Laplace Transforms and its applications: Laplace transforms: Basic concept, Existence conditions, transform of elementary functions, Properties of Laplace transforms, transform of derivatives and integrals, multiplication and division property, Evaluation of integrals by Laplace transforms Dirac’s Delta function, Application to linear differential equations and simultaneous linear differential equations with constant coefficients.

Ordinary Differential Equations and its applications: Exact differential equations, Equations reducible to exact differential equations, Applications of differential equations of first order and first degree to simple electric circuits, Newton’s law of cooling, heat flow and orthogonal trajectories.

Vector Calculus: Differentiation of Vectors, Scalar and vector point functions, Gradient of a scalar field and directional derivative, divergence and Curl of a vector field and their physical interpretation, line integrals, surface integral, volume integral, Green’s theorem in the plane, Stoke’s Theorem, Gauss Divergence Theorem (without proof) and their applications.