Course

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.

Objectives: To enable students to

• Acquaint with the knowledge of fourier analysis and Laplace transforms
• Solve the linear ordinary differential equations

Text books:

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

References :

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