MTH 649 SYLLABUS
SPRING 2009
REVISED 3/31/09
Instructor: Prof. C. O. Bloom
E-Mail: cobloom@acsu.buffalo.edu
Office: 230 Mathematics Building
Office Hours: Tuesday. 2:00 - 3:00 PM, Thursday. 2:00 - 3:00 PM, and
by appointment
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Lectures: Tuesday, Thursday, 9:30-10:50 A.M., 250 MATH
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Text #1(Required):
Title: Partial Differential Equations (Graduate Studies in Mathematics, Vol.
19)
Author: Lawrence C. Evans
Publisher: American Mathematics Society (1998)
Text #2(Required):
Title: Introduction to Partial Differential Equations with Applications
Author: Zachmanoglou & Thoe
Publisher: Dover
Text #3(Supplementary):
Title: Partial Differential Equations of Applied Mathematics
Author: Erich Zauderer
Publisher: Wiley-Interscience (1983)
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From Text 1 selected Topics from the following list:
1. Introduction
Part I: Representation Formulas for Solutions
2. Four Important Linear PDE
3. Nonlinear First Order PDE
4. Other Ways to Represent Solutions
From Text 2 selected Topics from the following list:
Chapter 1- Sections: 1.1-1. 4
Chapter 2- Sections: 2.1-2.4
Chapter 3 -Sections: 3.1-3.4
Chapter 6-Sections: 6.1-6.5
Chapter 7- Sections: 7.1-7.13
Chapter 8-Sections: 8.1-8.8
Chapter 9-Sections: 9.1-9.4
Chapter 10-Sections: 10.1-10.4
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Grading: Your final grade will be computed in the following way.
1. Homework problems will be given regularly in class. They will also be posted on
the website. The assignments will be collected and selected assignments will be
graded.
2. There will be one midterm exam (tentative date: Monday, March 3), and one final
exam (date TBA). Your course grade will be determined as follows: 25% homework
+ 25% midterm exam + 50% final exam
Letter grades (plus and minus) will be given.
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Tests
Date Due
Time and Location
FINAL EXAM
Read
Text 1: Introduction, Sections 1.1—1.3
Text 1: Appendix A.2-A.6
Text 2: Chap. 6, Sections 1-5 (Eqs. Of Math
Physics)
Assigned
Problem
Date
Assigned
Text 1:
Text 2: 1.1-1.3,
p.173
(Laplace’s
Equation)
Text 2: 2.1-2.5,
2.7 pp. 178-9
1/13/09
(Laplace’s
Equation)
Text 2: 3.2, 3.3,
3.5 p.186
(Laplace’s
Equation)
Submit for
Grading
Text2:
Prob.2.7, pp.
178-9
Due 1/22/09
(Tues.)
Text 1:
Text 2: 1.1-1.3,
p.173
(Laplace’s
Equation)
Text 1: Chap. 2, Section 2.1, 2.2
Text 1: Text 2: 2.1-2.5,
Appendix C.1-C.3
Text 2.7 pp. 178-9
1/22/09
2: Chap. 7, Sections 1-4 (Laplace’s Equation) (Laplace’s
Equation)
Text 2: 3.2, 3.3,
3.5 p.186
(Laplace’s
Equation)
Text 2:
Prob. 3.2,
p.186
Due 1/27/09
Text 1:Chap. 2, Section 2.1, 2.2
Text 1: Text 1:
Appendix C.1-C.4
Text Text 2: 1.1-1.3,
1/27/09
2: Chap. 7, Sections 4-7, 9 (Laplace’s
p.173(Laplace’s
Text 2:
Prob. 9.1,
p.226
Equation)
Text 1:Chap. 2, Section 2.1, 2.2
Text 1: Appendix C.1-C.4
Text 2: Chap. 7, Sections 4-7, 9 (Laplace’s
Equation)
Equation)
Text 2: 2.1-2.5,
2.7 pp. 178-9
(Laplace’s
Equation)
Text 2: 3.2, 3.3,
3.5 p.186
(Laplace’s
Equation)
Text 2: 5.1, 5.2,
5.4, 5.5, 5.6, 5.7
(Laplace’s
Equation)
Text 1:
Text 2: 1.1-1.3,
p.173
(Laplace’s
Equation)
Text 2: 2.1-2.5,
2.7 pp. 178-9
(Laplace’s
Equation)
Text 2: 3.2, 3.3,
3.5 p.186
(Laplace’s
Equation)
Text 2: 5.1, 5.2,
5.4, 5.5, 5.6, 5.7
pp. 196-197
(Laplace’s
Equation)
Due 2/3/09
2/05/09
Homework
problem #4
Due 2/10/09
Text 2 (Heat
Equation):
Sect. 9.1: Prob.
#1.1, 1.6, 1.7 p.
335-336
Text 2 (Heat
Equation):
Sect. 9.2:
Prob.# 2.9, 2.10
Text 2: Chap. 9 (Heat Equation): Sect. 9.1, 9.2,
p. 343
9.3
Text 2 (Heat
Equation):
Sect. 9.3: Prob. 2/19/09
# 3.1- 3.9, 3.12,
3.13, 3.14 p.
Text 1: Chap.2 (Heat Equation): Sect. 2.3
347-348
Text 2(Heat
Equation): 4.1,
4.3, 4.5, 4.6,
4.14, 4.15 p.
351-353
Homework
Assignment
#5
Text 2(Heat
Equation):
Prob. # 3.103.12, p. 348
Due 2/24/09
Text 1: Sect.
2.5 10-12 p. 87
Text 2: Chap. 9 (Heat Equation), Sect. 9.4
Text 1: Chap. 2 (Heat Equation):
Section 2.3
Text 2 (Heat
Equation):
Sect. 9.4: Prob.
# 4.1, 4.2, 4.3,
4.4 p.351
Homework
Assignment
2/24/09
#5
Text 2(Heat
Equation):
Prob. # 3.93.12, p. 347
Due 2/26/09
Text 1: Chap. 2, Section 2.4 (Wave Equation)
Text 2: Chap. 8, Section 8.1, 8.2, 8.3, 8.4, 8.5
(Wave Equation)









Text 1: Sect.
2.5 probs. 15,
17, 18
Text 2: 1.1, 1.5,
1.6, 1.8 p. 270
Homework
(Wave
Problem #6
Equation)
Text 2: Prob.
Text 2: 3.1-3.4
7.1, pp. 306pp. 279-280
307 (Wave
(Wave
Equation)
Equation)
Due 3/17/09
Text 2: 4.7, 4.8
Homework
p. 284 (Wave
3/03/09
Problem #8
Equation)
Text 2: 5.1-5.5
Due =
p. 290 (Wave
3/31//09
Equation)
Homework
Text 2: 6.5-6.7
Problem #9
p. 298-299
(Wave
Due =
Equation)
4/02/09
Text 2: 7.1-7.4,
7.6, 7.7 pp. 307308 (Wave
Equation)
http://www.geocities.com/aboutwaves/
The one dimensional wave equation
The three dimensional problem
Retarded Potentials
Waves in one space dimension
An alternative derivation of the 1D
Green's function
The two dimensional Green's function
A few problems:
Exercises
Books on Waves and Classical Mechanic
Text 3: Section 6.7 (pp.314-317)
Text 1: Chap. 3, Section 3.1, 3.2
Text 2: Chap. 3, Section 3.1, 3.2, 3.3, 3.4, 3.5,
3.6
3/03/09
Homework
#10
Prob.#1:
Use the
method of
characteristics
to solve prob.
3.1(e) on pg.
68 of Text 2.
(Due =)
Prob. #2: Use
the method of
Ex. 3.1 on p.
67 of Text 2 to
solve prob. 3.1
(e). (Due =).
Homework
#11
Last Day of Classes
4/23/09
(Thurs.)
GENERAL INFORMATION