Laplace Transform

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