Lecture Notes || SNS Courseware

Subject Details

Dept : AIML

Sem : 2

Regul : 2023

Faculty : Sunantha .D

phone : NIL

E-mail : sunantha.d.math@snsct.org

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Lecture Notes

UNIT 1:

Derivatives: Gradient of a scalar field, 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

Problems based on Stoke’s theorem

UNIT 2:

Higher order linear differential equations with constant coefficients

Method of Variation of parameters

Euler’s Linear differential equation

Legendre’s Linear differential equation

UNIT 3:

Formation of partial differential equations

Lagrange’s linear equation

Solutions of standard types of first order partial differential equations

Linear partial differential equations of second order with constant coefficients(Homogeneous Problems)

UNIT 4:

Dirichlet’s conditions

General Fourier series

Odd and even functions

Fourier transform pair

Sine and Cosine transforms

Parseval’s Identity

UNIT 5:

Definitions, properties, existence conditions

Transform of elementary function

Shifting Theorem

Laplace transform of periodic functions

Initial and final value theorem

Transforms of derivatives and integrals

Inverse Laplace transforms

Solution of linear second order ordinary differential equations with constant coefficients

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