Concept of Point-wise and Uniform convergence of sequence of functions and series of functions with special reference to power Series. Statement of Weierstrass M-Tests for Uniform convergence of sequence of functions and of series of functions. Simple applications.
Determination of Radius of convergence of power series. Term by term integration and Term by term differentiation of power Series.
Scalar and vector fields, differentiation of vectors, velocity and acceleration. Vector differential operators : Del, Gradient, Divergence and Curl, their physical interpretations. Formulae involving Del applied to point functions and their products. Line, surface and volume integrals, Greens Theorem in the Plane Parameterized Surface, Stokes Theorem and the Divergence Theorem. Applications of Green’s, Stoke’s and Divergence theorem.