Lecture Notes || SNS Courseware

Subject Details

Dept : MECH

Sem : 2

Regul : R2023

Faculty : Saranya C

phone : NIL

E-mail : saranya.c.math@snsct.org

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Lecture Notes

UNIT 1:

Derivatives: Gradient and Directional Derivative

Divergence & Curl of a vector field

Green’s theorem

Problems based on Green’s theorem

Gauss Divergence theorem

Problems based on Gauss Divergence theorem

Solenoidal and Irrotational of a vector

Application in evaluating line, surface and volume integrals.

Stoke’s theorem with problems

UNIT 2:

Homogeneous equation of Legendre’s type

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

Homogeneous equation of Euler’s type

Method of variation of parameters

Higher order linear differential equations with constant coefficients

Problems based on higher order linear differential equations with constant coefficients

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

UNIT 5:

Definitions, properties, existence conditions

Transform of elementary function

Shifting Theorem

Transforms of derivatives and integrals

Laplace transform of periodic functions

Initial and final value theorem

Inverse Laplace transforms

Solution of linear second order ordinary differential equations with constant coefficients

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