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UNIT I PARTIAL DIFFERENTIAL EQUATIONS

1.1 Formation of partial differential equations

1.2 Singular integrals

1.3 Solutions of standard types of first order partial differential equations

1.4 Lagrange’s linear equation

1.5 Linear partial differential equations of second and higher order with constant coefficients of both homogeneous and non-homogeneous types.

UNIT II FOURIER SERIES

2.1 Dirichlet’s conditions

2.2 General Fourier series

2.3 Odd and even functions

2.4 Half range sine series

2.5 Half range cosine series

2.6 Complex form of Fourier series

2.7 Parseval’s identity

2.8 Harmonic analysis

UNIT III APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS

3.1 Classification of PDE

3.2 Method of separation of variables

3.3 Solutions of one dimensional wave equation

3.4 One dimensional equation of heat conduction

3.5 Steady state solution of two dimensional equation of heat conduction

UNIT IV FOURIER TRANSFORMS

4.1 Statement of Fourier integral theorem

4.2 Fourier transform pair

4.3 Fourier sine and cosine transforms

4.4 Transforms of simple functions

4.5 Convolution theorem

4.6 Parseval’s identity

UNIT V Z - TRANSFORMS AND DIFFERENCE EQUATIONS

5.1 Z-transforms

5.2 Elementary properties

5.3 Inverse Z - transform (using partial fraction and residues)

5.4 Convolution theorem

5.5 Formation of difference equations

5.6 Solution of difference equations using Z - transform.