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.