UNIT – I
Laplace Transformation: Laplace Transformation, Inverse Laplace transformation Convolution Theorem, application to linear differential equations with constant coefficients, Unit step function, impulse functions / periodic Functions.
UNIT – II
Fourier Series: Fourier Series, Euler’s formulae, even and odd functions, having arbitrary periods, half range expansion, Harmonic Analysis.
Fourier Transforms: Fourier transform, Sine and Cosine transforms, Application to differential equations.
UNIT – III
Special Functions: Beta and Gamma functions, Bessels functions of first kind, Recurrence relations, modified Bessel functions of first kind, Ber and Be functions, Legendre Polynomial, Rodrigue’s formula, orthogonal expansion of function.
UNIT – IV
Partial Differential Equation: Formation of first and second order linear equations, Laplace, Wave and heat conduction equation, initial and boundary value problems.
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