Math 257/316 Assignment 8, Due Friday Nov 8 th
Problem 1: (Do not hand in) The motion of a string subject to a gravitational
load satisfies the following initial-boundary value problem:
utt = c2 uxx g
Math 257/316 Assignment 6
Due: Friday, October 29
1.
(a) Find the solution (in series form) of the following heat conduction problem with homogeneous Dirichlet boundary conditions:
ut = 2uxx , (0 < x
Math 257/316, Midterm 1, Section 101/102
8 October 2010
Last Name:
First Name:
Student Number:
Instructions. The exam lasts 55 minutes. Calculators are not allowed. A formula sheet is attached.
1
1. C
Math 257/316 Assignment 5
Due: Friday, October 22
1.
(a) Compute the Fourier Sine Series of f (x) = x3 x on [0, 1].
(b) Evaluate the series found in (a) at x = 1/2 to obtain
1
1
1
3
= 1 3 + 3 3 + .
32
Math 257-316: Assignment 22017
Note: This assignment is due at the beginning of class of Wednesday, September 20th.
[Power series solutions of ODE]
1. [Will be marked] Consider the ODE: (1 + x3 )y 00
c Anthony Peirce.
Introductory lecture notes on Partial Dierential Equations -
Not to be copied, used, or revised without explicit written permission from the copyright owner.
1
Lecture 2: Series sol
dx =
0.1
This example illustrates the evaluation of the Fourier Series for Example 10.1 Page 4 of the class n
x
=
0
0.1
0.2
0.3
0.4
0.5
f(x) =
0
0.2
0.4
0.6
0.8
1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Math 257/316 Assignment 1, 2017 (solutions)
Due Wednesday September 13 IN CLASS
Problem 1: (ODE Review)Find the general solutions of the following equations:
xC 1
a. 1 x 2 y 2xy cot x, Exact solution
Math 257-3162017 Assignment 5
The first midterm exam is on Wednesday Oct. 18 th - practice exams on web site.
You need not hand in this assignment the solutions will be posted.
[Separation of variab
Math 257/316 (sec. 103) Assignment 7
Due: Wednesday, November 10
1. There is a gas leak at one end of a long corridor 0 < x < 1. The concentration of gas satises
ut = uxx ,
0<x<1,
with boundary condit
ASMSW 4 W5
04va Q) W 03 Maria. [945%
6194 1e W8. HL i5 jVavvij
M '1. ML Wt M 62H)=Cek. We 524/4.
5mm, M Q(9)=3000 M 0(5)::0000. Mir-M
Cemtsooo (I)
Ce:+ '3 {3)
Dwight; {25 57(1), m, mm, e3*=5-=
M257/316 SolutionsAssignment 4
UBC M257/316 Resources (c) 2014 by Philip D. Loewen
1. (a) Its hard work to nd eigenvectors, but its pretty easy to test a specic vector
to see if it satises the dening
M257/316 SolutionsAssignment 3
UBC M257/316 Resources (c) 2014 by Philip D. Loewen
1. The function y satises the given dierential equation if and only if
ty ( t) + (4t 1)y ( t) + 20t3/2 y( t) = 0,
t
M257/316 SolutionsAssignment 1
UBC M257/316 Resources (c) 2014 by Philip D. Loewen
1
for each constant z satisfying |z| < 1, and that the
1z
k=0
series diverges whenever z obeys |z| 1. Careful account
M257/316 SolutionsAssignment 2
UBC M257/316 Resources (c) 2014 by Philip D. Loewen
1. Since the initial data are given at the point x = 0, we use that point as the expansion
centre for the desired ser
Name 30 0
UBC Student Number 3' I 2
Signature
The University of British Columbia
Midterm Examination 19 June 2014
Mathematics 257/316
Dieiential Equations II
Closed book examination T