QP010X/MXXXA

Al-Zaytoonah University of Jordan

Faculty of Science & IT

Page Issue Date Version Document Number

1/311-11-20091.1QF01/C4107AE

Course Brief Description Procedures of the Course Plan & Educational Resources Committee

Al-Zaytoonah University of Jordan

Faculty of Science & IT

Page Issue Date Version Document Number

6/711-11-20091.1QF01/C4107AE

Course Brief Description Procedures of the Course Plan & Educational Resources Committee

Department Math & Natural Sciences Computer Science Computer Information Systems Software Engineering

Computer

Networks Multimedia Systems

Course Plan No. Approval Date Number of Courses

Course No. Course Name

Credit Hours Prerequisite

0101101 1 (Calculus 1)3

( ).Functions, Limits, Continuity, Derivatives, Implicit Differentiation, Applications of Derivatives, Anti derivatives, Definite And Indefinite Integral, Applications Of Integration (Area Under A Curve, Area Between Two Curves, Volumes).

0101102 2 (Calculus 2)3010110

( ) .Inverse functions, Exponential, Logarithmic, Trigonometric functions and Inverse Trigonometric Hyperbolic and Inverse Hyperbolic Functions (Their Derivatives And Integrations), Methods Of Integration, Improper Integrals, Applications Of Integrals (Area, Volume, Arc Length, Surface Area), Polar Equations, Polar Coordinates And Its Applications.

0101133 (Statistics and Probability)3

.Introduction to Statistics, populations and samples, Frequency distributions, Measures of central tendency, Measures of dispersion, Measures of skeweness and kurtosis, correlation and regression, principles of probability, Rules of probability, Bayes, Theorem. The Random, Variables, discrete and continuous distributions expectation.

0101111 (Set Theory)3

( ) .

Logic, (Introduction to logical symbols, The common sentential connectives), Sets, Sets Operations, Family of Sets, Cartesian Product on Sets, Relations, Equivalence Relations, Order Relations, Functions, Operations on Functions, Inverse Functions, Binary Operations on Sets, Finite And Infinite Sets, Countable Sets.

0101161 (Euclidean Geometry)3

.The Axiomatic Method And Euclidean Postulates, The Postulates Of Connection, Distance, Angles And Their Measures, Congruence And Parallel Postulates, Similarity, Area, The Circle, Lines And Planes in Space, Solids.

0101201 3 ( Calculus 3 )30101102

: ( ) ( ) .Introduction to sequence And Series, Functions Of Several Variables, (Limits, Continuity), Partial Differentiation, Extreme Values, Lagrange Multipliers, Multiple Integrals (Double, Surface And Triple Integrals), Jacobeans, (polar, Cylindrical And Spherical) Coordinates, Center Of Mass, Moment Of Inertia.

0101211 1 (Real Analysis 1)30101102 0101111

R - R .

Properties of real numbers, Inequalities, completeness property of R, Applications of suprema and infirna, Sequences of real numbers, subsequences, Bolzano-weierstrass theorem, continuous functions, Uniform continuity, Lipchitz functions, Open and closed sets, Cantor sets, Compact sets, Heine-Borel theorem.

0101230 (Probability Theory)301011020101133

. .

Introduction, Sample Spaces, Events, The Probability Of An Event, Some Rule Of Probability, Conditional Probability, Independent Events, Baye's Theorem, Probability Distribution, Continuous Random Variable, Probability Denisty Function, Multivariate Distributions, Marginal Distributions, Conditional Distributions, The Expected Value Of A Random Variable, Moment, Moment Generating Functions, The Discrete Uniform Distribution, The Binomial, Poisson, Normal Distributions. Distribution of functions of random variables. Sampling Distributions.

0101240 1 (Linear Algebra 1)30101101

- .Matrices And Operation On Matrices, Determinants, Matrix Form Of Linear Systems, Euclidean Vector Space, Subspaces, Dimension, Rank, Linear Transformations From To , Eigenvalues And Eigenvectors, Characteristic Polynomial, Cayley-Hamilton Theory, Eigenvalues And Eigenvectors Of Hermitian And unitary Matrices.

0101241 2 (Linear Algebra 2)30101240

.

General Vector Space, Row Space, Column Space And Null Space, Rank And Nullity, Change of Basis, Eigenvalues and Eigenvectors, Similar Matrices and Diagonalization, Orthogonal Diagonalization, The Diagonalization of Symmetric Matrices, General Linear Transformations Kernel And Range, Inverse Linear Transformations, Matrices of General Linear Transformations. Isomorphisms, Bilinear Forms, Symmetric Bilinear Forms, Quadratic Forms, Diagonalization Of Quadratic Forms, Classification Of Quadratic Forms, Curves And Surfaces.

0101243 (Number Theory)30101111

.Properties Of Integer Numbers, Division Algorithm, Greatest Common Divisor, Least Common Multiple, Prime Numbers, Fundamental Theorem Of Arithmetic, Congruence, Linear Congruence, Chineese Remainder Theorem, Fermat's Theorem, Welson's Theorem, Diophentine Equations.

0101271 1 (Ordinary Differential Equations 1)30101102

( ) ( ) - .Classification Of Differential Equations, Differential Equation For Family Of Curves, First Order Differential Equations (Separable, Homogenous, Exact, Integrating Factors, Linear, Bernoulli, And Riccati), Second Order Linear Differential Equations (Homogenous, Reduction Of Order, Non-Homogeneous, Method Of Undetermined Coefficients, Variation Of Parameters), Higher Order Linear Equations, Wronskian, Differential Equations With Variable Coefficients, Cauchy-Euler Equation, Series Solutions Of Second Order Linear Equations.

0101301 (Advanced Calculus)30101201

.

Parametric equations of lines, vector equation of lines, planes in 3-space, calculus of vector-valued functions, Arc length, nit tangent, Normal and Binormal vectors, Curvature, Directional derivative, Gradient, Tangent Planes, Divergence and curl, line integrals, Independence of path, conservative vector field, Green's theorem, Triple integrals, surface integrals, Divergence theorem, Stokes' theorem.

0101310 1 (Complex Analysis 1)30101211

- - - .

Complex Numbers, Definitions, Algebraic Properties, Cartesian Coordinates, The Triangle Inequality, Polar Coordinates, Power And Roots, Functions Of A Complex Variable, Limits, Continuity, Derivatives, The Cauchy-Rieman Equations, The Cauchy Rieman Equations In Polar Form, Analytic Functions, Harmonic Functions, The Exponential Functions, Trigonometric Functions, Properties Of Trigonometric Functions, Hyperbolic Functions, Properties, Branches Of Logz, Complex Exponent, Inverse Trigonometric Functions, Contours, Line Integrals, The Cauchy-Goursat Theorem.

0101312 2 (Real Analysis 2)30101211

() - .

Derivatives, Dervative rules, chain rule, Local extrema, Monotonic functions, Rolle's theorem, Mean-value theorem, Generalized mean-value theorem, Intermediate value (Darboux theorem), Taylor's theorem, Functions of bounded variation, Total variation, Total variation, as a function, Riemann integral, Riemann-Stiettjes integrals, Integration by parts, change of variables, step functions, Euler's summation formula, upper and lower sums, Riemann's condition, Existence of Riemann stieltjes integral, pointwise and uniform convergence of sequences and series of functions, power series.

0101321 1 (Numerical Analysis 1)30101101

( - ) ( : : ) ( ) .

Introduction to Representation Of Numbers, Errors and their Sources, Numerical Solution Of Nonlinear Equations (Bisection, Regular Fulsi, Fixed Point, Newton-Rephson, Secant), Nonlinear System Of Equations, Numerical Solution Of System Of Linear Equation (Direct Methods, Cramer's Method, Inverse Method, Gauss, Gauss Elimination With P.P., Iterative Methods (Jacobi, Gauss-Seidel, Successive Relaxation), Interpolation (LaGrange, General Newton Formula, Newton Forward Formula, Newton Backward Formula, Error Formulas.

0101362 1 (Topology 1)30101211

(CLOSURE) Hausdorff .Topological Spaces, Open And Closed Sets, Interior Points, Boundary Points, Limit Points, Closure Sets, Subspace Topology, Bases And Subbases, Continuous Functions, Open And Closed Functions, Homeomorphisms, Hausdroff Space, Metric Spaces, Compact Spaces.

0101371 (Partial Differential Equations)30101271

.Basic Concepts, Linear Partial Differential Equations of the First Order, Non Linear Partial Differential Equation of the First Order, Second Order Partial Differential Equations, Classification Of Partial Differential Equations, Heat, Wave And Laplace Equations, Solutions Of Initial Value Problems In Partial Differential Equations.

0101431 (Mathematical Statistics)30101230

( ) T F ( ) : .

The Uniform Distribution, The Gamma; Exponential And Chi-Square Distribution, The Beta Distribution, The Normal Approximation To The Binomial Distribution, Distribution Function Technique, Transformation Technique (One Variable, Two Variables), Moment-Generating Function Technique, The Distribution Of The Mean: Finite Populations, The T-Distribution, The F-Distribution, Point Estimators, Unbiased Estimate, Consistent Estimators, Sufficient Estimators, The Method Of Moments, The Method Of Maximum Likelihood, Confidence Intervals For: Means, Difference Between Means, Proportions, Difference Between Proportions, Variance, Ratio Between Variances, Testing Statistical Hypothesis, Tests Concerning Means; Differences Between Means, Variances, Proportions Test power and test errors.

0101441 1 (Abstract Algebra 1)30101243

.

Groups And Subgroups, Cyclic Groups, Permutation Groups, Isomorphism's Of Groups, Direct Product Of Groups, Cosets And LaGrange's Theorem, Normal Subgroups And Factor Groups, Homomorphisms Of Groups, The First Isomorphism Theorem.

0101442 2 (Abstract Algebra 2)30101441

.Rings, subrings, integraldomain, factor ring and ideals. Ring Homomorphisms, Polynomial Rings, Factorization Of Polynomial, Reducibility And Irreducibility Tests, Divisibility In Integral Domain, Principal Ideal Domains And Unique Factorization Domains, Algebra Extension Of Fields.

0101472 (Applied Mathematics)30101371

( ) ( ) ( ) ( ).

Ordinary Differential Equations and their solution methods (Review) Boundary Value Problems (Sturm- Liouville Problem, Eigen function expansion, Fredholm Alternatives, Greens Function Approach, Modified Greens Function), Integral Equations (Integral equations with Separable Kernel, Fredholm alternatives, method of successive approximations) Calculus of Variations (Necessary conditions for Extrema, Euler-Lagrange equation), Newtonian Mechanics (Basic concepts, the Inverse square Law of Gravitation, Lagranges equation, Hamiltons principles of motion, Hamiltons equations).

0101493 (Combinatorial Mathematics)30101230

0101243

.

Mathematical Induction; The Binomial Theorem; Prime Numbers; Generating Functions; Recurrence Relations; An Introduction to Graph Theory; Inclusion-Exclusion Principle; Polya Enumeration; An Introduction to Coding Theory.

0101322 2

(Numerical Analysis 2)30101321

( ) ( ) .

Numerical Differentiation (Finite-Difference Formulas); Numerical Integration (Newton-Cotes Formulas, Gaussian Quadrature, Multiple integrals); Numerical Methods for Solving Ordinary Differential Equations (One-Step & Multistep methods); Applications on Boundary-Value Problems; Error Analysis.

0101351 (History of Mathematics)3

1600 .Number Systems, Decimal System, Numbering System, Arithmetic Systems, Arithmetic And Area In Egyptian And Babylonian, Greek Mathematics, Mathematics In Islamic World, European Mathematics Up To 1600, Modern European Mathematics.

0101372 2

(Ordinary Differential Equations 2)30101271

( ) .Linear Ordinary Differential Equations, The Existence And Uniqueness Theorem, Infinite Series Solutions (Frobenius Method), Basic Theory Of Systems Of First Order Linear Equations, Homogeneous Linear Systems With Constant Coefficients, Complex Eigenvalues, Repeated Eigenvalues, Fundamental Matrices, Nonhomogenous Linear Systems, Nonlinear Differential Equations And Stability.

0101374 (Special Functions)30101271

.Frobenius Method, Fourier And Laplace Transformations, Gamma And Beta Functions, Relation Between Gamma And Beta Functions, EPSI And Bessel Functions, Lagendre, Hermit, Lageere, Jacobi And Chebychev Polynomials, Differential Equations For These Polynomials And Its Solutions.

0101412 2

(Complex Analysis 2)30101310

: .

Connected Domains, Indefinite Integrals, The Cauchy Integral Formula, Derivative Of Analytic Functions, Morera's Theorem, Maximum Moduli Of Functions, The Fundamental Theorem Of Algebra, Convergence Of Sequences And Series, Power Series, Taylor Series, Laurent Series, Integration And Differentiation Of Power Series, Uniqueness Of Representations, Multiplication And Division, Zeros Of Analytic Functions, Residues, The Residue Theorem, The Principle Part Of A Function, Poles, Quotient Of Analytic Functions, Integration A Round A Branch Point.

0101471 (Mathematical Statistics)30101371

- .Fourier Series, Fourier Coefficients, Convergence Of Fourier Series, Applications, Sine And Cosine Series, Fourier Integration, Solutions Of Laplace And Heat Equation By Fourier Series, Fourier Solutions Of The Boundary Value Problems, Fourier-Legender Solutions Of The Boundary Value Problems.

0101474

(Calculus of Variations) 30101301

.The Method Of Variations In Problems With Fixed Boundaries, Euler's Equation, A Functional Dependent Of Several Functions, Functional Dependent On The Functions Of Several Variables, Variational Problems In Parametric Form Hamilton's Principle And Equation Of Motion, Variational Problems With Moving Boundaries, Sufficient Conditions For An Extremum, Conditional Problems, The Ritz Method.

0101490

(Seminar in Mathematics)3

.Topics In Mathematics Are Chosen By The Course Instructor At The Beginning Of The Term And Approved By The Department's Council.

0101494

Selected Topics In Mathematics3

.Topics In Mathematics Are Chosen By The Course Instructor At The Beginning Of The Term And Approved By The Department's Council.

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