Laplace Transforms and Fourier Series

Semester and Year Offered: Monsoon/Winter

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Pre-requisites: Mathematics at the XII grade level

Aim: The aim of the course is to offer a gentle introduction to the concepts of Laplace transforms, Inverse Laplace transforms, solution of ordinary differential equations using Laplace transform, Fourier series and their properties with applications in real life.

Course Outcomes:

1. After completing this course, students will be able to understand the applications of Laplace transform and Fourier series.
2. The students will be able to solve ordinary differential equations using Laplace transform.

Brief description of modules/ Main modules:

The main modules are as follows:

Laplace Transform

The Laplace Transform, Elementary properties of Laplace transform, Laplace transform of derivatives and integrals, Laplace transform of unit step function and Impulse functions, Initial value theorem and Final value theorem

Inverse Laplace transform and Solutions to Differential equations

Inverse Laplace transform, Convolution Theorem and its proof, Solution of ordinary differential equation using Laplace transform

Fourier Series

Definition of Fourier Series, Odd and Even Functions, Complex Fourier series, Half range series, Properties of Fourier Series, Parseval Identity

Assessment Details with weights:

Reading List:

• P. P. G. Dyke, An introduction to Laplace transform and Fourier Series, 4th Edition, Springer (2004).