# Laplace Transform

Ordinary and partial differential equations describe the way certain quantities vary with time, such as the current in an electrical circuit, the oscillations of a vibrating membrane, or the flow of h...

created by zeeshan saleem

Last updated 2021-12-26

Language: English

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## Your Coverages

- Laplace Transform

- Differential Equations

## Course Requirements

- Bsc in Mathmatics Student
- Msc in Mathmatical Student
- BS Engineers
- MS Engineers
- PHD Students

## Which Students must take this course

## Course Content

##
Laplace Transform

Laplace Introduction

00:04:10

Laplace Transform in a Linear Operator

00:02:56

##
Laplace Transform of a Differential Function by using Definition

Laplace Transform of a Constant Function

00:11:10

Laplace Transform of a Monomial Function

00:10:56

Laplace Transform of a Exponential Function

00:04:49

Laplace Transform of a Piecewise Continuous Function (Part-1)

00:12:11

Laplace Transform of a Piecewise Continuous Function (Part-2)

00:12:11

Laplace Transform of Sinkt

00:10:46

Laplace Transform of coshkt

00:08:46

Laplace Transform of Sumtopro

00:06:15

First Translation Theorem

00:05:28

Exp of First Translation Theorem

00:07:27

Laplace Transform of Sinhktcoshkt

00:03:43

Laplace Transform of coshktSinhktexp

00:04:52

Units Function

00:06:06

Second Translation Function

00:07:51

Exp of Second Translation Function

00:08:20

Laplace Transform of Exponential function by Direct Method

00:04:32

Laplace Transform of Monomial by Direct Method

00:06:35

Laplace Transform of Sinktcoskt by Direct Method

00:04:39

Laplace Transform of Monomial by Iterative Process

00:10:12

Proof of Derivative of Transformation

00:08:26

Example of Derivative of Transformation

00:10:45

## Description

Ordinary and partial differential equations describe the way certain quantities vary with time, such as the current in an electrical circuit, the oscillations of a vibrating membrane, or the flow of heat through an insulated conductor. These equations are generally coupled with initial conditions that describe the state of the system at time t = 0. A very powerful technique for solving these problems is that of the Laplace transform, which literally transforms the original differential equation into an elementary algebraic expression. This latter can then simply be transformed once again, into the solution of the original problem. This technique is known as the “Laplace transform method.”
We will study the following:
Basic Definition of Laplace Transform and its Existence, Exponential Order, Sufficient conditions for Existence, Laplace Transform is a linear Operator, Laplace Transform of a Constant Function, Laplace Transform of a Monomial Function, Laplace Transform of a polynomial Function, Laplace Transform of a Exponential Function, Laplace Transform of a Sine and cosine Function, Laplace Transform of a Hyperbolic Sine and cosine Function, Laplace Transform of a composition of a Function, Laplace Transform of a Piece-wise Function, Laplace Transform by First Translation Theorem, Unit Step Function, Laplace Transform by Second Translation Theorem, Derivatives of Transforms, Convolution Theorem and also inverse of Laplace.

$50

30 days money back guarantee

This course has

Full Lifetime Access

Access on mobile

Certificate of Completion

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