sdsuedu i Lecture Notes Laplace Transforms Part A 2526 Introduction Laplace

# Sdsuedu i lecture notes laplace transforms part a

• 7

This preview shows page 7 out of 7 pages.

[email protected] i Lecture Notes – Laplace Transforms: Part A — (25/26) Introduction Laplace Transforms Short Table of Laplace Transforms Properties of Laplace Transform Laplace Transform of Derivatives More Laplace Transforms Theorem Suppose that f is (i) piecewise continuous on any interval 0 t A , and (ii) has exponential order with exponent a . Then for any positive integer L [ t n f ( t )] = ( - 1) n F ( n ) ( s ) , s > a. Proof: F ( n ) ( s ) = d n ds n Z 0 e - st f ( t ) dt = Z 0 n ∂s n ( e - st ) f ( t ) dt = Z 0 ( - t ) n e - st f ( t ) dt = ( - 1) n Z 0 t n e - st f ( t ) dt = ( - 1) n L [ t n f ( t )] Corollary: For any integer, n 0, L [ t n ] = n ! s n +1 , s > 0 . Joseph M. Mahaffy, h [email protected] i Lecture Notes – Laplace Transforms: Part A — (26/26)
• Fall '08
• staff

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern