Basics of Mathematics

1.    The  real number system, Linear equations and inequalities

2.    Polynomials , roots of polynomial

3.    Functions and its types, Trigonometric functions

4.    System of Equations

5.    Matrices and Determinants

6.    Complex numbers, De Movie’s theorem, simple elementary functions of a complex variable

Differential Calculus

1.    Limit and continuity of functions of one variable

2.    Geometric meaning of the derivative ,tangent and normal

3.    Differentiation of  algebraic, trigonometric, logarithmic, exponential and hyperbolic functions

4.    Rolle’s Theorem, Lagrange’s mean value theorem.

5.    Curvature and radius of curvature, Circle of curvature

6.    Higher derivatives, Some Standard  nth derivatives and  Leibnitz  theorem,

7.    Function of several variables, partial derivatives, Euler theorem, Composite functions and Chain rule. Implicit functions, Maxima and Minima of a function of one variable

8.    Taylor and Meclaurin’s theorems

Integral Calculus

1.    Integration by substitution, by parts and by partial fractions.

2.    Definite integral and Reduction Formula

Differential Equations

Ordinary Differential Equations first order.