Math 551: Applied Partial Differential Equations and Complex Variables
(Fall 2014) (5005)
Mathematical methods for solving problems in linear partial differential
equations: linear operators and adjoint problems, eigenfunction expansions,
Fourier series, SturmLiouville problems, orthogonal functions
and generalized Fourier series. Solutions via Green's functions.
Complex variables for contour integrals and solutions via integral
representations. Integral transforms: Fourier and Laplace transforms.
Textbook:
Applied Partial Differential Equations (5th ed), by Richard Haberman,
Prentice Hall (2013)
Prerequisites
Background in linear algebra and ordinary differential equations:
[Math 221 and 356], or [Math 216 and 353], or equivalents.
Schedule
MWF 8:459:35 AM, Room 119 Physics Building
Instructor
Thomas Witelski, Professor, Dept of Math
Office hours
Mon 34, Tues 111,
Room 295 Physics Building,
or by email request
for an appointment for other times.
Problem sheets
Course materials
 Course outline/syllabus
 Review sheets
 Lecture notes
 Tests
 Test 1:Friday, Oct 3, in class  Solution of inhomogeneous ODE BVP via
eigenfunction expansions. Fourier series. Adjoint eigenvalue problems.
SturmLiouville problems. Integral equations: eigenvalue and inhomogeneous
problems. The Fredholm alternative theorem for
existence/uniqueness/nonexistence.
(Optional review session: Weds, Oct 1, 6:008:00pm, Room 119
 No new material will be covered. Questions will be answered and examples
worked out. Feel free to come to all/anypartof the review sesssion block
time.)
2014 Results: Avg: 71, 90s: 3, 80s: 2, 70s: 3, 60s: 6, less: 3
Old tests:
 Test 2: Monday, Nov 10, in class  Green's functions for ODE BVPs
(9.3), separation of variables and eigenfunction expansions
for PDEs (2.3, 2.4, 8.28.4, 8.6), Helmholtz equations, Bessel functions,
multidimensional problems (2.5,
7.27.10), material
covered on Homeworks 58, Lectures 1126.
Optional review session:
No new material will be covered. Questions will be answered and examples
worked out. Feel free to come to all/anypartof the review sesssion block
time.
 Math 211 Fall 2008 Test 2
(historical data: 90s: 2, 80s: 3, 70s: 1, less: 2)
 Math 211 Fall 2009 Test 2 (historical
data: High 82, Low 35, Avg 62)
 Math 211 Fall 2010 Test 2
(historical data: avg 58, 90s:0, 80s:1, 70s:3, 60s:8, 50s5, 40s:4, 30s:3)
 Math 211 Fall 2011 Test 2
(historical data: avg 59, 90s:1, 80s:3, 70s:1, 60s:5, 50s:4, 40s:4, less:3)
 Math 551 Fall 2013 Test 2
(historical data: avg 63, 90s:1, 80s:4, 70s:3, 60s:4, 50s:7, less:5)
 Math 551 Fall 2014 Test 2
(historical data: avg 66, 90s:3, 80s:0, 70s:4, 60s:4 50s:3, less:3)
 Test 3: MONDAY, DEC 1, in class  Complex Contour integration,
parametrization, complex analytic functions, path independence, Cauchy's
theorem, Cauchy's integral formula, residues, log branch cuts, evaluation of
real integrals, Jordan curve lemma. Material from Homeworks 9, 10 and all
lectures on complex variables.
Optional review session: Saturday, Nov 29, 2:004:00pm, Room 119 Physics.
No new material will be covered. Questions will be answered and examples
worked out. Feel free to come to all/anypartof the review sesssion block
time.
 Math 211 Fall 2008 Test 3
(historical data: 60s: 3, 90s: 2, 100: 3)
 Math 211 Fall 2009 Test 3 (historical
data: 90s:3, 80s:4, 70s:4, 60s:4, less:3, Average:74)
 Math 211 Fall 2010 Test 3: avg 73,
90s: 2, 80s: 8, 70s: 6, 60s: 3, 50s: 1, less: 3
 Math 211 Fall 2011 Test 3: avg 72,
100s:1, 90s: 4, 80s: 4, 70s: 3, 60s: 4, 50s: 2, less: 3
 Math 551 Fall 2013 Test 3:
results: avg 70, 90s: 4, 80s: 3, 70s: 5, 60s: 7, 50s: 3, less: 2
 Math 551 Fall 2014 Test 3:
results: avg 77, 90s: 2, 80s: 8, 70s: 4, less: 3

Final Exam: FRIDAY, Dec, 12, 9:00amNoon
 2010 results: avg 71, high 97, low 30s. Distribution: 90s: 5, 80s: 4,
70s:
4, 60s: 5: 50s: 2, less:3
 2011 results: avg 63, high 95, low 30s. Distribution: 90s: 1, 80s: 3,
70s: 2, 60s: 7, 50s: 3, less: 5
 2013 results: avg 66, high 91, low 30s. Distribution: 90s: 1, 80s: 4,
70s: 6, 60s: 6, 50s: 1, less: 6
 2014 results: avg 74, high 98, low 20s. Distribution: 90s: 4, 80s: 3,
70s: 4, 60s: 4, less: 2
Problems accessing the sheets?
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access locally from any *.duke.edu computers or
try
Duke OIT VPN (Start VPN @ portal.duke.edu).