# L74 - Fall 2003 Math 308/501–502 7 Laplace Transforms 7.4...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Fall 2003 Math 308/501–502 7 Laplace Transforms 7.4 Inverse Laplace Transform Mon, 13/Oct c 2003, Art Belmonte Summary Theorem If f and g are continuous functions whose Laplace transforms are such that L { f } ( s ) = L { g } ( s ) for s > a, then f ( t ) = g ( t ) for all t > . Definition For a continuous function f of exponential order whose Laplace transform is F , we call f the inverse Laplace transform of F and write f = L- 1 { F } . (The preceding theorem is what makes this definition possible.) Linearity Property For constants α and β and inverse Laplace transforms L- 1 { F } = f and L- 1 { G } = g , we have L- 1 { α F + β G } = α L- 1 { F } + β L- 1 { G } = α f + β g Short table of [inverse] Laplace transforms # f ( t ) = L- 1 { F } ( t ) L { f } ( s ) = F ( s ) 1. 1 1 s , s > 2. t n n ! s n + 1 , s > 3. sin at a s 2 + a 2 , s > 4. cos at s s 2 + a 2 , s > 5. e at 1 s- a , s > a 6. e at sin bt b ( s- a ) 2 + b 2 , s > a 7. e at cos bt s- a ( s- a ) 2 + b 2 , s > a 8. t n e at n ! ( s- a ) n + 1 , s > a Notes When computing inverse Laplace transforms strictly with a pencil, we typically use partial fraction decomposition, completing the square, and algebraic manipulation before finally employing table lookup. On the other hand, the MATLAB Symbolic Math Toolbox (SMT) command ilaplace computes inverse Laplace transforms at...
View Full Document

## This note was uploaded on 03/29/2008 for the course MATH 308 taught by Professor Comech during the Spring '08 term at Texas A&M.

### Page1 / 3

L74 - Fall 2003 Math 308/501–502 7 Laplace Transforms 7.4...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online