EXAM 2
Math 4163
3-29-13
Name
Instructions Work all of the following problems in the space provided. If there is not enough room, you may
write on the back sides of the pages. Give thorough explanations to receive full credit.
1. (25 points) Solve Laplace
Math 4163 Review for Exam 1
Exam 2 covers sections 2.3, 2.4, and part of 2.5 of the text. Some of the terminology from chapters 1 and
section 2.2 will also be useful to know (see below for details.) The relevant assignments are Assignments 1,
2, and 3.
Be
Math 4163 Review for Final Exam
The nal exam is comprehensive, though it will be somewhat weighted toward the latter half of the course.
It will be about one and a half times the length of the midterms exams. To see what material from the
text will be cov
SUPPLEMENTARY PROBLEMS
MATH 4163, INTRODUCTION TO PDE
1. FOURIER SERIES
_1.1. Are the following pairs of functions orthogonal over the interval indicated?
a. 1 and :c, {2, 2]
b. 1 and 2:, [0, 2]
c. sinz and sin 2:12,. [0, 1r]
d. sins: and cosz, [0,
Math 4163
Review for Exam 1
The rst exam will cover sections 2.1, 2.2, all of 2.3, 2.4.1, and 2.5.1 of the text. There are some
suggestions below as to how to review the text. You should also go over the two homework assignments and
the quiz, and maybe tr
Solution to problem 2.5.1(b)
2
2
1
1
Substituting the separated solution u(x, y ) = h(x)(y ) into Laplaces equation gives h d h = d .
dx2
dy 2
Both sides of this equation equal a constant, but before choosing a name for this constant we should pause
and i
Math 4163 Spring 2013
Review for Exam 2
Exam 2 covers sections 2.5.2, 3.2, 3.3, 4.4, 5.3, and 5.8 of the text. The relevant assignments are Assignments
4, 5, 6, and 7. Here is a study guide for the material we covered in these sections.
2.5.2. Laplaces eq
Solutions to Problems on Assignment 9
4.4.2(c) The PDE we have to solve is
0
2u
2u
= T0 2 + u,
t2
x
where 0 , T0 , are constants, and < 0.
First nd separated solutions which satisfy the boundary conditions: putting u(x, t) = (x)h(t), into
the PDE and divi
Review for Second Exam
The second exam will cover sections 1.5, 2.5, 3.1, 3.2, and 3.3 of the text. The relevant
assignments are Assignments 4, 5, and 6.
1.5. This section re-does the material from sections 1.1 and 1.2 in higher dimensions. You
should alr
Review for Final Exam
The nal exam is comprehensive, covering the material from all the assignments (1 to 9), and
all the sections of the book weve covered so far (1.1 through 1.5, 2.1 through 2.5, 3.1 through 3.5,
and 4.1 through 4.4). To review for it,
Math 4163 Spring 2013
Review for Exam 3
Exam 3 covers portions of sections 7.2, 7.3, 7.4, 7.6, 7.7, and 7.8 of the text. The relevant assignments are
Assignments 8 and 9. Here is a study guide for the material we covered in these sections.
7.2. Separation
Math 4163 Spring 2013
Review for Final Exam
The nal exam is comprehensive. To review for it, you can use the review sheets for the rst three exams to
study the material in sections 2.3, 2.4, 2.5, 3.2, 3.3, 4.4, 5.3, 5.8, 7.2, 7.3, 7.4, 7.6, 7.7, and 7.8 o
Math 4163 Review for Exam 2
Exam 2 covers sections 2.5.2, 3.2, 3.3, 4.4, 5.3, and 5.8 of the text. The relevant assignments are Assignments
3, 4, and 5. Here is a study guide for the material we covered in these sections.
2.5.2. Laplaces equation for a ci