamental form • Understanding the normal and Gaussian torsion of curves • Understanding asymptotic lines and main lines of surface • Understanding the mean torsion of surface

Course Description: • Curves theory: Basic definitions, curvature and torsion of regular curves, Frenet-Serret apparatus,

Frenet–Serret theorem, the fundamental theorem of curves. • Surfaces theory: Basic definitions, the 1st fundamental form, the 2ndfundamental form, normal

curvature, Geodesic curvature, Gaussian and mean curvatures, asymptotic lines and lines of curvature. Course Assessments:



The Textbook: - A First Course Differential Geometry, International Press, Cambridge, MA, (1997) Scientific References: - Differentiable curves and surfaces, M. do carmo, Prentice Hall, New Jersey, (1976) - Modern differential Geometry of curves and surface with Mathematic, Gray, 2ndEdition, CRC Press,Boca Raton, FL, (1998) - Elements of differential geometry.Richard , S. Millman , George , D. Parker . hall. 1977. INC

Prerequisite Level year Contact Hours



331 Math 8 4 3 - 3 443 Math Differential Geometry

____________________________________________________________________________________________________


40







Jazan University

Faculty of Science

Course summary: Applied Statistics is an important course in mathematics, enables student to use statistics in solving statistical problems such as industry, economy, agriculture, planning and others.


• Using statistics for solving different problems • Apply methods of statistics for data analysis • Know a good statistics studies • Use some software(MATLAB -FORTRAN- Java) in Applied statistics.

Course Description: • Parametric estimation: point estimation, intervals estimation, maximum value of error in estimation, sample size estimation,

confidence intervals estimation for population mean in large samples size (small sample size), confidence intervals estimation for proportion of population, confidence intervals estimation for variance and standard deviation, confidence intervals estimation for deference of two populations means in large samples size (small sample size), confidence intervals estimation for deference between two mean in dependent populations, confidence intervals estimation for deference of two proportions, confidence intervals estimation for ratio of two normal populations variances

• Hypotheses testing: testing the population mean (large and small sample), testing the population proportion, testing the population variance or standard deviation, testing the difference between two means (large and small sample), testing the difference between two proportions, testing the ratio of two variances, testing the pair samples.

• Chi-square tests: chi-square test of goodness-of-fit, Chi-square tests of independence and homogeneity • Analysis of variances: one-way analysis of variances for fixed variables, complete random design analysis, two-way analysis

of variances for fixed variables, complete randomize block design, two-way analysis of variance, the model of the impact of two factors and several levels and interaction between them.

• Regression and correlation: statistical inference about regression factors, coefficient of association and coefficient of contingency, coefficient of determination, multiple linear regression, multiple and partial correlation, transformations in linear regression.

• Nonparametric Statistics: the sign test, Wilcoxon’s signed rank test, Mann- Whiteny test, Kruskal-Wallis test, Run test.



The Textbook: - Elementary Statistics a Step by Step Approach Bluman, A. G 6thEdition, McGraw-Hill. (2006) Scientific References: - Principles of statistics and probability, Dr. Adnan Berry & others, 3rdedition 1997. - Concepts Methods of Statistical Analysis, Mahmoud Hnde and Khalaf Salman, Alrashed Library, 3rdedition, 2007. - Contribute in Applied Statistics, Dr. Nader Shaban Alsawah, University House –Alexandria.




251 Stat 7 4 3 - 3 453 Stat Applied statistics

____________________________________________________________________________________________________


41







Jazan University

Faculty of Science

Course summary: Fluid Mechanics is an important course in mathematics which shows the importance of fluids in practical life, derive mathematical expressions that controls motion of fluid (liquid – gas), apply information studied in complex variable course on complex potential function (upstream, downstream, bisexual, vortex motion in two dimensions, applications), and use mathematical methods, ordinary and partial differential equations in solution of fluid mechanics problems.


• Show the importance of fluids in practical life, and derive mathematical formulas that govern the movement of fluid (liquid - gas).

• Accustom the student to think logically and gain proper skills necessary to solve problems Course Description:

• Definitions, describing method of fluids motion (Euler, Lagrange), Continuity equation, Euler equations for fluid motion of the ideal non-negotiable compressing, examples of integration of Euler equations

• Complex potential function (upstream, downstream, bisexual, vortex motion in two dimensions, Applications)

• Fluid motion equations of viscous non-negotiable compressing (Navier-Stokes equations) • Exact solutions to Navier-Stokes equations (Sereean Kuwait, Sereean Boazel) • Time-dependent motion • Fundamentals of fluid dynamics experimental (dimensional analysis, Bay theorem, applications) • Forced motion (equations of forced motion, coefficient of forced viscosity, Brandel formal)



The Textbook: - A Brief Introduction to Fluid Mechanics, 3rdEdition, Young, Wiley 2007

Scientific References: -Fundamental Mechanics of Fluids, I.G. Currie, 3rdEdition (Kindle Edition), 2007. -An Introduction to Fluid Dynamics, G.K. Batchelor, Oxford University Press, 2006 - Continuum mechanics, Ismail Hassanein and others, Alrashed Library in Riyadh, 2008


Course Code

Course Name Credit hours

Sec/Lab Lectures

434 Math 8 4 3 - 3 464 Math Fluid Mechanics

____________________________________________________________________________________________________


42







Jazan University

Faculty of Science

Course summary: Mathematical Modeling is an important course in mathematics, which enables the student to learn skills necessary to convert applications to mathematical problems, to know the best control systems and to use software in modeling


• Learn the basis of mathematical modeling. • Transform applications to mathematical problems. • Use mathematical programs and (MATLAB) in modeling and simulation. • Use optimal control systems

Course Description: • The areas of mathematical modeling (mathematical models and others models, the mathematical model,

building steps) • Data relationship models: (sources of error, control data, evaluation of mathematical models). • Principles of mathematical modeling linear and nonlinear (continuous and discontinuous) • Simulation and analytical solution • Systems modeling, dynamic programming, the use of software in modeling and simulation, general

applications in different areas, linear statistical models, Design models Course Assessments:



The Textbook: - A Course in Mathematical Modeling, by Douglas Mooney and Randall Swi , Reviewed by Jan E. Holly, 1999. Scientific References: - Discrete Event System Simulation, Jerry Banks and John S. Cason, Prenice – Hall Inc., 1990 - Linear Models, D. Anies Ismail Kengo, D. Abdullah Abdul Karim Sheikh, Adaret Alnasher Alalme& Altawzeea 2005.


Course Code

Course Name Credit Hours

Sec/Lab Lectures

332 Math 8 4 3 - 3 472 Math Mathematical Modeling

____________________________________________________________________________________________________


43







Jazan University

Faculty of Science

Course summary: Operation research an important course in mathematics which enable the student to use operation research in decision making and find the best solution in different fields such as industry, economy, agriculture and others.


• Build models of operations research • Apply algorithms such as simplex method to solve problems of operations research . • Use operations research in solving different types of problems such as issues of transport and customization • Use some software (MATLAB - Fortran) in operations research.

Course Description: • Introduction to operation research • Methods of decision-making: Circles theorem, Bert method and application • Graph method for solving linear programming problems and associated problems, graph method, associated

problems or binary, Solve associated problems by graph method. • Solving linear programming simplex method, Basics simplex method, Tabular simplex method, Analysis of post-

optimal solution, some of the problems of linear programming and methods to overcome them, solving associated problems

• Transport and assignment problems: transport problem, allocation or selection problems. • Integer numerical programming: Approximate method to solve integer programming are problems, additional

conditions to solve integer programming problem, integer programming models of integer method and Reduction branch.

• Linear programming and statistics: random programming, Use of linear programming in Statistics • Non-linear programming: Objective non-linear function that can be set convergent sequences, Con– Tucker

Conditions and Lagrange multiplications, quadratic programming, Reduce the time and means of production, estimate.



The Textbook: -Nonlinear Programming, 2nd Edition. Bartsekas, Dimitri. Belmont, Ma Athena Scientific Press. ISBN:1886529000 ( 1999).

Scientific References: - Operations Research, P.K. Gupta& D.S. Hira. S. Chand. (2008). - Operations Research and Statistics, D. Ali Mahmoud Ajour, Dar Alfeqar Aljamaee, 2007




324 Math 8 4 3 - 3 473 Math Operation research