Mathematics-I – Adv

Program Class: Diploma / BCA CS

Year: I

Semester: II

Subject: BCA Bachelor of Computer Application

Course Title: Mathematics-I

Course Learning Outcomes:

Credits: 4

Core Compulsory

Max. Marks: –25+75

Min. Passing Marks: 33

Unit

Topics

I

Sets, Subsets, Equal Sets Universal Sets, Finite and Infinite Sets, Operation on Sets, Union, Intersection and Compliments of Sets, Cartesian Product, Cardinality of Set, Simple Applications.

II

Properties of Relations, Equivalence Relation, Partial Order Relation Function: Domain and Range, Onto, Into and One to One Functions, Composite and Inverse Functions, Introduction of Trigonometric, Logarithmic and Exponential Functions.

III

Partial Order Sets, Representation of POSETS using Hasse diagram, Chains, Maximal and Minimal Point, glb, lub, Lattices & Algebraic Systems, Principle of Duality

IV

Definition, Minors, Cofactors, Properties of Determinants MATRICES: Definition, Types of Matrices, Addition, Subtraction, Scalar Multiplication and Multiplication of Matrices, Adjoint, Inverse, Cramers Rule, Rank of Matrix Dependence of Vectors, Eigen Vectors of a Matrix, Caley-Hamilton Theorem (without proof).

V

Limit at a Point, Properties of Limit, Computation of Limits of Various Types of Functions, Continuity at a Point, Continuity Over an Interval, Intermediate Value Theorem, Type of Discontinuities

VI

Derivative, Derivatives of Sum, Differences, Product & Quotients, Chain Rule, Derivatives of Composite Functions, Logarithmic Differentiation Integral as Limit of Sum, Fundamental Theorem of Calculus ( without proof.), Indefinite Integrals, Methods of Integration Substitution, By Parts.