MA8353 Transforms and Partial Differential Equations Syllabus:

MA8353 Transforms and Partial Differential Equations Syllabus – Anna University Regulation 2017

UNIT I Partial Differential Equations

Formation of partial differential equations — Singular integrals — Solutions of standard types of first order partial differential equations — Lagrange?s linear equation — Linear partial differential equations of second and higher order with constant coefficients of both homogeneous and non-homogeneous types.

UNIT II Fourier Series

Dirichlet?s conditions — General Fourier series — Odd and even functions — Half range sine series — Half range cosine series — Complex form of Fourier series — Parseval?s identity — Harmonic analysis.

UNIT III Applications Of Partial Differential Equations

Classification of PDE — Method of separation of variables — Fourier Series Solutions of one dimensional wave equation — One dimensional equation of heat conduction — Steady state solution of two dimensional equation of heat conduction.

UNIT IV Fourier Transforms

Statement of Fourier integral theorem — Fourier transform pair — Fourier sine and cosine transforms — Properties — Transforms of simple functions — Convolution theorem — Parseval?s identity.

UNIT V Z — Transforms And Difference Equations

Z-transforms — Elementary properties — Inverse Z-transform (using partial fraction and residues) — Initial and final value theorems — Convolution theorem — Formation of difference equations — Solution of difference equations using Z — transform.