Course Catalogue

Course Code: MAT 102
Course Name:
Math-II (Co-ordinate Geometry and Liner Algebra)
Credit Hours:
3.00
Detailed Syllabus:

Coordinate Geometry:
Coordinates, polar coordinates, straight lines, changes of axes, pair of straight lines, circle parabola, ellipse, hyperbola, rectangular coordinate, plane.
Vector Analysis: vector components, vector components in spherical and cylindrical system, vector operators, scalar and dot product, application of vector geometry, derivative of vector, del, gradient, divergence and curl, physical significance, integration of vector, line surface and volume integration, Theorems (Green’s, Gauss’s, Liouville’s, Stoke’s) and their applications.

Linear Algebra:
Systems of Linear Equations (SLE): introduction to SLE, solution of a SLE, solution of a system of homogeneous LE, Gaussian and Gauss-Jordan elimination, Determinants: factorization, determinant, fundamental properties of determinants, minors and cofactors, Cramer’s rules for solving a SLE, Algebra of Matrices: Matrix, some special types of matrices, transpose, adjoint and inverse of a matrix, algebraic operation on matrices, quadratic forms solution of a LE by applying matrices, Vector Space: space and subspace, Euclidean n-space, basis and dimension, rank and nullity, Linear Transformations (LT) and its Matrix Representations: LT from to , properties of LT, matrix representation of a LT, diagonalization of LT, Eigen Values and Eigen Vectors: polynomials of matrices and linear operators, eigen values and vectors, diagonalizability, Cayley-Hamilton theorem, characteristic and minimum polynomial Inner Product Spaces: inner product spaces, Cauchy-Schwarz inequality, orthogonality, Gram-Schmidt orthogonalization process, linear functional and adjoint operators, Some Applications of LA.

Course Code: MAT 1101
Course Name:
Differential and Integral Calculus
Credit Hours:
3.00
Detailed Syllabus:

Functional Analysis and Graphical Information: function, properties of functions, graphs of functions, new function from old, lines and family of functions, Limit: Limits (an informal view), one sided limits, the relation between one sided and two sided limits, computing limits, Continuity: continuity and discontinuity, some properties of continuity, the intermediated value theorem. Derivatives: slop and rate of change, tangent and normal, derivative of a function, physical meaning of derivative of a function, techniques of differentiation, chain rule, successive derivatives. Derivative in graphing and applications: analysis of functions, maximum and minimum, Expansion of functions: Taylor's series, Maclaurian's series, Leibniz; Rolle's and Mean Value theorems, Partials and total derivatives of a function of two or three variables. Different technique of integration: integration, fundamental integrals, methods of substitutions, integration of rational functions, integration by parts, integrals of special trigonometric functions, reduction formulae for trigonometric functions. Definite integrals: general properties of definite integral, definite integral as the limit of sum and as an area, definition of Riemann integral, Fundamental theorem of integral calculus and its applications to definite integrals, determination of arc length, Improper integrals, Double integrals, Evaluation of Areas and Volumes. Introduction to MATLAB and LAB Sessions.

Course Code: MAT 1201
Course Name:
Co-Ordinate Geometry and Linear Algebra
Credit Hours:
3.00
Detailed Syllabus:

Coordinate Geometry: Coordinates, polar coordinates, straight lines, Changes of axes, Pair of straight lines, Circle, Parabola, Ellipse, Hyperbola, rectangular coordinate, plane. Vector Analysis: Vector components, vector components in spherical and cylindrical system, vector operators, scalar and dot product, application of vector geometry, Derivative of vector, del, gradient, divergence and curl, physical significance, integration of vector. Line, surface and volume integration, Theorems (Green's, Gauss's, Liouville's, Stoke's) and their applications. Linear Algebra: Systems of Linear Equations (SLE): introduction to SLE, solution of a SLE, solution of a system of homogeneous LE, Gaussian and Gauss-Jordan elimination, Determinants: factorization, determinant, fundamental properties of determinants, minors and cofactors, Cramer's rules for solving a SLE, Algebra of Matrices: Matrix, some special types of matrices, transpose, adjoint and inverse of a matrix, algebraic operation on matrices, quadratic forms solution of a LE by applying matrices, Vector Space: space and subspace, Euclidean n-space, basis and dimension, rank and nullity, Linear Transformations (LT) and its Matrix Representations: LT from to , properties of LT, matrix representation of a LT, diagonalization of LT, Eigen Values and Eigen Vectors: polynomials of matrices and linear operators, eigen values and vectors, diagonalizability, Cayley-Hamilton theorem, characteristic and minimum polynomial Inner Product Spaces: inner product spaces, Cauchy-Schwarz inequality, orthogonality, Gram-Schmidt orthogonalization process, linear functional and adjoint operators, Some Applications of LA.

Course Code: MAT 201
Course Name:
Differential Equation and Numerical Analysis
Prerequisite:
Credit Hours:
3.00
Detailed Syllabus:

Differential Equations:
Basic Definitions and Terminology: differential equation (de), classifications of de, formation and solution of a de and further terminology, Ordinary de (ode), des of the first order and first degree: variable separable, homogeneous equations, exact equations, linear equations, Linear Equations with constant coefficients: linear and nonlinear de, solution of linear de, 2nd order des, 2nd and higher order homogeneous des, Method of Variation of Parameter; Method of undetermined coefficients; System of Linear de: operator method matrices and system of linear first order equations, homogeneous linear systems, undetermined coefficients, variation of parameters, Solution by Series.

Numerical Analysis:
Errors in Numerical Calculations: numbers and their accuracy, errors and their computation, a general error formula, error in a series approximation, Solution of Algebraic and Transcendental Equations: bisection, iteration, false position, Newton-Raphson methods, Interpolation: finite difference, forward, backward and central differences, Newton’s formula for interpolation, Stirlings formula, Lagrange’s interpolation formula, divided differences and their properties, Numerical Differentiation and Integration, Matrices and Linear Systems of Equations, Numerical Solution of Ordinary Differential Equations.

Course Code: MAT 201
Course Name:
Math-III (Differential Equations and Numerical Analysis)
Credit Hours:
3.00
Detailed Syllabus:

Ordinary Differential Equations: Degree and order of ordinary differential equations, formation of differential equations. Solution of first order differential equations by various methods. Solution of general linear equations of second and higher orders with constant coefficients. Solution of homogeneous linear equations. Solution of differential equations of the higher order when the dependent or independent variables are absent. Solution of differential equation by the method based on the factorization of the operators. Frobenius method. Partial Differential Equations: Introduction. Linear and non-linear first order equations. Standard forms. Linear equations of higher order. Equations of the second order with variable coefficients. Wave equations. Particular solution with boundary and initial conditions.

Course Code: MAT 201
Course Name:
Differential Equation and Numerical Analysis
Credit Hours:
3.00
Detailed Syllabus:

Differential Equations:
Basic Definitions and Terminology: differential equation (de), classifications of de, formation and solution of a de and further terminology, Ordinary de (ode), des of the first order and first degree: variable separable, homogeneous equations, exact equations, linear equations, Linear Equations with constant coefficients: linear and nonlinear de, solution of linear de, 2nd order des, 2nd and higher order homogeneous des, Method of Variation of Parameter; Method of undetermined coefficients; System of Linear de: operator method matrices and system of linear first order equations, homogeneous linear systems, undetermined coefficients, variation of parameters, Solution by Series.

Numerical Analysis:
Errors in Numerical Calculations: numbers and their accuracy, errors and their computation, a general error formula, error in a series approximation, Solution of Algebraic and Transcendental Equations: bisection, iteration, false position, Newton-Raphson methods, Interpolation: finite difference, forward, backward and central differences, Newton’s formula for interpolation, Stirlings formula, Lagrange’s interpolation formula, divided differences and their properties, Numerical Differentiation and Integration, Matrices and Linear Systems of Equations, Numerical Solution of Ordinary Differential Equations.

Course Code: MAT 203
Course Name:
Mathematical Methods
Prerequisite:
Credit Hours:
3.00
Detailed Syllabus:

Laplace Transformations:
Laplace Transformation (LT), Inverse Laplace Transforms (ILT), Applications of LT to de, Complex Variable Theory: complex number system, polar form of complex numbers, operations in polar form, De Moivre’s theorem, roots of complex numbers, functions, limit, continuity, derivatives, Cauchy-Riemann equations, line integral formulas, Green’s theorem in the plane, Integrals, Cauchy’s theorem, Cauchy’s integral formulas, Taylor’s series, Singular points, Poles, Laurent’s series, residues, residues theorem, evaluation of definite integrals, Convergency and Divergency of infinite series: general properties of series, test of convergence and divergence of the series of constants, power series, uniform convergence, Cauchy criterion for uniform convergence. Power series solution of de: analytic and singular functions, ordinary and singular points of a differential equation, Solution in series of the de.

Fourier Analysis:
Beta and Gamma functions, Fourier series and Applications: Periodic functions and Trigonometric series, Definition of Fourier Series, Dirichlet conditions, Fourier sine and cosine series, Half-Range Fourier Sine and Cosine series, Perseval’s Identity, Integration and differentiation of Fourier series, Complex notation for fourier series, Some physical applications of fourier series, Fourier Integrals and Applications: Fourier integral, Fourier transforms, Fourier sine and cosine transforms, Persival’s Identities for Fourier Integrals, Convolution theorem for Fourier transforms, Applications of Fourier Integrals and transforms, Special functions: Legendere’s de and Legendere’s polynomials, Bessel’s de and Bessel functions, Hermite’s de and Hermit’s polynomials, Laguerre’s DE and Laguerre’s polynomials.

Course Code: MAT 203
Course Name:
Math-IV (Complex Variable and Mathematical Methods)
Credit Hours:
3.00
Detailed Syllabus:

Complex Variable: De-Moiver’s theorem & its application, Functions of a complex variable, Limit, Continuity & Differentiability of a function of complex variable, Analytic functions, Cauchy-Riemann equations, Cauchy’s theorem, Singularity & poles, Residues, Simple contour integration. Vector Analysis: Vector components, Vector components in spherical and cylindrical system, Derivative of vector, Vector operators, Del, Gradient, Divergence and Curl. Their physical significance, Vector integration, Line, Surface and Volume integration, Green’s and Stoke’s theorem and their applications. Laplace Transformation: Definition of Laplace transform (LT), LT of different functions, First Shift theorem, Inverse transform, Linearity, Use of first shift theorem and Partial functions, Transform of derivative, Transform of an integral, Heaviside unit function, The 2nd shift theorem, Periodic functions, Convolutions, Solution of ordinary differential equation by Laplace transform. Fourier Analysis: Real and Complex form, Finite transform, Fourier integral, Fourier series and convergence of Fourier series, Fourier transform and uses in solving boundary value problem.

Course Code: MAT 203
Course Name:
Math-III (Mathematical Methods)
Credit Hours:
3.00
Detailed Syllabus:

Laplace Transformations:
Laplace Transformation (LT), Inverse Laplace Transforms (ILT), Applications of LT to de, Complex Variable Theory: complex number system, polar form of complex numbers, operations in polar form, De Moivre’s theorem, roots of complex numbers, functions, limit, continuity, derivatives, Cauchy-Riemann equations, line integral formulas, Green’s theorem in the plane, Integrals, Cauchy’s theorem, Cauchy’s integral formulas, Taylor’s series, Singular points, Poles, Laurent’s series, residues, residues theorem, evaluation of definite integrals, Convergency and Divergency of infinite series: general properties of series, test of convergence and divergence of the series of constants, power series, uniform convergence, Cauchy criterion for uniform convergence. Power series solution of de: analytic and singular functions, ordinary and singular points of a differential equation, Solution in series of the de.

Fourier Analysis:
Beta and Gamma functions, Fourier series and Applications: Periodic functions and Trigonometric series, Definition of Fourier Series, Dirichlet conditions, Fourier sine and cosine series, Half-Range Fourier Sine and Cosine series, Perseval’s Identity, Integration and differentiation of Fourier series, Complex notation for fourier series, Some physical applications of fourier series, Fourier Integrals and Applications: Fourier integral, Fourier transforms, Fourier sine and cosine transforms, Persival’s Identities for Fourier Integrals, Convolution theorem for Fourier transforms, Applications of Fourier Integrals and transforms, Special functions: Legendere’s de and Legendere’s polynomials, Bessel’s de and Bessel functions, Hermite’s de and Hermit’s polynomials, Laguerre’s DE and Laguerre’s polynomials.

Course Code: MAT 205
Course Name:
Math-IV (Discrete Mathematics and Numerical Analysis)
Credit Hours:
3.00
Detailed Syllabus:

Discrete Mathematics: Mathematical logic: propositional calculus, predicate calculus. Permutations, Combinations and Discrete Probability. Set theory: sets, relations, partial ordered sets, functions. Graph theory: graphs, paths, trees. Recurrence Relations and Recursive Algorithms. Algebraic structures: binary operations, semi groups, groups, permutation groups, rings and fields, lattices. Numerical Methods: Solutions of polynomials and transcendental equations, Interpolation and polynomial approximation, Least square approximation, Solutions of systems of linear equations, Gauss elimination technique, Gauss-Siedel iteration technique, Numerical differentiation and integration.

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