Transforms Partial Differential Equations Premium Lecture Notes - Kavi Edition

Transforms and Partial Differential Equations Handwritten Premium Lecture Notes, Prepared by Kavi. Specially for Engineering Candidates. Syllabus Covered based on Anna University Third Semester.

TRANSFORMS PARTIAL DIFFERENTIAL EQUATION

UNIT-1
FOURIER SERIES
Periodic function
Fourier series
Uses of fourier series
Dirichlet condition
Even function
Odd function
Problem based on odd function
Half range sine series
Half range cosine series
Parseval’s theorem
Harmonic analysis

UNIT-2
PARTIAL DIFFERENTIAL EQUATION
Formulation of partial differential equation by elimination of arbitrary constants
Formulation of PDE by elimination of arbitrary function
Lagranges linear equation
Methods of grouping
Methods of multipliers
Higher order partial differential equation

UNIT-3
Problems on vibrating string with non – zero intial velocity
One dimensional heat equation
Two dimensional heat equation
Problems on polar co-ordination
UNIT-4
FOURIER TRANSFORM
Fourier transform pair
Shifting property
Parsevals identity
Modulation property

UNIT-5
Z- TRANSFORM AND DIFFERENTIAL EQUATION
Unit step function of z- transform
Partial fraction
Unit impulse function
Z-Transform
Standard formula
Linearty property
First shifting theorem
Differentiation in the z- domain
Second shifting theorem
Initial value theorem
Final value theorem
Inverse z- transform
Partial fraction method
Convolution theorem
Residue method
Solution of difference equation