VU Open Course Ware: MathematicsVirtual University of Pakistan: Open Course Warehttp://www.vu.edu.pk/MTH001: Elementary MathematicsLogic , Truth Table , Logic Equivalence, Laws of the Algebra of Propositions, Translating Word Statements to Symbolic Notation & Vice Versa, Bi-Conditional Statements and their Equivalence, Arguments, Valid and In Valid arguments, Sets, Venn Diagram and Membership Table , Operations on sets, Venn Diagrams for operations on sets , Ordered Pairs, Relations and Matrix Representation of a matrix, Types of relations and Directed graph, Irreflexive and antisymmetric relations and partially ordered relations, Functions, Domain Codomain and Range, Types of function, Sequence, Arithmetic and Geometric Sequence, Series ,Sum of Arithmetic and Geometric Series, Performing basic arithmetic operations using Microsoft Excel, Basic calculations of percentages and investments using Microsoft Excel , Discount, Simple and compound interest, Average due date, Annuity, Accumulated value, Accumulation Factor, Discount Factor, Discounted value, Matrix, its Dimension and Types of matrix, Operations on Matrices, Merchandising, Introduction to Statistics, Data Representation, The Central Tendency of a data-set, Median, Empirical Relation, Quartiles, Geometric mean, Harmonic mean & relationship between them, Measures of Dispersion, Mean Deviation, Standard Deviation and Variance & Coefficient of variation, Permutations, Combinations, Definitions of Probability, Relative Frequency, Axiomatic Definition & Laws of Probability, Independent and Dependent Events, Multiplication Theorem & Marginal Probability.http://ocw.vu.edu.pk/CourseDetails.aspx?cat=Mathematics&course=MTH001MTH100: General MathematicsSets, Real Numbers , Complex Numbers, Functions, Quadratic Functions, Matrices, Inverse of a Matrix, Determinants, Arithmetic Progression and Arithmetic Series, Geometric progression and Geometric Series, Permutations and Combinations, Binomial theorem, Graphs and Functions, Straight Lines and Circles, Trigonometry, Statistics Introduction, Introduction to data, Frequency Distributions, Graphical representation of data, Measures Of Central Tendency, Range, inter quartile deviation mean deviation, Moments, Skewness and kurtosis.http://ocw.vu.edu.pk/CourseDetails.aspx?cat=Mathematics&course=MTH100MTH101: Calculus And Analytical GeometryAbsolute value ,Coordinates plane and graphs , Distance; Circles, Quadratic Equations, Limits, Continuity, Differentiation, Tangent Lines, Rates of Change, The Derivative, Derivatives of Trigonometric Functions Maximum and Minimum Values of Functions, Newton''s Method, Roll''s Theorem and the Mean Value Theorem, Integration by Substitution, Sigma Notation, Definite Integral, First and second Fundamental Theorem of Calculus, Applications of the Definite Integral: ,.Area between two curves, Volumes by Cylindrical Shells, Length of Plane Curves, Improper Integral , L''Hopital''s Rule, Improper Integral, Infinite Series, Sequence and Monotone Sequences, Alternating Series; Conditional Convergence, Taylor and Maclaurin Series.http://ocw.vu.edu.pk/CourseDetails.aspx?cat=Mathematics&course=MTH101MTH201: Multivariable CalculusIntroduction to three dimensional geometry. Limits, continuity and Partial Derivatives of Multivariable Function. Vectors. Directional derivative. Tangent Planes and Normal Lines to the Surfaces. Maxima And Minima of Functions of two variables. Applications of Extrema of Functions. Double Integration in rectangular and polar coordinates. Vector Valued Functions. Integration of Exact differentials. Line integrals. Greens Theorem and its application. Divergence and Curl of a vector. Scalar Fields, Higher Order Derivative &amp; Leibniz Theorem, Taylor and Maclaurin Series and Numerical Integration.&nbsp;<br><table x:str="" border="0" cellpadding="0" cellspacing="0" width="293" style="border-collapse:
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<td height="18" class="xl65" width="293" style="height:13.5pt;width:220pt">&nbsp;</td></tr></tbody></table>http://ocw.vu.edu.pk/CourseDetails.aspx?cat=Mathematics&course=MTH201MTH202: Discrete MathematicsLogic, Sets & Operations on sets, Relations & Their Properties, Functions, Sequences & Series, Recurrence Relations, Mathematical Induction, Loop Invariants, Loop Invariants, Combinatorics, Probability, Graphs and Trees.http://ocw.vu.edu.pk/CourseDetails.aspx?cat=Mathematics&course=MTH202MTH301: Calculus IIIntroduction to three dimensional geometry. Limits, continuity and Partial Derivatives of Multivariable Function. Vectors. Directional derivative. Tangent Planes and Normal Lines to the Surfaces. Maxima And Minima of Functions of two variables. Applications of Extrema of Functions. Double Integration in rectangular and polar coordinates. Vector Valued Functions. Integration of Exact differentials. Line integrals. Greens Theorem and its application. Divergence and Curl of a vector. Scalar Fields, Vector fields, Volume and Surface integrals. Conservative Fields. Divergence Theorem. Fourier Series. Laplace Transforms.http://ocw.vu.edu.pk/CourseDetails.aspx?cat=Mathematics&course=MTH301MTH302: Business Mathematics & StatisticsPerform arithmetic operations. Simple and compound interest. Perform basic calculations of the percentages, averages, commission, brokerage and discount. Solve linear equations in one variable, Matrices, Mathematics of Merchandising, Break-even Analysis, Measures of central tendency. Measures of dispersion and skewness, Line fitting. Time series and Exponential smoothing. Permutations and Combinations. Elementary Probability, Chi-Square, Binomial Distribution, Normal Distributions, Estimating from Samples, Hypothesis testing: Chi-Square Distribution.http://ocw.vu.edu.pk/CourseDetails.aspx?cat=Mathematics&course=MTH302MTH303: Mathematical MethodsSeparable Equations, Homogeneous Differential Equations, Exact Differential Equations, Integrating Factor Technique, First Order Linear Equation, Bernoulli Equations, Applications of First Order Differential Equations, Radioactive Decay, Applications of Non Linear Equations, Higher Order Linear Differential Equations, Homogeneous Linear Equations with Constant Coefficients, Method of Undetermined Coefficients ( Superposition Approach), Method of Undetermined Coefficients (Annihilator Operator Approach), Variation of Parameters for Higher-Order Equations,Systems of Linear Equations, Row Reduction and Echelon Forms ,Vector Equations, The Matrix Equation, Solution Sets of Linear Systems, Linear Independence, Linear Transformations, The Matrix of a Linear Transformation, Matrix Algebra, Iterative Solutions of Linear Systems, Determinants, Cramer’s Rule and Linear Transformations, Vector Spaces and Subspaceshttp://ocw.vu.edu.pk/CourseDetails.aspx?cat=Mathematics&course=MTH303MTH401: Differential EquationsSeparable Equations, Homogeneous Differential Equations, Exact Differential Equations, Integrating Factor Technique, First Order Linear Equation, Bernoulli Equations, Applications of First Order Differential Equations, Radioactive Decay, Applications of Non Linear Equations, Higher Order Linear Differential Equations, Homogeneous Linear Equations with Constant Coefficients, Method of Undetermined Coefficients ( Superposition Approach), Method of Undetermined Coefficients (Annihilator Operator Approach), Variation of Parameters for Higher-Order Equations, Applications of Second Order Differential Equations, Damped Motion, Forced Motion, Differential Equations with Variable Coefficients, Cauchy-Euler Equation: Alternative Method of Solution, Power Series, Solution about Ordinary points, Solution about Singular Points, Bessel's Differential Equation, Legendre's Differential Equation, Systems of Linear Differential Equations, System of Linear First Order Equation, Eigen value Problem, Matrices and Systems of Linear First-Order Equations, Homogeneous Linear Systems, Linear and Repeated Eigen values, Non-Homogeneous System.http://ocw.vu.edu.pk/CourseDetails.aspx?cat=Mathematics&course=MTH401MTH501: Linear AlgebraSystems of Linear Equations, Row Reduction and Echelon Forms, Vector Equations, The Matrix Equation, Solution Sets of Linear Systems, Linear Independence, Linear Transformations, The Matrix of a Linear Transformation, Matrix Algebra, Iterative Solutions of Linear Systems, Determinants, Cramer&#8217;s Rule and Linear Transformations, Vector Spaces and Subspaces, Null Spaces, Column Spaces, and Linear Transformations, Linearly Independent Sets, Bases, Coordinate System, Dimension of a Vector Space, Rank, Change of Basis, Applications to Difference Equations,Eigenvalues and Eigenvectors, The Characteristic Equation,Diagonalization, Eigenvectors and Linear Transformations, Complex Eigenvalues, Discrete Dynamical Systems, Applications to Differential Equations, Iterative Estimates for Eigenvalues, Inner Product, Orthogonal and Orthonormal set, Orthogonal Decomposition, Orthogonal basis, Gram-Schmidt Process, Orthonormal basis, Least Square Solution, Inner Product Space, Application of inner product spaces.http://ocw.vu.edu.pk/CourseDetails.aspx?cat=Mathematics&course=MTH501MTH601: Operations ResearchAn Overview and Back Ground, OR Process, OR techniques and Applications, Networks, Inventory Control Models, Linear Programming, Duality Analysis, Transportation Problems, Assignments Problems, Queuing Theory, Replacement Models, Dynamic Programming, Miscellaneous (Introduction of some new programs).http://ocw.vu.edu.pk/CourseDetails.aspx?cat=Mathematics&course=MTH601MTH603: Numerical AnalysisNumber systems, Errors in computation, Methods of solving non-linear equations, Solution of linear system of equations and matrix inversion, Eigen value problems, power method, Jacobi’s method, Different techniques of interpolation, Numerical differentiation and integration, Numerical integration formulas, different methods of solving ordinary differential equations.http://ocw.vu.edu.pk/CourseDetails.aspx?cat=Mathematics&course=MTH603