393_pdfsam_math 54 differential equation solutions odd

# 393_pdfsam_math 54 differential equation solutions odd -...

This preview shows page 1. Sign up to view the full content.

CHAPTER 7: Laplace Transforms EXERCISES 7.2: Definition of the Laplace Transform, page 359 1. For s > 0, using Definition 1 on page 351 and integration by parts, we compute L { t } ( s ) = 0 e st t dt = lim N →∞ N 0 e st t dt = lim N →∞ N 0 t d e st s = lim N →∞ te st s N 0 + 1 s N 0 e st dt = lim N →∞ te st s N 0 e st s 2 N 0 = lim N →∞ Ne sN s + 0 e sN s 2 + 1 s 2 = 1 s 2 because, for s > 0, e sN 0 and Ne sN = N/e sN 0 as N → ∞ . 3. For s > 6, we have L { t } ( s ) = 0 e st e 6 t dt = 0 e (6 s ) t dt = lim N →∞ N 0 e (6 s ) t dt = lim N →∞ e (6 s ) t 6 s N 0 = lim N →∞ e (6 s ) N 6 s 1 6 s = 0 1 6 s = 1 s
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### 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