# Chapter 11: The Laplace Transform

Notes of the book Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin. This book is published by Ilmi Kitab Khana, Lahore - PAKISTAN. Solutions of Chapter 11: The Laplace Transform are given here in pdf form.

### Contents & Summary

Let $f$ be a real valued piecewise continuous function defined on $[0,\infty)$. The Laplace transform of $f$, denoted by $\mathcal{L}(f)$, is the function $F$ defined by $ F(s)=\int_0^{\infty} e^{-st} f(t) dt, $ provided the above improper integral converges. We have $F=\mathcal{L}(f)$.

Here is the list of other contents given in this chapter.

- The Laplace transform
- Properties of the Laplace transform
- Exercise 11.1
- Inverse Laplace transform
- Convolution
- Exercise 11.2
- Solution of initial value problem
- Exercise 11.3