Math 257/316 PDE Assignment 4
Due in class on Wednesday October 4, 2017
1. Separation of variables: Determine whether the method of separation of variables
can be used to replace the following PDEs by a pair of ODEs. If so, find the equations.
(a) x2 uxx
Introductory lecture notes on Partial Dierential Equations  by Anthony Peirce UBC
1
Lecture 30: SturmLiouville Problems involving the
CauchyEuler Equation  Applications
(Compiled 16 November 2012)
In this lecture we look at eigenvalue problems involvi
1
Introductory lecture notes on Partial Dierential Equations  by Anthony Peirce UBC
Lecture 27: Wedges with cutouts, Dirichlet and Neumann
problems on Circular domains
(Compiled 7 November 2012)
In this lecture we continue with the solution of Laplaces
1
Introductory lecture notes on Partial Dierential Equations  by Anthony Peirce UBC
Lecture 25: More Rectangular Domains: Neumann
Problems, mixed BC, and semiinnite strip problems
(Compiled 30 October 2012)
In this lecture we Proceed with the solution o
1
Introductory lecture notes on Partial Dierential Equations  by Anthony Peirce UBC
Lecture 24: Laplaces Equation
(Compiled 30 October 2012)
In this lecture we start our study of Laplaces equation, which represents the steady state of a eld that depends
1
Introductory lecture notes on Partial Dierential Equations  by Anthony Peirce UBC
Lecture 18: Heat Conduction Problems with
timeindependent inhomogeneous BC (Cont.)
(Compiled 11 October 2012)
In this lecture we continue to investigate heat conduction
1
Introductory lecture notes on Partial Dierential Equations  by Anthony Peirce UBC
Lecture 19: Heat conduction with distributed sources/sinks
(Compiled 11 October 2012)
In this lecture we consider heat conduction problems in which there is a distributed
1
Introductory lecture notes on Partial Dierential Equations  by Anthony Peirce UBC
Lecture 21: The one dimensional Wave Equation:
DAlemberts Solution
(Compiled 25 October 2012)
In this lecture we discuss the one dimensional wave equation. We review some
1
Introductory lecture notes on Partial Dierential Equations  by Anthony Peirce UBC
Lecture 23: The wave equation on nite domains  solution
by separation of variables
(Compiled 25 October 2012)
In this lecture we discuss the solution of the one dimensio
1
Introductory lecture notes on Partial Dierential Equations  by Anthony Peirce UBC
Lecture 22: Interpretating DAlemberts Solution in
SpaceTime: characteristics, regions of inuence and
domains of dependence
(Compiled 25 October 2012)
In this lecture we
Math 257/316, Midterm 2, Section 103
November 20, 2009
Instructions. The duration of the exam is 55 minutes. Answer all questions. Calculators are not allowed.
Maximum score 100.
1. Solve the following inhomogeneous initial boundary value problem:
ut
ux (
Math 257/316, Midterm 2, Section 103
17 November 2006
Instructions. The duration of the exam is 55 minutes. Answer all questions. Calculators are not allowed.
Maximum score 100.
1. Let f (x) be a function that has a period of 2 having the values:
0 when x
Math 257/316, Midterm 2, Section 101
17 November 2008
Instructions. The duration of the exam is 55 minutes. Answer all questions. Calculators are not allowed.
Maximum score 100.
1. Solve the following inhomogeneous initial boundary value problem for the h
Introductory lecture notes on Partial Dierential Equations  by Anthony Peirce UBC
Lecture 28: SturmLiouville Boundary Value Problems
(Compiled 7 November 2012)
In this lecture we abstract the eigenvalue problems that we have found so useful thus far for
1
Introductory lecture notes on Partial Dierential Equations  by Anthony Peirce UBC
Lecture 26: Circular domains
(Compiled 30 October 2012)
In this lecture we consider the solution of Laplaces equations on domains that have a boundary that has at least o
Math 257/316 Assignment 32017
Due Wednesday September 27 th in class
Problem 1: Find all singular points of the followings equations and
determine whether each of them is regular or irregular. For each regular
singular point, determine the indicial equati
Math 257/316 Assignment 1, 2017
Due Wednesday September 13 IN CLASS
Problem 1: (ODE Review)Find the general solutions of the following
equations:
a. 1 + x2 y 0 + 2xy = cot x
b. xy 0 = y ln y
c. y 00 5y0 + 4y = 0
d. 4y 00 + 4y0 + 2y = 0, y(0) = 2, y 0 (0)
Math 257/316, Quiz 5: June 20" 2017
Name: Student number:
Instructions: Test duration 40 minutes, closed book, 0.5 lettersized formula
sheet allowed
1. Answer all questions.
2. Write your answer on the same sheet as the question, or on the back if neede
Be sure that this examination has 20 pages including this cover
The University of British Columbia
Sessional Examinations  December 2016
Mathematics 257/316
Partial Dierential Equations
Time: 2 12 hours
Closed book examination
Name
Signature
Student Numb
Name
Signature
UBC Student Number
The University of British Columbia
Final Examination 24 April 2014
Mathematics 257/316
Partial Differential Equations/Elementary Differential Equations II
Closed book examination
Time: 150 minutes
Special Instructions:
To
The University of British Columbia
Final Examination  12 noon December 17, 2015
Mathematics 257/316
All Sections
Closed book examination
Last Name
Time: 2.5 hours
First
Signature
Student Number
Special Instructions:
No books, notes, or calculators are al
Math 257/316 Section 201
Total = 50 points
Midterm 2
Mar 8
[There are 2 questions.]
Problem 1.
a) [10 points] For the function f (x) = x2 on [0, 1], sketch (roughly) its odd, and even
2periodic extensions, and find its Fourier sine series, and its Fourie
Math 257/316 Section 201
Midterm 1
Total = 50 points
February 1
[There are 2 questions.]
Problem 1. Consider the second order differential equation:
2x2 y 00 + (3x x2 )y 0 y = 0.
Find the first three terms of a (nonzero) solution, in the form of a series
Math 257/316, Section 101, Midterm 1
14 October 2011
Instructions. The exam lasts 50 minutes. Calculators are not allowed. A formula sheet is attached.
1. Consider the ODE
2x2 y 00 + (3x + x2 )y 0 y = 0.
(a) Verify that the point x = 0 is a regular singul
Math 257/316, Midterm 2, Section 101
7 November 2011
Instructions. The exam lasts 50 minutes. Calculators are not allowed. A formula sheet is attached.
1. Consider the following problem for the heat equation with a source term, and nonhomogeneous Neumann
The University of British Columbia
Final Examination  April, 2007
Mathematics 257/316
Closed book examination
Time: 2.5 hours
Instructor Name:
Last Name:
, First:
Signature
Student Number
Special Instructions:
 Be sure that this examination has 9 pages.
The University of British Columbia
Final Examination  December 5, 2008
Mathematics 257/316
All Sections
Closed book examination
Last Name:
(USE CAPITALS)
Student Number
Time: 2.5 hours
, First:
Signature
Instructors Name & Section
Special Instructions:
