Course Description

This course covers topics from calculus and computational methods such as limits and continuity, differentiation and its applications, integration and its applications, differential equations, and various computational techniques. These are essential as mathematical foundations for computing.

Course Objectives

This course aims to enable students to understand the concepts of calculus and computational methods and their applications in social sciences and computer applications.

Unit Contents

1. Limits and Continuity

Teaching Hours: 6 hrs

This unit explores the limit of a function, indeterminate forms, and algebraic properties of limits (without proof). It includes theorems on limits of algebraic and transcendental functions, continuity of a function, and types of discontinuity. Students will work on exercises involving the evaluation of limits and testing continuity, using Mathematica.

2. Differentiation

Teaching Hours: 6 hrs

This unit covers ordered pairs, Cartesian products, relations, and the domain and range of relations. It discusses the inverse of a relation and types of relations such as reflexive, symmetric, transitive, and equivalence relations. The definition of a function, domain, range, inverse function, and special functions (identity, constant), as well as algebraic functions (linear, quadratic, cubic), trigonometric functions, and their graphs are explored. It also covers exponential and logarithmic functions and composite functions, with Mathematica used for exercises.

3. Application of Differentiation

Teaching Hours: 8 hrs

This unit includes the derivatives and slopes of curves, increasing and decreasing functions, convexity of curves, and maximization and minimization of functions. It examines differentiation and marginal analysis, including price and output, and competitive equilibrium of firms. Illustrations and drawing graphs of algebraic functions using first and second-order derivatives will be conducted with Mathematica.

4. Integration and Its Applications

Teaching Hours: 8 hrs

This unit discusses the Riemann integral and the fundamental theorem (without proof), techniques of integration, and the evaluation and approximation of definite integrals. It also covers improper integrals and their applications, including quadrature, rectification, volume, and surface integrals. Students will learn about the trapezoidal and Simpson's rules of numerical integration, using Mathematica.

5. Differential Equations

Teaching Hours: 7 hrs

This unit addresses differential equations, including their order and degree, first-order and first-degree differential equations, and differential equations with separable variables, as well as homogeneous and exact differential equations.

6. Computational Methods

Teaching Hours: 10 hrs

This unit involves linear programming problems (LPP), graphical solutions of LPP in two variables, and the simplex method (up to 3 variables). It covers solving systems of linear equations using Gauss elimination method, Gauss-Seidel method, and matrix inversion method. Additionally, it includes the bisection method and Newton-Raphson method for solving non-linear equations, with Excel or Matlab used for exercises.

Laboratory Works

Mathematica and/or Matlab should be used for the above-mentioned topics.