Math 211: Applied Partial Differential Equations and Complex Variables
(Fall 2011)
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 (4th ed), by Richard Haberman,
Prentice Hall (2003)
Prerequisites
Background in linear algebra and ordinary differential equations:
[Math 104 and 131], or [Math 107 and 108], or equivalents.
Schedule
MWF 1:302:20 PM, Room 119 Physics Building
Instructor
Thomas Witelski, Associate Professor, Dept of Math
Office hours
Tuesdays, 11:00am2:00pm,
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: Weds, Oct 5, 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: 
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.
 Test 2: Weds, Nov 9  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: Sunday, Nov 6, 46pm, 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 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
avg 59, 90s:1, 80s:3, 70s:1, 60s:5, 50s:4, 40s:4, less: 3
 Test 3: Weds, Dec 7  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: Sunday Dec 4, 46pm room 119 physics
 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

Final Exam: THURS, Dec, 15, 9:00Noon
 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
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or email me.