Module 1: Multivariable Integral Calculus: Double and Triple integrals, Evaluation of double
integrals, change of order of integration, change of variables, Evaluation of Triple integrals,
Simple applications involving areas, volumes. (8 L/ 1Q)

Module 2: Vector Calculus: Scalar and Vector point functions. Directional derivative,
Gradient, divergence and curl. Line integrals, Surface integrals, Volume integrals, Green's
theorem, Stokes theorem and Gauss divergence theorem (without proofs). (10 L/ 2Q)

Module 3: Higher order linear differential equations with constant and variable coefficients,
Method of variation of parameters, Cauchy’s and Legendre’s linear equations, Simultaneous
linear equations, Series solutions of differential equations, Bessel and Legendre’s equations
and its solution(without proof). Elementary properties of Bessel function and Legendre’s
polynomial. (10 L/ 2Q)

Module 4: Complex Variable - Differentiation:
Differentiation, Cauchy-Riemann equations, Analytic functions, Harmonic functions, finding
harmonic conjugate; Conformal mappings, Mobius transformations and their properties.
(6 L/ 1Q)

Module 5: Complex Variable - Integration:
Contour integrals, Cauchy Integral Theorem, Cauchy Integral formula (without proof)and for
derivatives also, zeros of analytic functions, singularities, Taylor’s se,riesLaurent’s series;

Residues, Cauchy Residue theorem (without proof), Evaluation of definite integral involving
sine and cosine.