Mathematics I Syllabus - BCIS (PU)

Course Objectives

The objective of this course is to familiarize students with the basic mathematical tools with emphasis on applications to business and economics situations. The course specifically aims to enable students to develop proficiency in the application of mathematical tools to solve business problems.

Course Description

This course basically deals with mathematical concepts like set theory and number system, functions and graphs, derivatives and their applications, vectors, matrices and determinants, and permutations and combinations.

Course Outcomes

By the end of this course, students should be able to:

• use the language of mathematics to communicate ideas;
• demonstrate proficiency in conceptual understanding, and adaptive reasoning;
• solve quantitative problems and perform quantitative investigations in which they discover ideas and gain insights that develop questioning and solution-building skills; and
• use mental strategies and technology accurately and appropriately.

Course Contents

Unit I: Set Theory and Real Number System                                                        6 hours

Sets, Types of sets, Venn diagram, Set operations, Laws of algebra of sets (without proof), Number of elements in a set Real number system, Representation of real numbers on the real line, Properties of real numbers (without proof), ordered sets, Inequalities, Intervals, Absolute value, Cartesian product, Relation.

Unit II: Functions and Graphs                                                                                6 hours

Constants and variables, Concept of functions, Domain and range of a function, Types of functions, Graphic representation (algebraic, logarithmic and exponential functions), Application of functions to business and economics.

Unit III: Derivatives                                                                                                  9 hours

Limit of a function at a particular point and at infinity, Properties of limits (without proof) Continuity, Types discontinuity, Test of continuity and discontinuity for simple algebraic functions; Derivative, Average rate of change, Derivate as a slope of tangent to curves, Methods of differentiation (power rule, sum rule, product rule, quotient rule and chain rule), Differentiation of implicit and parametric functions, Higher order derivatives.

Unit IV: Applications of Derivatives                                                                       6 hours

Increasing and decreasing functions, Derivative as a rate of change, Critical point, Point of inflection, Maximum and minimum of a function of one variable, Problems related to business and economics.

Unit V: Vectors                                                                                                         6 hours

Introduction, Vector representation, Magnitude of a vector, Types of vectors, Vector addition and multiplication, Scalar product of two vectors, Vector product of two vectors, Collinear and coplanar vectors, Vector space, Linear dependence and independence vectors.

Unit VI: Matrices and Determinants                                                                      9 hours

Introduction, Types of matrices, Matrix operations, Transpose of a matrix, Determinant of a matrix, Minors and cofactors of matrix, Properties of determinants, Singular and non-singular matrix, Adjoint and inverse of matrix, Solution of system of linear equations having unique solution up to three variables (Cramer’s rule, Inverse matrix method and Gaussian elimination method), linear transformations, rank of matrices.

Unit VII: Permutations and Combinations                                                            6 hours

Basic principles of counting, factorial notation, permutation, Permutation of objects alike, Permutation with restrictions, Circular permutation, Combination, Combination with restrictions.

Basic Texts

1. Yamane, t. Mathematics for Economics: Elementary Survey (2^nd). New Delhi: Prentice Hall of India.
2. Budnick, F. S. Applied Mathematics for Business, Economics and the Social Sciences. New Delhi: Tata McGraw Hill.

References

1. Calculus and Analytic Geometry, Thomas and Finney, Addison Wesley 9^th
2. Calculus with Finite Mathematics, Geoffrey C. Berresford, Andrew M. Rockett