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Course Description
This course includes the topics from calculus and computational methods such as limits and continuity, differentiation & its applications, integration and its applications, differential equation and different computational techniques which are essential as mathematical foundation for computing.
Course Objectives
This course makes students able to cognize the concept Calculus, Computational methods and their applications in the area of Social Science and Computer Application.
Course Contents
Limit of a function, Indeterminate forms, Algebraic properties of limit (without proof), Theorems on Limits of Algebraic and Transcendental Function, Continuity of a function, types of discontinuity, Exercises on evaluation of limits and test of continuity. (Mathematica)
Ordered Pairs, Cartesian Product, Relation, Domain and Range of a Relation, Inverse of a Relation; Types of Relations: Reflexive, Symmetric, Transitive, and Equivalence Relations, Definition of Function, Domain and Range of a Function, Inverse function, Special Functions (Identity, Constant, Algebraic (Linear, Quadratic, Cubic), Trigonometric and Their Graphs, Definition of Exponential and Logarithmic functions, Composite Function. (Mathematica)
The derivatives and slope of the curve; Increasing and decreasing function; convexity of curves; maximization and minimization of a function; Differentiation and marginal analysis; price and output; Competitive equilibrium of firm, Illustrations. Drawing graphs of algebraic function by using first and second order derivatives. (Mathematica)
Riemann Integral; Fundamental Theorem (Without Proof); Techniques of Integration; Evaluation and Approximation of Definite Integrals; Improper Integrals; Applications of Definite Integrals; Quadric, Rectification, Volume and Surface Integral, Trapezoidal and Simpson's Rules of Numerical Integration.(Mathematica)
Differential Equation and its Order and Degree, Differential Equations of First Order and First Degree; Differential Equations with Separable Variables, Homogeneous and Exact Differential Equations.
Linear Programming Problem (LPP), Graphical Solution of LPP in Two Variables, Solution of LPP by Simplex Method (up to 3 variables), Solution of System of Linear Equations by Gauss Elimination Method, Gauss Seidel Method and Matrix Inversion Method, Bisection method, Newton- Raphson Method for Solving Non-linear Equations. (Excel/Matlab)
Laboratory Works
Mathematica and/ or Matlab should be used for above mentioned topics.
Teaching Methods
The general teaching pedagogy includes class lectures, group works, case studies, guest lectures, research work, project work, assignments (theoretical and practical), tutorials and examinations (written and verbal). The teaching faculty will determine the choice of teaching pedagogy as per the need of the topics.