Double integration (Cartesian coordinates) – Change of order of integration – Applications of double integral (Area) – Triple Integration (Cartesian coordinates) – Applications: Volume as triple integrals and solids of revolution.

The gradient of a scalar field. Directional derivative – Divergence of a vector field – Curl of a vector field –Solenoidal and Irrotational of a vector – Greens Theorem, Gauss Divergence Theorem and Stoke’s Theorem (statements only).

Derivatives of f(z) -Analytic function – Cauchy-Riemann Equations- Harmonic function– Harmonic conjugate – Construction of an Analytic function - Conformal Mapping- Conformality of w= z + c, cz, 1/z, Mobius transformations – Application to flow problems.

Cauchy’s integral theorem – Cauchy’s integral formula – Taylor’s series – Laurent’s series – singularities –– Residues – Cauchy Residue theorem.

Conditions – Transforms of elementary functions – Properties - Transform of derivatives and integrals – Unit step function (Heaviside function) –Dirac’s Delta function – Laplace transform of periodic functions – Inverse Laplace transforms - Convolution theorem – Partial fraction method - Applications to solution of linear ordinary differential equations of second order with constant coefficients.