Post on 09-Jun-2019
5.3
Math 3331 Differential Equations5.3 The Inverse Laplace Transform
Jiwen He
Department of Mathematics, University of Houston
jiwenhe@math.uh.edumath.uh.edu/∼jiwenhe/math3331
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5.3 Basic Definition In-Class Exercises Partial Fractions Examples Examples
5.3 The Inverse Laplace Transform
Basic Definition
Uniqueness TheoremL-Transform PairsDefinition of the Inverse Laplace TransformTable of Inverse L-Transform
Worked out Examples from Exercises:
2, 4, 6, 7, 9, 11, 14, 15, 17
Partial Fractions
Inverse L-Transform of Rational FunctionsSimple Root: (m = 1)Multiple Root: (m > 1)Examples
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5.3 Basic Definition In-Class Exercises Partial Fractions Examples Examples
Uniqueness Theorem
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5.3 Basic Definition In-Class Exercises Partial Fractions Examples Examples
L-Transform Pairs
F (s) = L(f )(s) = L{f (t)}(s), s > a
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5.3 Basic Definition In-Class Exercises Partial Fractions Examples Examples
Definition of the Inverse Laplace Transform
F = L(f ) ⇔ f = L−1(F )
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5.3 Basic Definition In-Class Exercises Partial Fractions Examples Examples
Table of Inverse L-Transform
F = L(f ) ⇔ f = L−1(F )
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5.3 Basic Definition In-Class Exercises Partial Fractions Examples Examples
Exercise 5.3.2
2. Compute the inverse Laplace transform of Y (s) = 13−5s .
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5.3 Basic Definition In-Class Exercises Partial Fractions Examples Examples
Exercise 5.3.4
4. Compute the inverse Laplace transform of Y (s) = 5ss2+9
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5.3 Basic Definition In-Class Exercises Partial Fractions Examples Examples
Exercise 5.3.6
6. Compute the inverse Laplace transform of Y (s) = 23s4
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5.3 Basic Definition In-Class Exercises Partial Fractions Examples Examples
Exercise 5.3.7
7. Compute the inverse Laplace transform of Y (s) = 3s+2s2+25
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5.3 Basic Definition In-Class Exercises Partial Fractions Examples Examples
Exercise 5.3.9
9. Compute the inverse Laplace transform of Y (s) = 13−4s + 3−2s
s2+49
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5.3 Basic Definition In-Class Exercises Partial Fractions Examples Examples
Exercise 5.3.11
11. Compute the inverse Laplace transform of Y (s) = 5(s+2)3
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5.3 Basic Definition In-Class Exercises Partial Fractions Examples Examples
Exercise 5.3.14
14. Compute the inverse Laplace transform of Y (s) = 4(s−1)(s−1)2+4
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5.3 Basic Definition In-Class Exercises Partial Fractions Examples Examples
Exercise 5.3.15
15. Compute the inverse Laplace transform of Y (s) = 2s−3(s−1)2+5
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5.3 Basic Definition In-Class Exercises Partial Fractions Examples Examples
Exercise 5.3.17
17. Compute the inverse Laplace transform of Y (s) = 3s+2s2+4s+29
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5.3 Basic Definition In-Class Exercises Partial Fractions Examples Examples
Inverse L-Transform of Rational Functions
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5.3 Basic Definition In-Class Exercises Partial Fractions Examples Examples
Simple Root: (m = 1)
Simple Root: (m = 1)
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5.3 Basic Definition In-Class Exercises Partial Fractions Examples Examples
Multiple Root: (m > 1)
Multiple Root: (m > 1)
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5.3 Basic Definition In-Class Exercises Partial Fractions Examples Examples
Example 1
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5.3 Basic Definition In-Class Exercises Partial Fractions Examples Examples
Example 1(cont.)
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5.3 Basic Definition In-Class Exercises Partial Fractions Examples Examples
Example 2
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5.3 Basic Definition In-Class Exercises Partial Fractions Examples Examples
Example 3
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5.3 Basic Definition In-Class Exercises Partial Fractions Examples Examples
Example 4
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5.3 Basic Definition In-Class Exercises Partial Fractions Examples Examples
Example 5
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5.3 Basic Definition In-Class Exercises Partial Fractions Examples Examples
Example 6
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