Math Syllabus

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.