December 2020
Intermediate to advanced
1064 pages
49h 13m
English
Content preview from Advanced Engineering Mathematics, 7th Edition
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4.4 Additional Operational Properties
INTRODUCTION
In this section we develop several more operational properties of the Laplace transform. Specifically, we shall see how to find the transform of a function f(t) that is multiplied by a monomial tn, the transform of a special type of integral, and the transform of a periodic function. The last two transform properties allow us to solve some equations that we have not encountered up to this point: Volterra integral equations, integrodifferential equations, and ordinary differential equations in which the input function is a periodic piecewise-defined function.
4.4.1 Derivatives of Transforms
Multiplying a Function by tn
The Laplace transform of the product of a function f(t) with t can be found ...
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