## Transforms and Partial Differential Equations syllabus

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 – Solutions of one dimensional wave equation – One dimensional equation of heat conduction – Steady state solution of two dimensional equation of heat conduction (excluding insulated edges).

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) –Convolution theorem – Formation of difference equations – Solution of difference equations using Z – transform.

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