21MAT433 INTEGRAL TRANSFORMS AND FOURIER SERIES-

Unit I-

Fourier Analysis: Fourier series, Complex Form of Fourier Series, Parseval’s Identity.

Unit II-

Fourier Integrals, Fourier integral theorem.

Unit III-

Infinite Complex Fourier Transforms, Sine and Cosine Transforms, Properties, Convolution theorem and Parseval’s theorem.

Unit IV-

Laplace Transforms: Laplace Transforms, Inverse Transforms, Properties, Transforms of Derivatives and Integrals, Second Shifting Theorem, Unit Step Function and Dirac-Delta Function, Differentiation and Integration of Transforms.

Unit V-

Convolution, Initial and Final Value Theorems, Periodic Functions, Solving Linear Ordinary Differential Equations with Constant Coefficients, System of Differential Equations and Integral Equations.

TEXTBOOKS:

E Kreyszig, Advanced Engineering Mathematics, John Wiley and Sons, 2002, Eighth Edition.

REFERENCES:

1) Larry C. Andrews and Bhimson. K. Shivamoggi, The Integral Transforms for Engineers, Spie Press, Washington, 1999.
2) J. L. Schiff, The Laplace Transform, Springer, 1999.
3) Stanley J Farlow,’ Partial Differential Equations for Scientists and Engineers’ Dover Book on Mathematics, 1993