Subject Code: MA2L005	Subject Name: Mathematics V (Transform Calculus)	L-T-P: 3-0-0	Credit: 3
Pre-requisite(s): MA1L001
Laplace Transform: Definition of Laplace Transform, linearity property, conditions for existence of Laplace Transform. First and second shifting properties, Laplace Transform of derivatives and integrals, unit step functions, Dirac delta-function, error function. Differentiation and integration of transforms, convolution theorem, inversion, periodic functions. Evaluation of integrals by Laplace Transform. Solution of initial and boundary value problems. Fourier Series: Periodic functions, Fourier series representation of a function, half range series, sine and cosine series, Fourier integral formula, Parseval’s identity. Fourier Transform: Fourier Transform, Fourier sine and cosine transforms. Linearity, scaling, frequency shifting and time shifting properties. Self reciprocity of Fourier Transform, convolution theorem. Other Transforms: Brief Introduction of Z-Transform, Mellin transform and Wavelet Transform, Hilbert Transform, Radon Transform. Text Books: Jain R. K. and Iyengar S. R. K. Advanced Engineering Mathematics, Narosa Dyke P. P. G. Introduction to Laplace Transform and Fourier Series, Springer Reference Books: Watson E. J. Laplace Transforms and Applications Pinkus A. & Zafrany S. Fourier Series and Integral Transforms, Cambridge University Press Rao K. S. Introduction to Partial Differential Equations, Prentice Hall of India Private Ltd

Subject Code: MA2L005

Subject Name: Mathematics V
(Transform Calculus)

L-T-P: 3-0-0

Credit: 3

Pre-requisite(s): MA1L001

Laplace Transform: Definition of Laplace Transform, linearity property, conditions for existence of Laplace Transform. First and second shifting properties, Laplace Transform of derivatives and integrals, unit step functions, Dirac delta-function, error function. Differentiation and integration of transforms, convolution theorem, inversion, periodic functions. Evaluation of integrals by Laplace Transform. Solution of initial and boundary value problems.
Fourier Series: Periodic functions, Fourier series representation of a function, half range series, sine and cosine series, Fourier integral formula, Parseval’s identity.
Fourier Transform: Fourier Transform, Fourier sine and cosine transforms. Linearity, scaling, frequency shifting and time shifting properties. Self reciprocity of Fourier Transform, convolution theorem.
Other Transforms: Brief Introduction of Z-Transform, Mellin transform and Wavelet Transform, Hilbert Transform, Radon Transform.

Text Books:

Jain R. K. and Iyengar S. R. K. Advanced Engineering Mathematics, Narosa
Dyke P. P. G. Introduction to Laplace Transform and Fourier Series, Springer

Reference Books:

Watson E. J. Laplace Transforms and Applications
Pinkus A. & Zafrany S. Fourier Series and Integral Transforms, Cambridge University Press
Rao K. S. Introduction to Partial Differential Equations, Prentice Hall of India Private Ltd