100% satisfaction guarantee Immediately available after payment Both online and in PDF No strings attached
logo-home
Previously searched by you
Previously searched by you
logo
Summary Differential Equations with Boundary-Value Problems, Exercise 7.1, 7 to 10 R55,73   Add to cart
Quickly navigate to
Preview
  2.  
  3. Transformada De Funciones
  4.  
  5. Transformada de Funciones

Summary

Summary Differential Equations with Boundary-Value Problems, Exercise 7.1, 7 to 10
 6 views  0 purchase
  • Course
  • Transformada de Funciones
  • Institution
  • Transformada De Funciones
  • Book
  • Differential Equations with Boundary-Value Problems

Proposed solutions for exercises 7.1 from 7 to 10. All of them are solved by using the definition of the Laplace transform.

Preview 2 out of 5  pages

Document information

  • No
  • Problems 7.1
  • August 15, 2022
  • 5
  • 2022/2023
  • Summary

Subjects

  • laplace transform
  • differential equations
  • dennis z gill

Connected book

book image

Book Title:

Author(s):

  • Edition:
  • ISBN:
  • Edition:

More summaries for

  • Differential Equations with Boundary-Value Problems, Exercise 7.1, 11 to 18
  • Differential Equations with Boundary-Value Problems, Exercise 7.1, 1 to 6
  • WTW 256 Lecture Notes
All for this textbook (9)

Written for

  • Transformada de Funciones
All documents for this subject (1)

Seller

avatar-seller
leomilenio1

Content preview

Dennis G. Zill - Differential Equations with
Boundary-Value Problems, Exercise 7.1. From 11 to 18
Leonardo J. Perez Gomez
14 de agosto de 2022


1. Let the figure 1


2.00



1.75



1.50



1.25
f(t)




1.00



0.75



0.50



0.25



0.00


0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00
t




Figura 1: Problem 7



0 0≤t<1
∴f (t) =
f1 (t) t≥1
If f1 (t) = t

0 0≤t<1
∴f (t) =
t t≥1
Z ∞ Z 1 Z ∞
∴ L {f (t)} = −st
e f (t)dt = −st
e (0)dt + e−st (t)dt
Z0 ∞ 0 1

= e−st (t)dt
1




1

, e−st (t)dt
R
1.

dv = e−st dt e−st t e−st
Z Z
u=t −st
−st ∴ e dt = − − − dt
du = dt v = − e s s s
e−st t 1 e−st t 1
Z  −st 
−st e
=− + e dt = − + −
s s s s s
−st −st
 
e t e t 1
=− − 2 = e−st − − 2
s s s s

  b
t 1
∴ L {f (t)} = lı́m e − − 2 −st
b→∞ s s 1
 
−s 1 1
=e − − 2
s s

2. Let the figure 2


4.0



3.5



3.0



2.5
f(t)




2.0



1.5



1.0



0.5



0.0


0.0 0.5 1.0 1.5 2.0 2.5 3.0
t




Figura 2: Problem 8



0 0≤t<1
∴ f (t) =
f1 (t) t≥1
If f1 (t) = 2t − 2

0 0≤t<1
∴ f (t) =
2t − 2 t≥1
Z 1 Z ∞ Z ∞
∴ L {f (t)} = e −st
(0)dt + e−st
(2(t − 1))dt = e−st (2(t − 1))dt
0 1 1




2

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

Guaranteed quality through customer reviews

Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.

Quick and easy check-out

Quick and easy check-out

You can quickly pay through EFT, credit card or Stuvia-credit for the summaries. There is no membership needed.

Focus on what matters

Focus on what matters

Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!

Frequently asked questions

What do I get when I buy this document?

You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.

Satisfaction guarantee: how does it work?

Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.

Who am I buying this summary from?

Stuvia is a marketplace, so you are not buying this document from us, but from seller leomilenio1. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy this summary for R55,73. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

72042 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy summaries for 14 years now

Start selling

Recently viewed by you

Exam (elaborations) ·

(0)

Swaps - Introduction Questions & Answers 2024.

R55,73
  • (0)
  Buy now