Courses Details

Techniques of integration: integration by substitution; integration by parts, integrating powers of trigonometric functions, trigonometric substitutions, integrating rational functions, partial fractions,

rationalization, miscellaneous substitution; improper integrals; application of definite integral: volumes, length of a plane curve, area of a surface of revolution polar coordinates and parametric equations: polar coordinates, graphs in polar coordinates, area in polar coordinates; infinite series: sequences, infinite series, convergence tests, absolute convergence, conditional convergence; alternating series; power series: Taylor and Maclurine series, differentiation and integration of

power series

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The concept of set and its notations, classification of sets, ordered pairs, Cartesian product, product set, function on mapping, mappings, graph of function, function as sets of ordered pairs, relations, partition of asset ,equivalence class, composite mapping and its inverse, mathematical logic, number system.

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Sequences and infinite series; Convergence and divergence, alternating series, Power series, Taylor series, Vectors in R2 and R3 and, Lines, Planes, Cylindrical and Spherical coordinate systems, Function of several variables: Limits,  Continuity, Differentiation, The chain rule, Gradient, Extreme of functions of two variables, Lagrange multipliers

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Transcendental functions: Exponential and Logarithmic functions,   The hyperbolic functions, The inverse function of the trigonometric and hyperbolic functions, Technique, Integration by parts; Trigonometric substitutions partial fraction, Quadratic expressions The conic sections, Plane curves and polar coordinates: parametric equations, Area in polar coordinates, surface of revolution, Indeterminate   forms and improper integrals.

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the primary objective of the course is to introduce to Fourier series, beta and gamma functions, the definition of the Laplace transform, calculating inverse Laplace transforms, Legendre and associated Legendre functions, eigenvalues, and Eigenfunctions, strum- Liouville boundary value problems, series solutions near regular singular points (Bessel functions).

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Introduction to Partial Differential Equations(PDEs), Classification of PDEs; some physical models: the heat equation, the wave equation, and Laplace's equations; separation of variables for linear homogeneous PDEs; Eigenfunction expansions, Fourier transforms: properties and some applications; Laplace transform, Duhamel’s Principle, the heat equation for a finite rod, the wave equation for finite string, D’ Alembert solution, second order equations and classification into canonical forms (parabolic, elliptic, and hyperbolic), the method of characteristics, The Laplace equation in Cartesian & polar coordinates.

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This course covers the foundations of main topics in real analysis variables such as; Real Numbers, Metric spaces, Sequences, Continuity and compactness, Riemann Integration.

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The objective of this course is to introduce the fundamental ideas of the functions of complex variables and developing a clear understanding of the fundamental concepts of Complex Analysis such as analytic functions, complex integrals and a range of skills which will allow students to work effectively with the concepts.

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Discrete Distribution and continuous Distribution moment, moment Generating Function, Expectation and variance using M.g.f probability density function for two random variables, Expectation, Cumulative distribution function for two random variables, conditional Expectation, conditional variance, M .g .f for two random variables Expectation,  distributions of functions of random variables (distribution function method, moment generating function method, and the Jacobian transformation method); limiting distributions.

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The evolution of some concepts, facts and mathematical algorithms in arithmetic, algebra, triangles, planar geometry, analytical geometry and calculus across ancient, Egyptian, Babylonian, Greek, Indian, Chinese, Islamic and European civilizations, the development of some intuitions and open problems and attempts to solve them

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Forming a mathematical model for  Linear programming problems, solving the  Linear programming  by graphical method, simplex method and big M, Duality (definition of the dual problem, interpretations, the duality theorem, the complementary slackness theorem, dual simplex algorithm 

Solving the transportation problems, finding the optimal solution by using stepping stone method

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Division algorithm; divisibility; greatest common divisor and least common multiple; Diophentine equations; prime numbers and their distribution; fundamental theorem of arithmetic; congruence; linear congruence equations; Chinese remainder theorem; tests of divisibility. Fermat little theorem; Wilson's theorem; arithmetic functions; cryptography as an application of number theoryDivision algorithm; divisibility; greatest common divisor and least common multiple; Diophentine equations; prime numbers and their distribution; fundamental theorem of arithmetic; congruence; linear congruence equations; Chinese remainder theorem; tests of divisibility. Fermat little theorem; Wilson's theorem; arithmetic functions; cryptography as an application of number theory

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Central limit Theorem , Estimation Theory, Point Estimation – Confidence Interval, Testing Hypothesis Theory, X2 – test(for independence and goodness of fit), Test of variance analysis of variance, Non parametric Tests, Sign test, Rank sign test (Wilcoxon),  Sum of Rank Test (Man- Whitney test), Rank sum test Kruskal- Wallis test, Test of Randomness.

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Functions: domain, operations on functions, graphs of functions; trigonometric functions; limits: meaning of a limit, computational techniques, limits at infinity, infinite limits; continuity; limits and continuity of trigonometric functions; the derivative: techniques of differentiation, derivatives of trigonometric functions; the chain rule; implicit differentiation; differentials; Roll’s Theorem; the mean value theorem; the extended mean value theorem; L’Hopital’s rule; increasing and decreasing functions; concavity; maximum and minimum values of a function; graphs of functions including rational functions (asymptotes) and functions with vertical tangents (cusps); antiderivatives; the indefinite integral; the definite integral; the fundamental theorem of calculus ; logarithmic and exponential functions and their derivatives and integrals; limits (the indeterminate forms); some techniques of integration.

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A three Credit Hours compulsory course for students in the college of Science & Information Technology. The course content includes some presentation techniques and description of statistical data. Probability: concept of probability, basic rules of probability includes independence and conditional probability. Random variables and probability distributions, expectation, Binomial distribution, Poisson distribution, Normal distribution. Sampling distributions, t-distribution, CLT. Estimation, point and interval estimation for normal population mean and the difference of two population means. Testing hypotheses, the z-test, the t-test, testing the difference between two means (small and large sample sizes). Correlation and simple linear regression, residuals analysis, interval estimation of regression parameters.

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This course includes the study of Systems of Linear Equations. Solve the system of linear equations by using (Gaussian and Gauss-Jordan elimination). Matrices; their operations and their algebraic properties, Inverse of a matrix and its properties, methods for finding the inverse; solve the system of linear equations by using inverse of a matrix. Determinants with minors and cofactors; solve the system of linear equations by Crammers rule. Vector Spaces, subspaces, linear independence, basis, dimension, Eigenvalues and eigenvectors and their applications.

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