Download خطة قسم الرياضيات - قسم الرياضيات والإحصاء

‫بسم هللا الرحمن الرحيم‬
Al Imam Muhammad Bin Saud
Islamic University
Faculty of Sciences
Department of Mathematics
Bachelor of Science
in
Applied Mathematics
‫الوولكة العربية السعودية‬
‫جاهعة اإلهام هحود بن سعود‬
‫اإلسالهية‬
‫كلية العلوم‬
‫قسن الرياضيات‬
KINGDOM OF SAUDI ARABIA
AL-IMAM MUHAMMAD BIN SAUD
ISLAMIC UNIVERSITY
FACULTY OF SCIENCES
DEPARTMENT OF MATHEMATICS
Calculus (1)
Course
Code
MAT
Course
Num.
101
Course Name
Credit
Hours
Lec
Lab
Tut
4
3
0
2
Calculus (1)
Prerequisites
Objectives:
-
To understand the concept of limits and continuity of a function.
To be able to find and interpret the derivatives of functions.
To understand the meaning of derivative in terms of a rate of change and local linear
approximation and to use derivatives to solve a variety of problems.
To understand the meaning of definite integral as a limit of Riemann sum.
To be able find the integral of elementary functions.
Syllabus:
-
-
-
-
Limits and Continuity: The Concept of Limit, Computation of Limits, Continuity and
its Consequences, The Method of Bisections, Limits Involving Infinity, Asymptotes,
Formal Definition of the Limit, Exploring the Definition of Limit Graphically.
Differentiation: Tangent Lines and Velocity, The Derivative, Computation of
Derivatives: The Power Rule, Higher Order Derivatives, The Product and Quotient Rules,
The Chain, Derivatives of Trigonometric Functions and their inverses, Derivatives of
Exponential and Logarithmic Functions, Hyperbolic functions and their inverses,
Derivatives of hyperbolic functions, Implicit Differentiation, The Mean Value Theorem,
Numerical Differentiation.
Applications of Differentiation: Linear approximation and Newton’s Method,
Indeterminate Forms and L’Hopital’s Rule, Extrema Values, Monotonic Functions and
the First Derivative Test, Concavity and the Second Derivative Test, Overview of Curve
Sketching, Optimization, Related Rates.
Integration: Anti-derivatives, Sums and Sigma Notation, Partitions and Reimann sums,
Area, The Definite Integral, The Fundamental Theorem of Calculus, Indefinite Integral
and Integration by Substitution, Area between curves.
References:
-
Calculus, Early Transcendental Functions, Robert Smith, Roland Minton, McGrawHill Science Engineering, 2007.
Calculus, O. Swokowski, et al, PWS Pub. Co.; 6th edition (1994).
Calculus Early Transcendentals, C. Henry Edwards, David E. Penney, Prentice Hall,
2008.
2
‫الوولكة العربية السعودية‬
‫جاهعة اإلهام هحود بن سعود‬
‫اإلسالهية‬
‫كلية العلوم‬
‫قسن الرياضيات‬
KINGDOM OF SAUDI ARABIA
AL-IMAM MUHAMMAD BIN SAUD
ISLAMIC UNIVERSITY
FACULTY OF SCIENCES
DEPARTMENT OF MATHEMATICS
General Physics (1)
Course
Code
Course
Num.
PHY
101
Course Name
Credit
Hours
Lec
Lab
Tut
4
4
2
0
General Physics (1)
Prerequisites
Objectives:
Students will develop an understanding of some of the fundamental laws of nature and their
mathematical representation. This will provide them with skills in interpreting natural
phenomena in terms of the motion and interaction of masses on macroscopic, microscopic
and molecular levels. They will extend their understanding of macroscopic phenomena to
include the effects of stationary and moving charges and the role they play in electromagnetic
and atomic and nuclear interactions.
Syllabus:
-
-
-
-
-
-
Vectors: Coordinate systems and frame of reference, vector and scalar quantities, some
properties of vectors, components of a vector and unit vectors.
Motion in one dimension: Displacement, velocity and acceleration, one dimensional
motion with constant acceleration, freely falling objects, kinematics equations derived
from calculus.
Motion in two dimensions: Displacement, velocity and acceleration vectors , two
dimensional motion with constant acceleration, projectile motion, uniform circular
motion, tangential and radial acceleration, relative velocity and relative acceleration.
Particle dynamics: the concept of force, Newton’s first law, Newton’s second law,
Newton’s third law, some applications of Newton’s law, Newton’s second law applied to
circular motion, non uniform circular motion.
Electric field: properties of electric charges, insulators and conductors, Coulomb's law,
electric field created by one charge and group of charges, electric field lines, motion of
charged particles in uniform electric field, the oscilloscope.
Electric potential: potential difference and electric potential, potential difference in a
uniform electric field, electric potential and potential energy due to point charges,
potential of a charged conductor.
Current and resistance: Electric current, resistance an Ohm’s law, resistance and
temperature, electrical energy and power.
Direct current circuits: electromotive force, resistors in series and in parallel,
kirchhoff’s rules, RC circuits, electrical instruments.
Magnetic fields: the magnetic field, magnetic force on a current-carrying conductor,
torque on a current loop in a uniform magnetic field, motion of a charged particle in a magnetic
field, the hall effect, the quantum hall effect.
References:
-
Physics for Scientists and Engineers (with modern physics) –by Raymond A. Serway,
and John W. Jewett – Brooks Cole, 2003.
Physics for Scientists and Engineers with modern physics, Randall D. Knight,
3
‫الوولكة العربية السعودية‬
‫جاهعة اإلهام هحود بن سعود‬
‫اإلسالهية‬
‫كلية العلوم‬
‫قسن الرياضيات‬
KINGDOM OF SAUDI ARABIA
AL-IMAM MUHAMMAD BIN SAUD
ISLAMIC UNIVERSITY
FACULTY OF SCIENCES
DEPARTMENT OF MATHEMATICS
General Chemistry
Course
Code
Course
Num.
CHE
101
Course Name
Credit
Hours
Lec
Lab
Tut
4
4
2
0
General Chemistry
Prerequisites
Objectives:
To familiarize the student with the basic principles and concepts of Inorganic Chemistry.
Syllabus:
-
-
-
-
-
-
-
-
Atoms, Molecules and Ions: The atomic theory, the structure of the atom, Atomic
number, Masse number and Isotopes, the periodic table, Molecules and ions, Chemical
formulas, Naming compounds
Masse Relationships in chemical reactions: Atomic mass, Avogadro’s number and
molar mass, Molecular mass, the mass spectrometer, Experimental determination of
empirical formulas, chemical reaction and chemical equations, Amounts of reaction and
reactants and products, Limiting reagents
Reaction in aqueous solutions: General proprieties of aqueous solutions, Precipitation
reactions, Acid-Base reactions, Oxidation-Reduction reactions; Concentration solutions,
Gravimetric Analysis, Acid Base Titrations, Redox Titrations.
Gases: Substance that exist as Gases, Pressure of a Gas; The Gas Laws, The ideal gas
equation, Gas Stoichiometry, Dalton’s Law of Partial Pressures; The kinetic molecular
theory of gases.
Intermolecular forces and liquids and solids: The kinetic molecular theory of liquids
and solids, Intermolecular forces, Proprieties of liquid, Phase changes, Phase Diagrams.
Physical proprieties of solutions: Types of solutions, a molecular view of the solutions
process, concentration units, the effect of the temperature on the solubility, the effect of
pressure on the solubility of gases, colloids
Chemical equilibrium: The concept of equilibrium and the equilibrium constant, writing
equilibrium constant expression, the relationship between chemical kinetics and chemical
equilibrium, what does the equilibrium constant tell us? Factor that affect chemical
equilibrium.
Chemical Kinetics: The rate of reaction, the rate Law, the relationship between reactant
concentration and time, Activation Energy and temperature dependence of rate constants,
reaction mechanisms, Catalysis.
Molecule bonding: Molecular geometry, dipole Moment, valance bond theory,
Hybridization of atomic orbitals, Molecular orbital theory, Molecular orbital
configurations,
References:
-
Chemistry, Raymond Chang, Williams College, Mc Graw Hill, Higher Education, 9 th
Edition.
Chemistry & Chemical Reactivity, by Kotz, John C. & Treichel, Paul, 5th edition
4
‫الوولكة العربية السعودية‬
‫جاهعة اإلهام هحود بن سعود‬
‫اإلسالهية‬
‫كلية العلوم‬
‫قسن الرياضيات‬
KINGDOM OF SAUDI ARABIA
AL-IMAM MUHAMMAD BIN SAUD
ISLAMIC UNIVERSITY
FACULTY OF SCIENCES
DEPARTMENT OF MATHEMATICS
Calculus (2)
Course
Code
MAT
Course
Num.
102
Course Name
Credit
Hours
Lec
Lab
Tut
4
3
0
2
Calculus (2)
Prerequisites
MAT 101
Objectives:
-
To learn different techniques of integration.
To understand the applications of definite integrals to physics and Engineering.
To develop the basics of the calculus of infinite series, and their applications.
To demonstrate ability to work with polar coordinates and parametric equations.
Syllabus:
-
-
-
Integration Techniques: Brief Review of Integration by Substitution, Integration by
Parts, Integration of Rational Functions Using Partial Fractions, Trigonometric Techniques
of Integration, Integrals involving logarithmic, exponential, and hyperbolic functions,
Improper Integrals, Numerical Integration. Applications of definite integrals.
Applications of Definite Integrals: Volumes By slicing, Volumes using Cylindrical
Shells, Arc Length and Surface Area, Application to physics and Engineering.
Infinite Series: Sequences of Real Numbers, Convergence and Divergence of Infinite
Sequences, Infinite Series, Remarkable Infinite Series (geometric series, p-series,
alternating series, telescoping series), Convergence Tests for Positive Series (ratio test,
root test, comparison and limit comparison test, integral test), Alternating Series,
Absolute and Conditional Convergence, Power Series, Differentiation ad Integration of
power series, Taylor and Maclaurin Series, Convergence of Taylor series, Applications of
Taylor and Maclaurin Series, Fourier Series, Periodic Functions, Convergence of Fourier
Series, Fourier Cosine and Sine Series.
Parametric Equations and Polar Coordinates: Plane Curves and Parametric Equations,
Calculus and Parametric Equations, Arc Length and Surface in Parametric Equations,
Polar Coordinates, Calculus and Polar Coordinates, Conic Sections, Study of Conic
Sections in Polar Coordinates.
References:
-
Calculus, Early Transcendental Functions, Robert Smith, Roland Minton, McGrawHill Science Engineering, 2007.
Calculus, O. Swokowski, et al, PWS Pub. Co.; 6th edition (1994).
Calculus Early Transcendentals, C. Henry Edwards, David E. Penney, Prentice Hall,
2008.
5
‫الوولكة العربية السعودية‬
‫جاهعة اإلهام هحود بن سعود‬
‫اإلسالهية‬
‫كلية العلوم‬
‫قسن الرياضيات‬
KINGDOM OF SAUDI ARABIA
AL-IMAM MUHAMMAD BIN SAUD
ISLAMIC UNIVERSITY
FACULTY OF SCIENCES
DEPARTMENT OF MATHEMATICS
Introduction to Probability & Statistics
Course
Code
Course
Num.
STA
111
Course Name
Credit
Hours
Lec
Lab
Tut
Introduction to Probability &
Statistics
3
3
0
1
Prerequisites
MAT 101
Objectives:
This course is designed to equip the students with a working knowledge of probability,
statistics. The major objective of the course is to help the students to develop an intuition and
an interest for random phenomena, and to introduce both theoretical issues and applications
that may be useful in real life. By the completion of the course, students will be familiar with
ideas of statistical modeling, data analysis and interpretation. They will have learned to use
one of the statistical package EXCEL.
Syllabus:
-
-
-
-
Descriptive Statistics: Variables and Data, Types of Variables, Graphs for Categorical
Data, Graphs for Quantitative Data, Relative Frequency Histograms, Describing a set of
Data with Numerical Measures, Measures of Center, Measure of Variability, On the
Practical Significance of the Standard Deviation, Bivariate Data, Graph for Qualitative
Variables. Using Technology: Creating, Listing and Describing Data in EXCEL.
Counting: Counting Principles, Factorial Notation, Binomial Coefficients, Permutations,
Combinations, Tree Diagrams.
Basic Probability: Sample Space and Events, Axioms of Probability, Finite Probability
Spaces, Infinite Sample Spaces.
Conditional Probability and Independence: Conditional Probability, Finite Stochastic
Processes and Tree Diagrams, Total Probability and Bayes’ Rule, Independent Events,
Independent Repeated Trials.
Random Variables: Random Variables, Probability Distributions of Finite Random
Variable, Expectation of a Finite Random Variable, Variance and Standard Deviation,
Functions of Random Variables, Discrete Random Variables in General, Continuous
Random Variables, Cumulative Distribution Function. Using Technology: Generating a
Random Sample in EXCEL.
Discrete and Continuous Univariate Distributions: Bernoulli Trials, Binomial
Distribution, Poisson Distribution, Normal Distribution, Evaluating Normal Probabilities,
Normal Approximation of the Binomial Distribution, Geometric Distribution,
Exponential Distribution. Using Technology: Binomial Probabilities, Normal
Probabilities, and Normal Probability Plots in EXCEL.
References:
-
Probability and Statistics in Engineering, William W. Hines, Douglas C. Montgomery,
Connie M. Borror, David M. Goldsman, John Wiley & Sons Inc, 2004.
Introduction to Probability and Statistics, William Mendenhall, Robert J. Beaver,
Barbara M. Beaver, Duxbury Press, 2006.
6
‫الوولكة العربية السعودية‬
‫جاهعة اإلهام هحود بن سعود‬
‫اإلسالهية‬
‫كلية العلوم‬
‫قسن الرياضيات‬
KINGDOM OF SAUDI ARABIA
AL-IMAM MUHAMMAD BIN SAUD
ISLAMIC UNIVERSITY
FACULTY OF SCIENCES
DEPARTMENT OF MATHEMATICS
Computer Programming (1)
Course
Code
CS
Course
Num.
140
Course Name
Credit
Hours
Lec
Lab
Tut
4
4
2
0
Computer Programming (1)
Prerequisites
Objectives:
-
Introduce the student to the fundamentals of object-oriented programming, with emphasis
on understanding functions, methods, variables, and control structures.
Introduce the student to the basic concepts of classes and objects, and how to design
object-oriented solutions for problems.
Introduce the student to various tools used in programming, including editors, compilers,
linkers, and loaders.
Syllabus:
-
Fundamental concepts of object-oriented programming.
Data types, control structures, functions, and arrays.
Algorithms and problem-solving.
An introduction to the concept of abstract data types and their implementation using
classes.
Analysis of problems using object-oriented concepts.
Program correctness and verification.
The mechanics of running, testing, and debugging.
References:
-
C++ HOW TO PROGRAM, 5th edition, Deitel & Deitel, Prentice Hall.
7
‫الوولكة العربية السعودية‬
‫جاهعة اإلهام هحود بن سعود‬
‫اإلسالهية‬
‫كلية العلوم‬
‫قسن الرياضيات‬
KINGDOM OF SAUDI ARABIA
AL-IMAM MUHAMMAD BIN SAUD
ISLAMIC UNIVERSITY
FACULTY OF SCIENCES
DEPARTMENT OF MATHEMATICS
Calculus (3)
Course
Code
MAT
Course
Num.
203
Course Name
Credit
Hours
Lec
Lab
Tut
4
3
0
2
Calculus (3)
Prerequisites
MAT 102
Objectives:
-
To be able to apply derivatives and integrals to problems of arc length, and curvature.
To be able to differentiate functions of two and three variables and to find the limits and
extrema for multivariable functions;
To be able to evaluate double and triple integrals in different systems of coordinates.
To be able to define vector fields; find the line and surface integrals; be familiar with
conservative fields and path independence, and use Green’s, divergence, and Stokes’s
theorems.
Syllabus:
-
-
-
Vectors and Geometry of Space: Vectors in Space, Dot Product, Cross Product, Lines
and Planes in Space, Cylindrical and Spherical Coordinates.
Vector-Valued Functions: Vector-Valued Functions of one variable, Calculus of Vector
Functions, Motion in Space, Curves and Parameterization, Tangent and Normal Vectors.
Functions of several variables and Partial Differentiation: Functions of Several
Variables, Limits and Continuity, Partial Derivatives, The Total Derivative, The Gradient
and Directional Derivatives, Tangent Plane, Chain Rule, Extrema, Taylor's Series and
Approximations for functions of two variables.
Multiple Integrals: Double Integrals in Cartesian Coordinates, Areas and Volumes,
Double Integrals in Polar Coordinates, Triple Integrals in Cartesian Coordinates, Triple
Integrals in Cylindrical and Spherical Coordinates.
Vector Calculus: Line and Surface Integrals, Curl and Divergence, Green’s Theorem,
Divergence Theorem, Stoke’s Theorem, Some Physical Application of Vector Calculus.
References:
-
Calculus, Early Transcendental Functions, Robert Smith, Roland Minton, McGrawHill Science Engineering, 2007.
Calculus, O. Swokowski, et al, PWS Pub. Co.; 6th edition (1994).
Calculus Early Transcendentals, C. Henry Edwards, David E. Penney, Prentice Hall,
2008.
Calculus, L. Hostetler & Edwards, Houghton Mifflin Publisher, 8th ( 2005).
Advanced Engineering Mathematics, E. Kreyszig, John Wiley & Sons , INC 8th ed
(1998).
8
‫الوولكة العربية السعودية‬
‫جاهعة اإلهام هحود بن سعود‬
‫اإلسالهية‬
‫كلية العلوم‬
‫قسن الرياضيات‬
KINGDOM OF SAUDI ARABIA
AL-IMAM MUHAMMAD BIN SAUD
ISLAMIC UNIVERSITY
FACULTY OF SCIENCES
DEPARTMENT OF MATHEMATICS
Elements of Sets & Structures
Course
Code
MAT
Course
Num.
220
Course Name
Credit
Hours
Lec
Lab
Tut
Elements of Sets & Structures
3
2
0
2
Prerequisites
MAT 101
Objectives:
-
To give students the rudiments of mathematical logic and set theory and introduce the
important concepts of relations and their types.
To let students be familiar to the formal definitions of function and binary operations and
study their elementary properties.
To expose students to some abstraction by presenting the group concept and studying
some of its elementary properties.
Syllabus:
-
-
-
Elementary logic and set theory: Simple and compound statements, Logical
connectives, Truth tables, Basic logic laws, Methods of proofs, Mathematical induction,
Operations on sets, Basic laws of set theory, Cartesian product of sets.
Relations and functions: Basic definitions on relations, Binary relations and their types,
Equivalence relation and set partition, Functions and their types, Bijective function and its
inverse.
Binary operations: Definitions and basic properties, Identity and inverse elements,
Semigroups and monoids.
Groups: Definitions and basic properties, Cayley tables, Subgroups, Group order, Order of an
element and cyclic groups, Modular groups and symmetric groups.
References:
-
Set Theory and Related Topics, K. Heal & K. Rickard, Cambridge University Press
(1997)
An Introduction to Mathematical Reasoning: Numbers, Sets and Functions, P.
Eccles, Academic Express, 1997.
Modern Abstract Algebra, F. Ayres, Schaum's Outline, McGraw-Hill (1965).
9
‫الوولكة العربية السعودية‬
‫جاهعة اإلهام هحود بن سعود‬
‫اإلسالهية‬
‫كلية العلوم‬
‫قسن الرياضيات‬
KINGDOM OF SAUDI ARABIA
AL-IMAM MUHAMMAD BIN SAUD
ISLAMIC UNIVERSITY
FACULTY OF SCIENCES
DEPARTMENT OF MATHEMATICS
Math Software
Course
Code
Course
Num.
MAT
251
Course Name
Credit
Hours
Lec
Lab
Tut
2
2
2
0
Math Software
Prerequisites
MAT 101
Objectives:
-
-
To provide an introduction to the use of some of the high-level mathematical
programming language such MATLAB, Maple and Mathematica, as a practical aid in
doing mathematics.
To provide the student with some basic skills in the use of this software without
attempting deep coverage.
In the following the phrase “math software “ refers to the specific math language used by the
instructor.
Syllabus:
-
-
-
-
-
Starting with MATLAB: Introduction to the software, Command window, help and
lookfor commands, arithmetic operations, Display Formats, Built-in functions, Variables
assignment, Command line editing…
Arrays: Creating arrays (vectors, matrices), linspace command, some major matrices,
operators, Matrix operations in MATLAB, Array addressing, Adding and deleting
elements, Strings…
Operators: Operator Precedence, Relational operations, Logical operations, all and any
commands, find command, sort command, max and min command…
2D and 3D graphs: Plot and ezplot command, fplot command, multigraphs plots, others
plot commands, histograms, formatting a plot, 3D line plot, Mesh and Surface plots, view
command…
Script files: Creating and saving a file, disp and fprintf commands, loading a file, search
path, defining functions, structure of a function file, inline function, feval command, local
and global variables…
Programming: If-else structure, for and while loops, Break and continue commands,
Switch-case statement…
Symbolic toolbox: Symbolic object and expressions, algebraic expression manipulation,
factorization, simplification, solving equations…
References:
-
MATLAB: An Introduction with Applications, 3rd Edition Amos Gilat, The Ohio
State Univ. 2008.
MATLAB Primer, K. Sigmon & T. Davis, Champan & Hall, 6th ed., 2002 .
Maple V: learning Guide, K. Heal & K. Rickard, Springer Verlag, 1996.
Mathematica by example, M. Abell & J. Braselton, Academic Express, 1997.
10
‫الوولكة العربية السعودية‬
‫جاهعة اإلهام هحود بن سعود‬
‫اإلسالهية‬
‫كلية العلوم‬
‫قسن الرياضيات‬
KINGDOM OF SAUDI ARABIA
AL-IMAM MUHAMMAD BIN SAUD
ISLAMIC UNIVERSITY
FACULTY OF SCIENCES
DEPARTMENT OF MATHEMATICS
General Physics (2)
Course
Code
PHY
Course
Num.
106
Course Name
Credit
Hours
Lec
Lab
Tut
4
4
2
0
General Physics (2)
Prerequisites
PHY 101
Objectives:
Students will develop an understanding of some of the fundamental laws of nature and their
mathematical representation.
Syllabus:
-
-
-
Sources of the Magnetic Field: the Biot-Savart’s law, the magnetic force between two
parallel conductors, ampere's law, the magnetic field of a solenoid, magnetic flux, Gauss's
law in magnetism, displacement current and the generalized Ampere's law.
Faraday's law: Faraday's law of induction, motional emf, Lenz's law, induced emfs and
electric fields, generators and motors, Eddy currents.
Inductance: self-inductance, RL circuits, energy in a magnetic field, mutual inductance,
oscillation in an LC circuit, the RLC circuit.
Image Formation: reflection, refraction, Dispersion and prisms, images formed by flat
mirrors, images formed by spherical mirrors, Images formed by refraction, thin lenses,
applications.
Interference and Diffraction of Light Waves: conditions for interference, Young’s double
–slit experiment, intensity distribution of the double-slit interference pattern, introduction
to diffraction patterns, phasor addition of waves, diffraction patterns from narrow slits.
References:
-
Physics for Scientists and Engineers (with modern physics) –by Raymond A. Serway,
and John W. Jewett – Brooks Cole – 6th Edition (July 21, 2003)
Randall D. Knight, physics for scientists and engineers with modern physics,
(December, 2003)
11
‫الوولكة العربية السعودية‬
‫جاهعة اإلهام هحود بن سعود‬
‫اإلسالهية‬
‫كلية العلوم‬
‫قسن الرياضيات‬
KINGDOM OF SAUDI ARABIA
AL-IMAM MUHAMMAD BIN SAUD
ISLAMIC UNIVERSITY
FACULTY OF SCIENCES
DEPARTMENT OF MATHEMATICS
Introduction to Number Theory
Course
Code
MAT
Course
Num.
222
Course Name
Credit
Hours
Lec
Lab
Tut
3
3
0
1
Introduction to Number
Theory
Prerequisites
MAT 220
Objectives:
-
To expose students to the fascinating subject of number theory.
To let students gain basic knowledge in number theory which is essential for subsequent
courses in mathematics and computer science.
To prepare student for abstract mathematics courses like “ Modern Algebra”.
Syllabus:
-
-
-
Basics: Classical and strong mathematics inductions, well-order principal, binomial
theorem.
Divisibility and factorizations: Divisibility properties, the division algorithm,
representation of a number relative to arbitrary base, the binary digit system,
Fundamental theorem of arithmetic, infinitude of prime numbers, greatest common
divisors and least common multiple, Euclidean algorithm and Bezout’s identity.
Congruences: Congruence and modular arithmetic, Diophantine linear equation, Chinese
Remainder Theorem and system of linear Diophantine equations. Wilson’s Theorem,
Little Fermat's Theorem, Euler phi function and Euler Theorem .
Applications: divisibility tests, round-robin tournaments, pseudo primes, pseudorandom
numbers, linear codes, Pythagorean triples and sum of two squares.
References:
-
Elementary Number Theory, K. Rosen, ddison Wesley; 5th ed. (2004).
An Introduction to Mathematical Reasoning : Numbers, Sets and Functions, P.
Eccles, Academic Express, (1997).
Elementary Theory of Numbers, W. Le Veque, Dover Publications (1990).
12
‫الوولكة العربية السعودية‬
‫جاهعة اإلهام هحود بن سعود‬
‫اإلسالهية‬
‫كلية العلوم‬
‫قسن الرياضيات‬
KINGDOM OF SAUDI ARABIA
AL-IMAM MUHAMMAD BIN SAUD
ISLAMIC UNIVERSITY
FACULTY OF SCIENCES
DEPARTMENT OF MATHEMATICS
Linear Algebra
Course
Code
Course
Num.
MAT
223
Course Name
Credit
Hours
Lec
Lab
Tut
4
3
0
2
Linear Algebra
Prerequisites
Objectives:
-
To introduce students to the subject of linear algebra, this is essential for subsequent
courses in mathematics and computer science.
To let students be familiar with basics of matrix theory.
To let students be familiar with basics of vector spaces and linear transformations.
To prepare students for more abstract math courses like “Modern Algebra”.
Syllabus:
-
-
-
-
Matrices and Gauss Elimination: Elementary row operations, Transpose of a matrix,
Inverse of a square matrix, Linear equation systems and Gauss eliminations,
Determinants and their properties, classical adjoint; Cramer’s rule.
Vectors in R2 and R3: Dot product, projections, cross product, mixed product.
Vector spaces: Basic definitions, subspaces, linear dependence and independence, bases
and dimensions, Rank of a Matrix, Inner product spaces and Gram-Schmidt
normalization, orthogonal matrices.
Linear transformations: Basic definitions, the matrix of a transform, Kernel and Range
of a linear transformation, Matrices of linear transformations, Coordinates and change of
basis, homomorphism and isomorphism .
Eigenvalues and Eigenvectors: Characteristic polynomial, diagonalization of matrices,
Applications involving Powers of matrices.
References:
-
Linear Algebra, Schaum's Outline, S. Lipschutz, M. Lipson, McGraw-Hill 3rd ed.
(2000).
Linear Algebra, S. Leduc, Cliffs Notes (1996).
Linear Algebra: A Modern Introduction, D. Poole, Brooks Cole; 1st ed. (2002).
13
‫الوولكة العربية السعودية‬
‫جاهعة اإلهام هحود بن سعود‬
‫اإلسالهية‬
‫كلية العلوم‬
‫قسن الرياضيات‬
KINGDOM OF SAUDI ARABIA
AL-IMAM MUHAMMAD BIN SAUD
ISLAMIC UNIVERSITY
FACULTY OF SCIENCES
DEPARTMENT OF MATHEMATICS
Introduction to Differential Equations
Course
Code
Course
Num.
MAT
231
Course Name
Credit
Hours
Lec
Lab
Tut
3
3
0
1
Introduction to Differential
Equations
Prerequisites
MAT 203
Objectives:
-
To be familiar with techniques for solving first order.
To be familiar with techniques for solving second order equations with constant
coefficients.
To study The differential operator of order n and its use in solving general linear
homogeneous differential equations with constants coefficients .
To apply the power series method in searching for a solution of the second order linear
differential equations with polynomial coefficients.
To learn some techniques of simplifying differential equations by reducing equation order
or exchanging variables.
To know how to solve some types nonlinear differential equations.
To be exposed to matrix calculus and use it in solving linear system of differential
equations..
Syllabus:
-
-
First order differential equations: separable equations, exact differential equations,
homogeneous differential equations, and solution of general first order linear equations.
Second order linear differential equations with constants coefficients: general
solution of the homogeneous equation, particular solution of the none-homogeneous
equation, the undetermined coefficients and variation of constants methods.
Solving linear system of differential equations.
The differential operator of order n and its properties: General linear homogeneous
differential equations with constants coefficients.
Power series solutions of second order linear differential equations with polynomial
coefficients. Reducing order of differential equations. Exchanging variables. Bernoulli
equations, Riccati equations.
References:
-
A first course in differential equations with applications, Dennis G. Zill, 5th ed, PWS
Kent Publishing Company (2000)
Differential Equations, F. Ayres, Schaum's Outline, McGraw-Hill (1964).
Ordinary Differential Equations, M. Tenenbaum and H. Pallard, Dover Publications
(1985).
14
‫الوولكة العربية السعودية‬
‫جاهعة اإلهام هحود بن سعود‬
‫اإلسالهية‬
‫كلية العلوم‬
‫قسن الرياضيات‬
KINGDOM OF SAUDI ARABIA
AL-IMAM MUHAMMAD BIN SAUD
ISLAMIC UNIVERSITY
FACULTY OF SCIENCES
DEPARTMENT OF MATHEMATICS
Mathematical Statistics
Course
Code
Course
Num.
STA
211
Course Name
Credit
Hours
Lec
Lab
Tut
Mathematical Statistics
4
3
0
2
Prerequisites
MAT 102, STA 111
Objectives:
-
To teach students some important scientific concepts of statistics.
To let students be familiar with distributions of random vectors.
To expose students to concepts of Expectation and moments.
To let students know limit theorems and some of their applications.
To teach students techniques of estimations.
To let students learn and use some tests of hypothesis.
Syllabus:
-
-
-
-
Basics: Moment generating functions and characteristic functions.
Some special distributions: beta, uniform, gamma, Student, Chi-square and Fisher
distributions. Geometric, hyper-geometric and multinomial distributions.
Discrete and continuous multivariate distributions: Random vectors; multivariate
density functions, conditional and marginal density functions. Independent random
variables and their sum. Multivariate normal distribution, mean and covariance.
Limits Theorems and inequalities: Convergence in law, in Probability and almost sure;
Weak and strong law of large numbers; central limit theorems. Chebyshev, Hölder and
Minkowski inequalities.
Parameter estimations: introduction, maximum likelihood estimators, interval estimates,
estimating the difference in means of two normal populations, approximate confidence
interval for the mean of a Bernoulli random variable.
Hypothesis testing: significance levels, tests concerning the mean of a normal
population, testing the equality of means of two normal populations, hypothesis tests concerning
the variance of a normal population.
References:
-
Probability and Statistics in Engineering, William W. Hines, Douglas C. Montgomery,
Connie M. Borror, David M. Goldsman, John Wiley & Sons Inc, 2004.
Introduction to Probability and Statistics, William Mendenhall, Robert J. Beaver,
Barbara M. Beaver, Duxbury Press, 2006.
Probability and Statistics for Engineering and the Sciences, Jay L. Devore, Duxbury
2004.
Introduction to Mathematical Statistics, R. Hogg, et al, Prentice Hall, 2004.
15
‫الوولكة العربية السعودية‬
‫جاهعة اإلهام هحود بن سعود‬
‫اإلسالهية‬
‫كلية العلوم‬
‫قسن الرياضيات‬
KINGDOM OF SAUDI ARABIA
AL-IMAM MUHAMMAD BIN SAUD
ISLAMIC UNIVERSITY
FACULTY OF SCIENCES
DEPARTMENT OF MATHEMATICS
Real Analysis
Course
Code
Course
Num.
MAT
311
Course Name
Credit
Hours
Lec
Lab
Tut
4
3
0
2
Real Analysis
Prerequisites
MAT 203
Objectives:
-
To give a careful and rigorous treatment of the main ideas of differential calculus which
was taught to students in Calculus I and Calculus II .
To let students gain experience in dealing with axiomatic thinking and concise proofs of
calculus.
To expose students to the rudiments of metric and topological spaces.
Syllabus:
-
-
Fundamentals: Elementary set theory, Countable and uncountable sets, The real
numbers, Sequence of real numbers.
Metric spaces: Definition, Open set, closed set, Neighborhood, Convergence and
divergence of sequences, Cauchy sequences, Completeness, Completion of metric spaces.
Continuity and derivative: Left and right limits, limits, continuity, and uniform
continuity. Discontinuity of first and second kind. Variation and fluctuation of a function.
Left and right derivatives. Derivatives of functions. Mean value theorem.
Riemann’s Integral: The Riemann sum and the Riemann integral. The Fundamental
Theorem. First and second mean value theorems. Zero sets and Riemann integrability.
The Riemann integral on unbounded set.
References:
-
Elementary Analysis, K. Ross, Springer Verlag 14th ed. (2003)
Introduction to Real Analysis, R Bartle, D. Sherbert, Wiley; 3rd ed. (1999).
16
‫الوولكة العربية السعودية‬
‫جاهعة اإلهام هحود بن سعود‬
‫اإلسالهية‬
‫كلية العلوم‬
‫قسن الرياضيات‬
KINGDOM OF SAUDI ARABIA
AL-IMAM MUHAMMAD BIN SAUD
ISLAMIC UNIVERSITY
FACULTY OF SCIENCES
DEPARTMENT OF MATHEMATICS
Numerical Analysis (1)
Course
Code
MAT
Course
Num.
333
Course Name
Credit
Hours
Lec
Lab
Tut
4
3
2
1
Numerical Analysis (1)
Prerequisites
MAT 231, MAT 223
Objectives:
This course provides an introduction of computational techniques for finding approximate
solutions to difficult mathematical problems. Theory and practice approaches are taught. The
error sources and the convergence of the algorithms will be estimated with respect to the
various techniques used. The course will involve the use of Matlab or C++ in Lab.
Syllabus:
-
-
Introduction to data representation: Numerical Errors; Floating Point Representation;
Round-off; Significant Digit; Error Propagation.
Root Finding: Bisection Method, Newton’s Method, Secant Method, Fixed Point
Iterations.
Interpolation and Approximation: Taylor polynomials, Approximation of order n,
Polynomial Error, Linear and Quadratic Interpolation, Lagrange Interpolation, Newton
Divided Difference Method, Error Evaluation, Spline Interpolation.
Numerical Integration and Differentiation: The Trapezoidal and Simpson Rules,
Gaussian Quadrature, Numerical Differentiation.
Numerical Solution of Linear Systems: Gauss Elimination, LU and Cholesky
Decompositions, Iterative Methods: Jacobi and Gauss-Siedel Methods, Error Analysis
Numerical solution of differential equations: Euler method, Runge-Kutta methods.
Error and convergence analysis.
References:
-
Elementary Numerical Analysis, 3rd Edition, Kendall Atkinson; Weimin Han; (2004).
An Introduction to Numerical methods and Analysis, James F. Epperson, Wiley;
(2002).
Numerical Analysis, R. Burden and J. Faires, 8th ed., Brooks/Cole, 2001.
17
‫الوولكة العربية السعودية‬
‫جاهعة اإلهام هحود بن سعود‬
‫اإلسالهية‬
‫كلية العلوم‬
‫قسن الرياضيات‬
KINGDOM OF SAUDI ARABIA
AL-IMAM MUHAMMAD BIN SAUD
ISLAMIC UNIVERSITY
FACULTY OF SCIENCES
DEPARTMENT OF MATHEMATICS
Mathematical Methods
Course
Code
Course
Num.
MAT
332
Course Name
Credit
Hours
Lec
Lab
Tut
4
3
0
2
Mathematical Methods
Prerequisites
MAT 231
Objectives:
-
To tech students some important applied mathematical tools.
To let students be familiar with the some special function.
To let students study Fourier series in more depth and concise way.
To let students be familiar with Laplace transforms and some of its applications for
solving ordinary differential equations.
Syllabus:
-
-
-
Series solutions of differential equations: Gamma and beta functions; Stirling’s
formula; series solution of differential equations, power series solution of differential
equations, Forbeniu's method for solving second order linear differential equations with
non-analytic; Euler-Cauchy equations, Bessel’s equations and Bessel’s functions.
Fourier Series: Complex form of Fourier series; the Fourier transform; Plancherel’s
theorem; orthogonal and orthonormal functions; the mean convergence of Fourier series
and Bessel’s inequality; closed and complete set of functions; the piecewise convergence
of Fourier series; Dirichlet kernel and piecewise smoothness; differentiation and
integration of Fourier series.
Laplace Transforms: Basic Definitions and properties; first shifting theorem; partial
fractions; differentiation and integration of Laplace transforms, Laplace transform of
some particular discontinuous functions, the unit step function; Dirac function, shifting on
the t- axes and second shifting theorem, inverse of Laplace transform, solving differential
equations, linear system of differential equations.
References:
- Advanced Engineering Mathematics, E. Kreyszig, John Wiley & Sons, INC 8th ed.
-
(1998).
Methods of Mathematical Physics, R. Courant & D. Hilbert, Wiley-Interscience; 1st ed
(1989)
Mathematics of Physics and Modern Engineering, I. Sokolnikoff & R. Redheffer,
McGraw-Hill College; 2nd ed. (1966).
18
‫الوولكة العربية السعودية‬
‫جاهعة اإلهام هحود بن سعود‬
‫اإلسالهية‬
‫كلية العلوم‬
‫قسن الرياضيات‬
KINGDOM OF SAUDI ARABIA
AL-IMAM MUHAMMAD BIN SAUD
ISLAMIC UNIVERSITY
FACULTY OF SCIENCES
DEPARTMENT OF MATHEMATICS
Introduction to Operations Research
Course
Code
Course
Num.
MAT
351
Course Name
Credit
Hours
Lec
Lab
Tut
3
3
0
1
Introduction to Operations
Research
Prerequisites
MAT 223
Objectives:
The core subject of this course is Linear Programming (LP)، basically an optimization
technique applicable to the solution of problems in which the objective function (expression
to be optimized) and constraints are linear. Such techniques find applications across a very
wide variety of subjects in engineering، economics، finance and manufacturing. The course
should be accompanied by Lab sessions in order to learn students a known software of linear
programming (e.g. TORA provided with Taha’s book).
Syllabus:
-
-
Introduction to Operations Research.
Introduction to Linear programming: Linear programming formulations; Graphical
Linear Programming Solution, Graphical Sensitivity analysis.
The Simplex Method: Standard Linear Programming; Determination of Basic Feasible
Solutions; The Simplex Algorithm.
Special Cases of the Simplex: Degeneracy, Alternative optimum, Unbounded solution,
Infeasibility.
Duality and Sensitivity Analysis: Formulation of the Dual Problem; Relationship
between Optimal Primal and Optimal Dual Solutions; Economic interpretation of Duality,
Dual Simplex and Sensitivity Analysis.
Special linear programming models: The transportation model; The assignment model,
Critical Path and PERT.
Introduction to Integer Linear Programming: Illustrative applications, Branch and
Bound algorithm, Application to the Traveling Salesman Problem.
References:
-
Introduction to Operations Research، by F. Hillier and G. Lieberman، 7th Edition،
McGraw Hill، (2001).
Operations Research: Applications and Algorithms by Wayne L. Winston,
Wadsworth, 3rd Edition (1997).
Operations Research: An Introduction by H. Taha، 8th Edition, Prentice Hall, 8th
Edition، (2006).
19
‫الوولكة العربية السعودية‬
‫جاهعة اإلهام هحود بن سعود‬
‫اإلسالهية‬
‫كلية العلوم‬
‫قسن الرياضيات‬
KINGDOM OF SAUDI ARABIA
AL-IMAM MUHAMMAD BIN SAUD
ISLAMIC UNIVERSITY
FACULTY OF SCIENCES
DEPARTMENT OF MATHEMATICS
Complex Variables
Course
Code
Course
Num.
MAT
312
Course Name
Credit
Hours
Lec
Lab
Tut
4
3
0
2
Complex Variables
Prerequisites
MAT 311
Objectives:
-
To let students learn the complex extensions of elementary functions.
To let students visualize the geometric meaning of complex functions.
To let students learn complex derivatives and the Cauchy-Riemann equations, and the
relationship between these concepts.
To let students learn complex sequences, series, and power series.
To let students learn complex integration, contour integrals, and Cauchy’s theorem
Syllabus:
-
-
-
-
-
Basics: Euler formula and exponential form of a complex number, basic topological
properties, functions of complex variable, elementary functions. Limits, continuity and
uniform continuity.
Continuity and differentiability: Limits , continuity and uniform continuity, derivative
of a complex function at a point, Cauchy -Riemann equations and differentiability
complex functions, derivatives of elementary functions, analytic function at a point,
singular points, analytic function and harmonic functions, L’Hopital's rule.
Complex integral: line integral and complex integral, complex form of Green’s theorem,
Cauchy's and Cauchy-Goursat theorems, complex indefinite integral. Cauchy's integral
formula, Argument, Rouche’s, Liouville's, and modulus theorems.
Complex sequences and series: Basic definitions, tests of series absolute convergence,
power series and uniform convergence, circle of convergence, differentiation and
integration of power series, Taylor's series and Laurent's series. type of singular points,
Picard’s theorem.
Residues: Residues and the residue theorem with applications.
Basic concepts of conformal mapping.
References:
- Complex Variables, M. Spiegel, Schaum's Outline, McGraw-Hill (1968).
- Complex Variables and applications, R. Churchill and others, McGraw-Hill 5th ed.
(1989).
- Complex Variables: Introduction and Applications, M. Ablowitz, et al, 2nd ed. (2003).
20
‫الوولكة العربية السعودية‬
‫جاهعة اإلهام هحود بن سعود‬
‫اإلسالهية‬
‫كلية العلوم‬
‫قسن الرياضيات‬
KINGDOM OF SAUDI ARABIA
AL-IMAM MUHAMMAD BIN SAUD
ISLAMIC UNIVERSITY
FACULTY OF SCIENCES
DEPARTMENT OF MATHEMATICS
Modern Algebra
Course
Code
Course
Num.
MAT
321
Course Name
Credit
Hours
Lec
Lab
Tut
4
3
0
2
Modern Algebra
Prerequisites
MAT 222, MATH 223
Objectives:
-
To provide the student with a firm foundation in the abstract structure of algebra.
To understand and practice the axiomatic methods of thinking.
To be familiar with basics of group theory.
To be familiar with rudiments of ring theory and integral domains.
Syllabus:
-
Group theory: Definition of a Group, Subgroups, Cyclic Groups, Permutation Groups,
Homomorphisms, Cosets Lagrange's theorem, Normal Subgroups, and Factor Groups
-
Structures of groups: Isomorphism Theorems, Conjugacy, Groups Acting on Sets, The
Sylow Theorems. Finite Abelian Groups. Solvable Groups, Simple Groups.
-
Rings: Basic Definitions. Ring Homomorphisms, Quotient Rings. Ideals. Fields.
Euclidean Domains. Principal Ideal Domains. Unique Factorization Domains.
-
Polynomial Rings: Definitions and Basic Properties. Polynomial Rings over Fields.
Irreducibility criteria.
References:
-
-
Abstract Algebra, D. Dummit, R. Foote, John Wiley, 3rd edition (2004)
Contemporary Abstract Algebra, J. Gallian, Houghton Mifflin Company; 5th Ed.
(2001).
A first course in Abstract Algebra, J. Fraleigh, Pearson Education, 1st Indian edition
(2203).
Abstract Algebra: An Introduction, T. Hungerford, Brooks Cole; 2nd ed. (1996).
21
‫الوولكة العربية السعودية‬
‫جاهعة اإلهام هحود بن سعود‬
‫اإلسالهية‬
‫كلية العلوم‬
‫قسن الرياضيات‬
KINGDOM OF SAUDI ARABIA
AL-IMAM MUHAMMAD BIN SAUD
ISLAMIC UNIVERSITY
FACULTY OF SCIENCES
DEPARTMENT OF MATHEMATICS
Combinatorics and Graphs
Course
Code
Course
Num.
MAT
353
Course Name
Credit
Hours
Lec
Lab
Tut
4
3
0
2
Combinatorics and Graphs
Prerequisites
MAT 223
Objectives:
This course is divided in two parts: Combinatorics and Graphs.
The objectives of the first part are to learn basics of counting, recursion and recurrence
relations.
The objective of the second part is to introduce students to graph theory, especially Euler and
Hamiltonian graphs, planar graphs, coloring graphs, shortest paths, isomorphisms of graphs,
spanning trees and network flow.
Syllabus:
Combinatorics:
- Principles of counting: Addition and multiplication principles; inclusion-exclusion
principle; Application of inclusion-exclusion; pigeonhole principle and applications,
generating functions, multiplication of generating functions.
- Recursion: Recurrence definitions. Recurrence relations; generalized binomial theorem.
- Linear recurrence equations: Homogeneous and non homogeneous linear recurrences
with constant coefficients; binary trees; random walks.
Graphs:
- Introduction to Graphs: Concepts and definitions, Isomorphisms of graphs, Subgraphs,
Matrices of graphs.
- Eulerian Graphs: characterization of Eulerian graphs, Chinese Postman problem;
- Hamiltonian Graphs: Necessary and sufficient conditions for Hamiltonian graphs,
Traveling Salesman problem;
- Planar graphs: Euler's Formula, Kuratowski's theorem.
- Graph colorings: Vertex colorings. Greedy algorithm.
- Shortest path: Shortest path problems, Optimality principle, BFS, DFS, Djkstra's
algorithm,
- Trees: Spanning trees, minimum spanning trees, Kruskal's algorithm, Prim's algorithm,
Greedy algorithm
- Networks flow: Definitions, flow augmenting paths, cut sets, maximum flow; FordFullkerson algorithm, Minimum cost capacited flow problem.
References:
-
Applied Combinatorics by Alan Tucker, Wiley; 5th Edition (2006).
Discrete Mathematics and Its Applications by K. Rosen, Mc Graw-Hill, 6th Edition
(2006).
Graph Theory by V. Balakrishnan, Schaum's Outline, McGraw-Hill; 1st Edition. (1997).
22
‫الوولكة العربية السعودية‬
‫جاهعة اإلهام هحود بن سعود‬
‫اإلسالهية‬
‫كلية العلوم‬
‫قسن الرياضيات‬
KINGDOM OF SAUDI ARABIA
AL-IMAM MUHAMMAD BIN SAUD
ISLAMIC UNIVERSITY
FACULTY OF SCIENCES
DEPARTMENT OF MATHEMATICS
Partial Differential Equations
Course
Code
MAT
Course
Num.
434
Course Name
Credit
Hours
Lec
Lab
Tut
Partial differential Equations
4
3
0
2
Prerequisites
MAT 332
Objectives:
The aim of this course is to introduce the students to the theory and applications of partial
differential equations (PDEs), and to explore various methods of solution. On successful
completion of this unit, students should be able to classify PDEs and solve them by using
appropriate methods.
Syllabus:
-
Introduction to PDEs: Definition of a PDE; degree, linearity; homogeneous and
inhomogeneous equations; First order partial differential equations; The method of
characteristics.
-
Scond-order equation: Classification as Parabolic, Hyperbolic, and Elliptic equations.
-
Classical PDEs of mathematical physics and Boundary-Value Problems: wave
equation, heat equation, Laplace equation. Boundary Conditions; Definition of a
Boundary-Value Problem. Dirichlet, Neumann, and Mixed BVP.
-
Analytic methods for solving PDEs: Separation of variables method; Method of
characteristics; Fourier series; Solution of PDEs by Fourier series; Fourier and Laplace
transform; Solving PDEs using Fourier and Laplace transform s.
References:
-
Partial Differential Equations of Mathematical Physics R.B. Guenther & J.W. Lee.
Prentice Hall/Dover publication
Partial Differential Equations Methods and Applications, R. McOwen, Prentice
Hall/Pearson Education.
23
‫الوولكة العربية السعودية‬
‫جاهعة اإلهام هحود بن سعود‬
‫اإلسالهية‬
‫كلية العلوم‬
‫قسن الرياضيات‬
KINGDOM OF SAUDI ARABIA
AL-IMAM MUHAMMAD BIN SAUD
ISLAMIC UNIVERSITY
FACULTY OF SCIENCES
DEPARTMENT OF MATHEMATICS
Introd. to Cryptography and Coding
Course
Code
MAT
Course
Num.
461
Course Name
Credit
Hours
Lec
Lab
Tut
4
3
0
2
Introd. to Cryptography and
Coding
Prerequisites
MAT 321
Objectives :
This course is divided in two parts: Cryptography and Coding Theory.
The objective of the first part is to learn students basics of Cryptography through classical
ciphers, cryptanalysis and some applications.
The objective of the second part is to introduce students to elementary coding theory.
Syllabus:
Cryptography:
-
Classical Ciphers: Shift ciphers ،affine ciphers and substitution ciphers. Introduction to
stream ciphers ،including linear recursive ciphers.
-
Introduction to cryptanalysis: the four levels of attack: known ciphertext, known
plaintext, chosen plaintext and chosen ciphertext. Exponential ciphers and key
distribution. Public-key cryptosystems: RSA, ElGamal and Massey-Omura. Signature
schemes with applications.
Coding Theory:
-
Introduction to codes: Error-detection ،error correction and information rate. Linear
codes, Perfect codes. Cyclic codes.
References:
-
Introduction to Modern Cryptography by J. Katz and Y. Lindell, Chapman and
Hall/CRC, 1st Edition(2007)
Elementary Number Theory by K. Rosen ،Addison Wesley; 5th Edition (2004).
A First Course in Coding Theory، by R. Hill, Oxford University Press (1997).
Coding Theory: A First Course by San Ling and Chaoping Xing, Cambridge University
Press (2004).
24
‫الوولكة العربية السعودية‬
‫جاهعة اإلهام هحود بن سعود‬
‫اإلسالهية‬
‫كلية العلوم‬
‫قسن الرياضيات‬
KINGDOM OF SAUDI ARABIA
AL-IMAM MUHAMMAD BIN SAUD
ISLAMIC UNIVERSITY
FACULTY OF SCIENCES
DEPARTMENT OF MATHEMATICS
Numerical Analysis (2)
Course
Code
MAT
Course
Num.
433
Course Name
Credit
Hours
Lec
Lab
Tut
4
3
1
1
Numerical Analysis (2)
Prerequisites
MAT 333, MAT 434
Objectives:
- To study basic finite difference methods for partial differential equations.
- To understand the concepts of consistency, stability, and convergence.
- To learn to solve partial differential equations on the computer.
- To introduce finite element method.
The course will involve the use of Matlab or C++ in Lab.
Syllabus:
-
Advanced Numerical Linear Algebra: Least Squares Method, Matrix Eigenvalue
Problems, Power Method, QR Factorisation.
Finite difference techniques: difference equation replacement; implicit and explicit
finite difference method.
Boundary Value Problems for ODEs: Multistep Methods, Finite Difference Methods
for Systems of Differential Equations.
Finite Difference Method for PDEs: Numerical Solution of Elliptic PDEs, Numerical
Solution of Parabolic PDEs, Numerical Solution of Hyperbolic PDEs, Finite Difference
Method for Boundary Value Problems.
Introduction to Finite Element Method: application to heat and Laplace equations.
References:
-
Elementary Numerical Analysis, 3rd Edition, Kendall Atkinson; Weimin Han; (2004).
Numerical Solution of Partial Differential Equations: An Introduction, K. W. Morton
& D. F. Mayers: Cambridge University Press.
An Introduction to Numerical methods and Analysis, James F. Epperson, Wiley;
(2002).
Numerical Analysis, R. Burden and J. Faires, 8th ed., Brooks/Cole, 2001.
25
‫الوولكة العربية السعودية‬
‫جاهعة اإلهام هحود بن سعود‬
‫اإلسالهية‬
‫كلية العلوم‬
‫قسن الرياضيات‬
KINGDOM OF SAUDI ARABIA
AL-IMAM MUHAMMAD BIN SAUD
ISLAMIC UNIVERSITY
FACULTY OF SCIENCES
DEPARTMENT OF MATHEMATICS
Modeling and Simulations
Course
Code
Course
Num.
MAT
463
Course Name
Credit
Hours
Lec
Lab
Tut
4
3
0
2
Modeling and Simulations
Prerequisites
Mat 333 and Mat 334
Objectives:
This course provides an introduction to system modeling using both computer simulation and
mathematical techniques. Emphasis will be on continuous and discrete-events simulation
model development methodologies and implementation techniques.
Syllabus:
Introduction to Mathematical Modeling Process: Concept; Objectives; Methods and tools
Mathematics is the natural modeling language; Definition of mathematical models.
Modeling Continuous Systems: Modeling with Differential Equations: Population dynamic;
Electrical Circuits; Mechanical Systems; Biological models (Lotka-Volterra systems,
Predator-Prey systems). Modeling with Partial Differential Equations: Linear Temperature
Diffusion; One-dimensional Hydrodynamic model. Case Studies:
Heat diffusion, Wave
vibration, Laplace Equation.
Modeling Discrete Systems: Modeling with difference equations; Modeling with data;
Discrete Velocity Models; Continuous Vs. Discrete Models
Simulation: Block-Digrams; State-Space Model; Transfer Functions, State-space Vs. transfer
function. Stability and pole locations; Introduction to Matlab\Simulink (Starting Simulink,
Basic Elements, Building a System , Running Simulations); Simulation of some models
(case study models) and Analysis of Simulation results
References:
-
Kai Veltn, Mathematical Modeling and Simulation: Introduction for Scientists
and Engineers, Wiley 2009.
Steven T. Karris: Introduction to Simulink® with Engineering Applications,
Orchard Publications (2006).
26