UNIT I : PARTIAL DIFFERENTIAL EQUATIONS
Formation of partial differential equations –Solutions of standard types of first order partial differential equations – First order partial differential equations reducible to standard types- 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 and cosine series – Root mean square value – 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 (Cartesian coordinates only).
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 – Convergence of Z-transforms – – Initial and final value theorems – Inverse Z-transform using partial fraction and convolution theorem – Formation of difference equations – Solution of difference equations using Z – transforms.
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