INTEGRAL TRANSFORM

BR THAKUR · HARI KISHAN · GAJENDRA UJJAINKAR · VK GUPTA

Ram Prasad Publications(R.P.H.)

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Unit-I Laplace Transform :

1.1 Linearity property 1.2 Existence theorem

1.3 Shifting theorem 1.4 Change of scale property

1.5 Laplace transforms of derivatives and integrals

1.6 Differentiation and integration of the Laplace transforms

1.7 Multiplication and division by 't'

1.8 Periodic function

Unit-II Inverse Laplace Transform :

2.1 Linearity property 2.2 Shifting theorem

3.3 Change of scale property

2.4 Inverse Laplace transforms of derivatives and integrals

2.5 Multiplication and division by powers of p

2.6 Convolution theorem

2.7 Heaviside expansion theorem

Unit-III Application of Laplace Transform :

3.1 Solution of ordinary differential equations with constant 

coefficients

3.2 Solution of ordinary differential equations with variable

coefficients

Unit-IV Fourier Transform :

4.1 Linearity property 4.2 Shifting theorem

4.3 Change of scale property 4.4 Modulation

4.5 Convolution theorem

4.6 Fourier transform of derivatives

4.7 Relations between Fourier transform and Laplace transform

4.8 Parseval's identity for Fourier transform

4.9 Solution of differential equations using Fourier transform