In this section, Laplace transforms are taught with emphasis on solving of Differential equations by Laplace transforms.

Introduction of Laplace Transforms Basic properties of Laplace Transforms First and Second Shifting theorems in Laplace transforms Laplace Inverse Laplace transform of exponential functions Laplace transform of step functions Differentiation of Laplace Integration of Laplace Solution of ordinary differential equations with Laplace Convolution theorem

Course

In the subject of Mathematics, Laplace transforms are majorly used to solve the differential equations. It is an efficient alternative to solve differential equations as compared to variation of parameters and undetermined coefficients. **In particular, Laplace method is useful for input terms which are piecewise, periodic or impulsive. **

To complete this section you must know the basics of integration and functions. Topics covered in this section are as follows:

- Introduction to Laplace transforms.
- Basic Laplace transform properties.
- Use of Laplace transforms to solve differential equations.