COURSE SUMMARY
Course Title:
Transforms and Partial Differential Equations
Course Code:
15MAT204
Year Taught:
2015
2016
2017
2018
Semester:
3
Type:
Foundation Core
Degree:
School:
School of Engineering
Campus:
Chennai
Coimbatore

'Transforms and Partial Differential Equations' is a course offered in the third semester of B. Tech. programs at School of Engineering, Amrita Vishwa Vidyapeetham.

#### SYLLABUS

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 / REFERENCE BOOKS

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.