MAT 1228 Series and Differential Equations Section 4.1 Definition of the Laplace Transform

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Presentation transcript:

MAT 1228 Series and Differential Equations Section 4.1 Definition of the Laplace Transform

Quiz Monday Quiz 3.7, 4.1

Preview Specially designed for Initial Value Problems Definition in the form of an improper integral Transforms of elementary functions Transforms of piecewise defined functions

Solutions Principals/Ideas

A Tale of Two Worlds

Definition Notation:

Theoretical Background

WebAssign

Example 1

Warning All Improper integrals are defined by limits. In particular, do not use the following notation:

Theorem 4.1

Property

Example 2

Example 3

Warning There is no such rule as:

Example 4 (Piecewise Defined Functions)

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