Derivatives: Gradient and Directional derivatives Divergence and Curl of a vector field Solenoidal and Irrotational of a vector Green᎙s, Gauss divergence and Stoke᎙s theorems (statements only) Verification of theorems and application in evaluating line, surface and volume integrals.

Higher order linear differential equations with constant coefficients Method of variation of parameters Homogenous equation of Euler᎙s and Legendre᎙s type Solution of system of simultaneous linear first order differential equations with constant coefficients.

Derivatives of f(z) Analytic function Cauchy-Riemann Equations Harmonic function Harmonic conjugate Construction of Analytic function Conformal Mapping Mapping by functions: w = z + c, cz, 1/z Bilinear transformations Application to flow problems.

Cauchy᎙s integral theorem Cauchy᎙s integral formula Taylor᎙s series Zeros of an analytic function singularities Laurent᎙s series Residues Cauchy Residue theorem .

Definition, properties, existence conditions Transforms of elementary functions Shifting theorem Transforms of derivatives and integrals Periodic functions Initial and final value theorem Inverse transforms Application to solution of linear second order ordinary differential equations with constant coefficients.