UNIT-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. 
 
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. 
 

UNIT-II 
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. 


UNIT-III 
FUNCTIONS OF SEVERAL VARIABLES: Partial Differentiation, Change of Variables, 
Chain Rule, Extrema of Functions of 2 Variables, Euler’s Theorem. 
 
3D COORDINATE GEOMETRY: Review of 2D Coordinate Geometry: Equations of 
Straight Lines, Circle, Ellipse, Parabola, Hyprbola. 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. Equations of Ellipsoid, Paraboloid, Hyperbolid and 
Cylinder in Cartesian coordinate. 
 

UNIT-IV 
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.