'Transforms and Partial Differential Equations' is a course offered in the third semester of B. Tech. programs at School of Engineering, Amrita Vishwa Vidyapeetham.
Unit 1
Laplace Transform: Laplace Transforms, Inverse Transforms, Linearity, Shifting, Transforms of Derivatives and Integrals, Differential Equations, Unit Step Function, Second Shifting Theorem, Dirac’s Delta Function. Differentiation and Integration of Transforms.
Unit 2
Convolution, Integral Equations, Partial Fractions, Differential Equations, Systems of Differential Equations. (Sections: 6.1 to 6.7)
Fourier Series: Fourier series, Half range Expansions, Parseval’s Identity, Fourier Integrals, Fourier integral theorem. Sine and Cosine Integrals. (Sections:11.1 -11.3)
Unit 3
Fourier Transforms: Sine and Cosine Transforms, Properties, Convolution theorem. (Sections: 11.1 -11.3, 11.7-11.9)
Partial Differential Equations: Basic Concepts, Modeling; Vibrating String, Wave Equation, Separation of Variables, Use of Fourier Series, Heat Equation; Solution by Fourier Series. (Sections: 12.1-12.5)
TEXTBOOK
- Advanced Engineering Mathematics, E Kreyszig, John Wiley and Sons, Ninth Edition, 2012.
REFERENCE BOOKS
- Advanced Engineering Mathematics by Dennis G. Zill and Michael R.Cullen, second edition, CBS Publishers, 2012.
- Larry C. Andrews and Bhimson. K. Shivamoggi, The Integral Transforms for Engineers, Spie Press, Washington, 1999.
- J. L. Schiff, The Laplace Transform, Springer, 1999.
