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
APM2611 Assignment 4 (COMPLETE ANSWERS) 2024 - DUE 25 September 2024 R48,65   Add to cart
Quickly navigate to
Preview
  2.  
  3. University Of South Africa
  4.  
  5. Differential Equations - APM2611 (APM2611)

Exam (elaborations)

APM2611 Assignment 4 (COMPLETE ANSWERS) 2024 - DUE 25 September 2024
 15 views  1 purchase

APM2611 Assignment 4 (COMPLETE ANSWERS) 2024 - DUE 25 September 2024 ;100 % TRUSTED workings, explanations and solutions. For assistance call or W.h.a.t.s.a.p.p us on ...(.+.2.5.4.7.7.9.5.4.0.1.3.2)........... Question 1 1. Find the radius and interval of convergence of the following series: �...

[Show more]

Preview 3 out of 22  pages

Document information

  • June 12, 2024
  • 22
  • 2023/2024
  • Exam (elaborations)
  • Questions & answers

Subjects

  • apm2611 assignment 4 2024 due 25 september 2024

Connected book

book image

Book Title:

Author(s):

  • Edition:
  • ISBN:
  • Edition:

More summaries for

All for this textbook (12)

Written for

All documents for this subject (4)

Seller

avatar-seller
LIBRARYpro

Reviews received

Content preview

APM2611
ASSIGNMENT 4 2024
UNIQUE NO.
DUE DATE: 25 SEPTEMBER 2024

, APM2611/101/0/2024


ASSIGNMENT 04
Due date: Wednesday, 25 September 2024
-

ONLY FOR YEAR MODULE

Series solutions, Laplace transforms and Fourier series, solving PDE’s by separation of
variables.

Answer all the questions. Show all your own and personalized workings, you get ZERO
to a question if we see that you have copied someone’s else solution word by word.

If you choose to submit via myUnisa, note that only PDF files will be accepted.

Note that all the questions will be marked therefore, it is highly recommended to attempt all of them.

Question 1


1. Find the radius and interval of convergence of the following series:
X∞ (−1) n−1 x 2n−1

n=1
(2n − 1)!

2. Rewrite the expression below as a single power series:
X∞ X∞
cn+1 x n−2 − 4cn x n−1 .
n=2 n=1


3. Use the power series method to solve the initialvalue problem
00 0
(x + 1)y − (2 − x)y + y = 0, y(0) = 2, y0(0) = −1;

where c0 and c1 are given by the initial conditions.

4. Use the power series methodPto solve the initialvalue problem.In particular, find c 0, c1 , c2, c3
and c4 in the equation y(x) = ∞n=0 cn x n .

y00− x 2y = 0; y(0) = 3, y0(0) = 7.



Question 2

Using the method of separation of variables, find a solution for the following PDEs:

1.
∂ 2u ∂u
=4 .
∂x 2 ∂y



19

, 2.
∂u ∂u
= .
∂x ∂y

3. the initial value problem:

y00+ 4y 0 + 3y = 1 − U(y − 2) − U(t − 4) + U(t − 6),
y(0) = 0, y0(0) = 0.



Question 3

Compute the following Fourier series:

1. Fourier series for f (x) = x 2
on [−π, π].

2. Sine series for f (x) = x 2 on [0, π].

3. Cosine series for f (x) = x 2 on [0, π].


Question 4

Using the method of separation of variables, find a solution for the following PDEs:
∂ 2u ∂u
1. = .
∂x 2 ∂y
∂u ∂u
2. =4 .
∂x ∂y


Question 5

Find the temperature u(x, t) in a rod of length L if the initial temperature is f (x) throughout and if
the ends x = 0 and x = L are insulated.


– End of assignment –




20

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 LIBRARYpro. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy this summary for R48,65. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

72841 documents were sold in the last 30 days

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

Start selling
R48,65  1x  sold
  • (0)
  Buy now