Mathematics - II Book BCA 2nd Semester As Per UP Unified Syllabus

Unit

Topics

I

Sets

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

II

Relations and Functions

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 Trignometric, Logarithmic and Exponential Functions

III

Partial Order Relations and Lattices

Partial Order Sets, Representation of POSETS using Hasse Diagram, Chains, Maximal and Minimal Point, Glb, lub, Lattices & Algebric Systems, Principle of Duality, Basic Properties, Sublattices, Distributed & Complemented Lattics

IV

Functions of Several Variables

Partial Differentiation, Change of Variables, Chain Rule, Extrema of Functions of 2 Variables, Euler’s Theorem

V

3d Coordinate Geometry

3D Coordinate Geometry: Coordinates in Space, Direction Cosines, Angle Between Two Lines, Projection of Join of Two Points on a Plane, Equations of Plane, Straight Lines, Conditions for a Line to Lie on a Plane, Conditions for Two Lines to be Coplanar, Shortest Distance Between Two Lines, Equations of Sphere, Tangent Plane at a Point on the Sphere

VI

Multiple Integration

Double Integral in Cartesian and Polar Coordinates to Find Area, Change of Order of Integration, Triple Integral to Find Volume of Simple Shapes in Cartesian Coordinates.