Syllabus Mathematics - 1 Total Credits L+T+ (PR/2) Assessment Pattern and Marks Total Marks C Theory Tutorial / Practical ESE (E) PA / CA (M) PA/CA (I) ESE (V) 4 70 30 - - 100 Unit No. Content 1. Set Theory : • Concept of set theory. • Methods of representation of set. • Types and operations of set operations (Union, intersection, Complement of a set. Difference of sets, symmetric difference, Cartesian product of sets). • Properties of set operations (Commutative, Associative, Distributive, De-Morgan’s laws). • Power set and cardinality of sets. • Venn diagram. • Practical applications of set theory. (Chapter - 1) 2. Functions : • Introduction and Definition of Function. • Domain Co-domain and Range of a function. • Graph of a functions. • Types of Functions (Linear, Quadratic, Polynomial, Implicit and Explicit functions and examples related with it). • Exponential and Logarithmic with their properties and related examples, Introduction to Trigonometric functions. (Chapter - 2) 3. Matrix and Determinant : • Definition of Matrix. • Types of Matrices (Square, Row, Column, Zero, Diagonal, Scalar, Identity, Transpose, Symmetric, Skew - symmetric). • Arithmetic operations of Matrices (Addition, Scalar Multiplication, Matrix Multiplication). • Introduction to Determinants. • Invertible matrix. • Matrix inversion using adjoint matrix method. • Derive solution of set of Linear equations for 2 variables using Cramer’s - Rule. • Row and column operation on Matrix. • Rank of Matrix (Chapter - 3) 4. Co-ordinate Geometry : • Introduction to Co-ordinates, • Quadrants and Lines, • Distance formula in R2 (without proof), • Section Formula (without proof), • Area of a triangle (without proof) and related examples, • General Equation of a Straight line, • Slope and intercepts of a line, • Parallel Lines, • Perpendicular Lines, • Angle between two lines (without proof) and related examples. (Chapter - 4)
