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Subject Details

Dept : MECH

Sem : 2

Regul : 2023

Faculty : Gomathi P

phone : NIL

E-mail : gomathisenthilkumar2011@gmail.com

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Lecture Notes

UNIT 1:

Derivatives: Gradient and Directional Derivative

Divergence & Curl of a vector field

Solenoidal and Irrotational of a vector

Green’s theorem

Problems based on Green’s theorem

Gauss Divergence theorem

Problems based on Gauss Divergence theorem

Stoke’s theorem with problems

Application in evaluating line, surface and volume integrals.

UNIT 2:

Higher order linear differential equations with constant coefficients

Problems based on higher order linear differential equations with constant coefficients

Method of variation of parameters

Homogeneous equation of Euler’s type

Homogeneous equation of Legendre’s type

Solution of system of simultaneous linear first order differential equations with constant coefficients

UNIT 3:

Derivatives of f(z) - Analytic function

Cauchy-Riemann Equations

Harmonic Function

Harmonic Conjugate

Construction of Analytic functions

Conformal mapping

Mapping by functions w = c+z, w = cz , w = 1/z

Bilinear Transformations

Application to flow problems

UNIT 4:

Cauchy’s integral theorem

Problems based on Cauchy’s integral formula

Taylor’s series

Zeros & Singularities of an analytic function

Laurent’s series

Residues

Cauchy Residue theorem

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