Sets and their Applications

Real Number System

Its properties and the real axis, Definitions and rules

Functions of a Single Variable

Concept of a function, Description and classification of functions, The inverse function, Maximum and minimum, Sketching curves, Limiting behavior of functions, Indeterminate forms, Continuity, Differentiability, Leibnitz theorem, Method of mathematical induction

 2-D Coordinate Geometry

Cartesian coordinate system
Conic sections
Polar, intrinsic and the padal coordinate system in 2-D
Curvature, radius and centre of curvature

3-D Euclidean Geometry

3-D Euclidean Coordinate Geometry

2

Complex Numbers

A review, Polar coordinates of a complex number, Demoivre's theorem, Application to trigonometric equations, Loci in complex plane, Eular form of complex numbers and its operations

Function of positive integers

Sequence (monotonic sequence and bounded sequence)
Convergence, divergence and oscillation of a sequence
Examples of common sequences

 Recurrence Relation

Related to sequence
Numerical computation of roots of an equation

Infinite Series

Standard examples of infinite series
Conditions for convergence
Alternating series
Absolute and conditional convergence

Real Power Series

Power series of function f(x)
Binomial expansion
Maclaurin and Taylor series approximation

2

Special Functions

Integrations

Function of Several Variables

Partial derivatives, Total differential
Approximation, Chain rule, Higher derivatives

Introduction to Differential Equations

Examples
Motion in a resistive medium (simple harmonic motion)
Solution techniques for first order differential equations