Page 7 - LAPLACE TRANSFORM

TABLE OF CONTENT

ACKNOWLEDGMENT ....................................................................................................... I

AUTHOR BIODATA .......................................................................................................... II
SYNOPSIS ..................................................................................................................... III

TABLE OF CONTENT .........................................................................................................

LAPLACE TRANSFORM .................................................................................................... 1
1.0 DEFINITION OF LAPLACE TRANSFORM .................................................................... 1

1.1 What is the Laplace Transform? ............................................................................... 1

1.2 Laplace Transform Formula ...................................................................................... 2
1.2.1 Laplace Transform Method For Solving Differential Equations ......................................... 2
2.0 PROPERTIES OF LAPLACE TRANSFORM ...................................................................14

2.1 THEOREM 1 : LINEARITY THEORAM ......................................................................14
2.1.1 Table Of Laplace Transforms ................................................................................................. 15

2.2 THEOREM 2 : THE FIRST SHIFTING THEOREM ..........................................................26

2.3 THEOREM 3 :MULTIPLICATION BY t n ........................................................................34
3.0 INVERSE LAPLACE TRANSFORM ...........................................................................43

3.1 SIMPLE FUNCTIONS METHOD ..............................................................................43
3.1.1 Definition Of Inverse Laplace Transform :- ......................................................................... 43

3.2 PARTIAL FRACTION METHOD ..............................................................................57
3.2.1 Table Of Partial Fractions ...................................................................................................... 57
4.0 DIFFERENTIAL EQUATION METHOD ..........................................................................69

4.1 SOLVE DIFFERENTIAL EQUATIONS USING LAPLACE TRANSFORM ...............................69
4.1.1 Table of Laplace Transform .................................................................................................. 69
BIBLIOGRAPHY ..............................................................................................................81