Vector field: divergence, curl, identities involving divergence and curl, scalar potential.
Line integral, independence of path, irrotational and solenoidal vector fields, Green’s theorem for
plane, parameterized surface, surface area and surface integral, flux, Gauss’ divergence theorem,
Stokes' theorem.
Numerical sequences, Cauchy sequence, convergence of sequences, series, convergence of series,
tests for convergence, absolute convergence. Sequence of functions, power series, radius of
convergence, Taylor series, periodic functions and Fourier series expansions, half-range expansions.
Existence and uniqueness of solution of first order ordinary differential equations (ODE)s, methods of
solutions of first order ODE, linear ODE, linear homogeneous second order ODEs with constant
coefficients, fundamental system of solutions, Wronskian, linear independence of solutions, method of
undetermined coefficients, solution by variation of parameters, Euler-Cauchy differential equations,
applications of ODEs.
Laplace transform, sufficient condition for existence, inverse Laplace transform, Dirac delta function,
transforms of derivatives and integrals, shifting theorems, convolution, differentiation and integration
of transform, solution of differential equations and integral equations using Laplace transform.