Partial Dierential Equations Math 442 C13/C14 Fall 2009 Homework 3 Solutions
1. Here we will prove that solutions to the heat equation satisfy (some of) the invariance principles mentioned in class, or in the book in 2.4. That is, if u(x, t) is a solution
Mathematics 346 Section [ A01 CRN 22106 ]
COURSE OUTLINE January, 2017
INSTRUCTOR
Dr. Robert Steacy ([email protected])
DTB A521, Ph: 721-7440. Please note that the phone does not have a
message waiting feature, so if you are asked to leave a message please
MATHEMATICS 346 Spring 2017
REQUIRED PROBLEM LIST
TEXT
Elementary Applied Partial Differential Equations
by Richard Haberman (Fifth Edition, 2013, or you may use Fourth Edition, 2004).
Section
Problem Numbers
1.2
1.3
1.4
1.5
8,9
1, 2, 3
1, 2, 3*(challenge
MATHEMATICS 346 Homework #1
Due Thursday, January 19, 2017 at the start of class.
No late assignments will be accepted.
Instructor: Dr. R. Steacy
Total marks: 20. Note: Please be sure to include all necessary steps in your solutions.
All questions from Ha
Partial Dierential Equations Math 442 C13/C14 Fall 2009 Homework 2 due September 18
1. (Strauss 2.1.1.) Solve utt = c2 uxx , u(x, 0) = ex , ut (x, 0) = sin x. Solution: We use dAlemberts formula with (x) = ex , Then we have
x+ct
(x) = sin x.
sin s ds = c
Partial Dierential Equations Math 442 C13/C14 Fall 2009 Homework 1 Solutions
1. Determine which of the following operators are linear: (a) Lu = uxx + uxy (b) Lu = uux (c) Lu = 4x2 uy 4y 2 uyy Solution: compute: (a) L(u + v ) = (u + v )xx + (u + v )xy = ux
Partial Dierential Equations Math 442 C13/C14 Fall 2009 Homework 6 Solutions
1. Let D = cfw_(x, y ) : x2 + y 2 < 4, and solve u = 0, in D, u = 3 2 cos ,
r = 2.
Solution: Using the formula generated in class, we have that u(r, ) = A0 + rn (An cos(n) + Bn s
Partial Dierential Equations Math 442 C13/C14 Fall 2009 Homework 5 Solutions
1. (Strauss 5.2.2.) Show that cos(x) + cos(x) is periodic if is a rational number and compute its period. What happens if is not rational? Solution: Let us rst notice that if f,
Partial Dierential Equations Math 442 C13/C14 Fall 2009 Homework 4 due October 9
1. Consider the boundary value problem A + A = 0, A (0) + aA(0) = 0, A(L) = 0.
(a) Show that if a < 0, then there is no negative eigenvalue. (b) Under which conditions is the
MATHEMATICS 346
COURSE SCHEDULE
Department of Mathematics and Statistics
University of Victoria
January, 2017
Week
Dates
Holiday?
Lecture
(Haberman, Applied PDE)
Hwk Due or Test?
Always Thursday class
5th or 4th ed.
0
1
2
3
4
5
6
7
8
9
10
11
12
13
Jan. 4