Integral Calculus and its applications: Multiple Integrals: Evaluation of double and triple integrals, change of order of integration, changing to polar coordinates. Areas and volume using double integration. Beta and Gamma functions: Definitions, properties, relation between Beta and Gamma functions.

Vector calculus and its applications: Vector differentiation: Scalar and vector fields, gradient of a scalar field, directional derivatives, divergence of a vector field, solenoidal vector, curl of a vector field, irrotational vector, physical interpretation of gradient, divergence and curl and scalar potential. Vector Integration: Line integrals, Statement of Green’s and Stokes’ theorem without verification problems.

Numerical Methods-1 : Solution of algebraic and transcendental equations: Regula-Falsi method, and Newton-Raphson method. Finite Differences and Interpolation: Forward and backward differences, Interpolation, Newton forward and backward interpolation formulae, Newton’s divided difference interpolation formula and Lagrange’s interpolation formula. Numerical Integration: Trapezoidal rule, Simpson’s 1/3rd rule and Simpson’s 3/8th rule.

Numerical Methods-2: Numerical solution of ordinary differential equations of first order and first degree: Taylor’s series method, Modified Euler’s method, Runge-Kutta method of fourth order, Milne’s predictor corrector method and Adam-Bashforth predictor-corrector method.

Laplace transforms: Definition and Formulae of Laplace Transforms, Laplace Transforms of elementary functions. Properties–Linearity, Scaling, shifting property, differentiation in the s domain, division by t. Laplace Transforms of periodic functions, square wave, saw-tooth wave, triangular wave, full and half wave rectifier, Heaviside Unit step function. Inverse Laplace Transforms: Definition, properties, evaluation of Inverse Laplace Transforms using different methods, and applications to solve ordinary differential equations.