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Subject Details

Dept : CSE

Sem : 2

Regul : 2019

Faculty : Gomathi P

phone : NIL

E-mail : gomathisenthilkumar2011@gmail.com

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Lecture Notes

UNIT 1:

Double integration (Cartesian Coordinates)

Change of order of integration

Applications: Volume as triple integrals and solids of revolution.

Double integration (Cartesian Coordinates)

Change of order of integration

Triple Integration(Cartesian Coordinates

Applications of double integral(Area)

Applications: Volume as triple integrals and solids of revolution.

Triple Integration(Cartesian Coordinates

UNIT 2:

Derivatives: Gradient of a scalar field, Directional Derivative

Divergence & Curl of a vector field

Solenoidal and Irrotational of a vector

Problems based on Stoke’s theorem

Problems based on Gauss Divergence theorem

Problems based on Green’s theorem

Problems based on Gauss Divergence theorem

UNIT 3:

Derivatives of f(z) - Analytic function

Harmonic Function

Construction of Analytic functions

Conformal mapping

Mobius Transformations

Conformal mapping

Mobius Transformations

Construction of Analytic functions

Derivatives of f(z) - Analytic function

UNIT 4:

Cauchy’s integral theorem

Taylor’s series

Laurent’s series

Cauchy Residue theorem

Taylor’s series

Laurent’s series

Cauchy’s integral theorem

Cauchy Residue theorem

UNIT 5:

Conditions -Transforms of standard functions , Properties

Transforms of derivatives and integrals

Laplace transform of periodic functions

Inverse Laplace transforms

Convolution theorem

Applications to solution of linear ordinary differential equations of second order with constant coefficients

Simultaneous linear equations with constant coefficients

Inverse Laplace transforms

Transforms of derivatives and integrals

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