Functions and Limits: Constants, variables and functions, limits - Differentiation- Standard forms – Differentiation of Inverse functions - Differentiation of Hyperbolic functions –Differentiation of Inverse Hyperbolic functions – Differentiation of implicit functions – Successive Differentiation: Leibnitz formula for nth derivative. – Maxima and Minima – Applications.

Introduction - Definite Integral – Methods of Integration – Substitution method -Integration of (f'/ (x))/(f(x)) , (f'/ (x))/√(f(x)) , (px+q)/√(ax^2+bx+c), ,√(((x-a))/(b-x)) , √((x-a)(b-x)), 1/√((x-a)(b-x)), 1/(acosx+bsinx+c), 1/(acos^(2 ) x+bsin^(2 ) x+c) and Integration by parts.

Vector differential operators, Gradient, Divergence, curl and their simple properties - Directional derivatives- Solenoidal- Irrotational vectors.

Permutation and Combinations – Probability – Discrete Random variables - Conditional probability –Baye’s theorem –Continuous distribution function.

Null hypothesis- alternative hypothesis- Calculation of errors- small sample test – t test for single mean and difference of means - F test for single variance, difference between two sample variance.