May 2022
Intermediate to advanced
487 pages
9h 22m
English
Content preview from Differential Equations, 3rd Edition
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8Laplace Transforms
The idea of the Laplace transform
The Laplace transform and differential equations
Derivatives and the Laplace transform
Integrals and the Laplace transform
Convolutions
Step and impulse functions
Discontinuous input
8.0 Introduction
The idea of the Laplace transform has had a profound influence on the development of mathematical analysis. It also plays a significant role in mathematical applications. More generally, the overall theory of transforms has become an important part of modern mathematics.
The concept of a transform is that it turns a given function into another function. We are already acquainted with several transforms:
The derivative D takes a differentiable function f (defined ...
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