MA8353 -TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS Syllabus And Study Material Engineeringboysoff
MA8353 TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS SYLLABUS/BOOKS AND MATERIALS
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.
FOR OTHER SECOND YEAR BOOKS:SECOND YEAR
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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