## MA8353 TPDE Syllabus

Anna University Regulation 2017 MECH MA8353 TPDE Syllabus for all 5 units are provided below. Download link for MECH 3rd SEM MA8353 TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS Engineering Syllabus is listed down for students to make perfect utilization and score maximum marks with our study materials.

### Anna University Regulation 2017 MECH Engineering (MECH) 3rd SEM MA8353 TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS Engineering Syllabus

MA8353 TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS
OBJECTIVES:
 To introduce the basic concepts of PDE for solving standard partial differential equations.
 To introduce Fourier series analysis which is central to many applications in engineering apart
from its use in solving boundary value problems.
 To acquaint the student with Fourier series techniques in solving heat flow problems used in
various situations.
 To acquaint the student with Fourier transform techniques used in wide variety of situations.
 To introduce the effective mathematical tools for the solutions of partial differential equations
that model several physical processes and to develop Z transform techniques for discrete time
systems.
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.

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MA8353 TPDE Syllabus

Anna University 3rd Sem MECH TPDE Syllabus