Laplace Transform

Laplace transform is a fundamental tool in integral calculus. It is used to solve various types of differential equations, difference equations, integral equations etc., which arise naturally in engineering and basic sciences. Laplace transform techniques are therefore very useful for applications in science and technology. INTENDED AUDIENCE :2nd year BE/BSc onwardsPREREQUISITES :Differential and integral calculusINDUSTRIES SUPPORT :None

Week 1:Introduction and basic definitions, with brief review of limits and Riemann integration, with special emphasis on improper Riemann integralsWeek 2:Functions of exponential order and existence theorem for Laplace transforms- with lots of examples and some non-examples; Properties of Laplace transforms with applications in computing them for various functionsWeek 3:Inverse Laplace transforms, criteria for uniqueness, computation of inverse Laplace transform via various examples Week 4:Applications of Laplace transform techniques for solving integrals, differential equations, difference equations, integral equations and integro-differential equations