Partial Differential Equations
MATH 371
Winter 2010
Alina Stancu
General Information
Lectures: TJ 10:15-11:30 am in H-625
Office Hours: Wednesdays 4:00-5:30 pm and by appointment.
Office: LB 921-27.
Textbook: Basic Partial Differential Equations by David Bleecker & George Csordas
International Press 1997, ISBN: 1-57146-036-5.
Course goals: Differential equations originated in attempts to give mathematical
descriptions of problems in various sciences. This is an introductory course in partial differential equations. It
touches upon the qualitative study of solutions and it
concentrates on the basic methods for solving special types of
partial differential equations. Three basic types of PDEs are discussed in detail: the heat equation,
the wave equation and the Laplace's equation, respectively.
(MATH 370 is useful for a better understanding, but other courses can substitute for it.)
Assignments: The homework problems for each section are posted below. The homework from the sections
covered the preceding week will be collected
each Thursday. The
homework counts for part of your grade, and will account for an even more
substantial part of your learning. If you do the homework you will also find the exams much easier.
Grading Policy: There will be one midterm examination worth 30% of the grade. The
homework average of your ten best assignments will count for 10%, and the final exam, which is
comprehensive, will count for another
60%. However, if it is in your advantage, the final exam will count for 100% of the grade, replacing the weighted
average described above.
Exam Schedule
Midterm -- 02/18/10 in class
Final Exam -- Check MyConcordia portal.
News
April 16, 2010:
The last office hours before the final exam are Wednesday, April 21st, 2-4pm.
April 10, 2009
Please note that next Wednesday, April 14, the office hours are 10-noon (and NOT 4-5:30pm). Also,
note that the
last day to complete the on-line course evaluations is Monday, April 12.
April 6, 2010 - A review session will be held at 2pm on Tuesday, April 13 in LB 921-4.
April 2, 2010 - For practice, you may use this old final exam.
However, solving these problems should not substitute reviewing all the sections in preparation
for your final examination. Some of the above problems will be discussed during Thursday's review.
April 1, 2010 - Please complete the on-line evaluations for this course. Thank you.
February 11, 2010 - Please see the recent changes to the syllabus, including the sections
covered by the midterm on February 18.
Note that, in preparation for the midterm, the solutions to Assignment #5 will be posted by Monday, February 15 and the
graded assignments will be returned to you on Tuesday, February 16. Finally, note that Assignment #6 is due the day of the midterm.
Those problems should help you review section 3.1. For any related questions, you may come to office hours on Wednesday.
Solutions to selected problems
Check periodically for updates.
Various material
Here you have the solution of the Extra Credit problem
of Assignment 2.
Here you have the solution of the Extra Credit problem
of Assignment 3.
Here you have the solution of the Extra Credit problem
of Assignment 8.
Here you have the solution of the first Extra Credit problem
of Assignment 10.
Here you have the solution of the second Extra Credit problem
of Assignment 10.
Syllabus
This may be adjusted as the course progresses.
Week #1 (January 5, 7):
Section 1.1 -- A Review of ODEs
Assignment: Problems 1) a, b, g; 4) a, b; 6) b, c, e, i; 17) a.
Section 1.2 -- Generalities about PDEs (Part I)
Assignment: Problems 1) a, b, c.
Week #2 (January 12, 14):
Section 1.2 -- Generalities about PDEs (Part II)
Assignment: Problems 5), 12). Extra Credit (4 pts): Problem 7).
Section 1.3 -- General Solutions and Elementary Techniques (Part I)
Assignment: Problems 1) b, c; 2) b, c; 4) a, c.
Week #3 (January 19, 21):
Section 1.3 -- General Solutions and Elementary Techniques (Part II)
Assignment: Problems 6) b, d, e; 9) c. Extra Credit (4 pts): Problem 12).
Section 2.1 -- First Order Linear PDEs (Constant Coefficients)
Assignment: Problems 1) a, c, e; 2); 3), 4), 8).
Week #4 (January 26, 28):
Section 2.2 -- First Order Linear PDEs (Variable Coefficients)
Assignment: Problems 1) b, c; 2) b; 3) a, d; 4); 8).
Week #5 (February 2, 4):
Section 2.3 -- Higher Dimensions, Quasi-linearity
Assignment: Problems 2), 5), 6).
Section 3.1 -- Derivation of the Heat Equation and Solutions of Standard Initial/Boundary-value Problems (Part I)
Assignment: Problem 1).
Week #6 (February 9, 11):
Section 3.1 -- Derivation of the Heat Equation and Solutions of Standard Initial/Boundary-value Problems (Part II)
Assignment: Problems 2), 3) b; 6) c; 7).
Section 3.2 -- Uniqueness and the Maximum Principle (Part I)
No Assignment.
Week #7 (February 16, 18):
Section 3.2 -- Uniqueness and the Maximum Principle (Part II)
Assignment: Problems 1), 3), 5), 7), 8) (due the first Thursday after the break).
MIDTERM EXAMINATION on Chapters 1, 2 and Section 3.1.
Midterm Break - Classes resume Monday, March 1.
Week #8 (March 2, 4):
Section 3.3 -- Time Independent Boundary Conditions and/or Midterm Discussion
Assignment: Problems 1), 3), 4), 6). Extra Credit (2 pts): Problem 8).
Week #9 (March 9, 11):
Section 4.1 -- Orthogonality and the Definition of Fourier Series
Assignment: Problems 2), 3), 4), 5) a) only.
Section 4.2 -- Convergence Theorems for Fourier Series - selective
Assignment: Problems: 1), 2), 3).
Week #10 (March 16, 18):
Section 4.3 -- Sine and Cosine Series and Applications
Assignment: Problems 4), 5), 9), 11). Extra Credit (3 pts): Problem 17).
Section 5.1 -- The Wave Equation - Derivation and Uniqueness
Assignment: Problems: 1) a, b, c; 9). Extra Credit (3 pts): Problem 2).
Week #11 (March 23, 25):
Section 5.2 -- D'Alembert Solution for Wave Problems
Assignment: Problems 1) a, d, e); 4), 7).
Week #12 (March 30, April 1):
A few more comments on the wave equation. No assignment.
Section 6.1 -- Laplace's Equation - General Orientation
Assignment: Problems 1), 3), 5).
Section 6.2 -- The Dirichlet Problem for a Rectangle
Assignment: Problems 1), 2) b; 4).
Week #13 (April 6, 8):
Section 6.3 -- The Dirichlet Problem for Annuli and Disks
Problems for self-study (not for grading): Problems 1) a, c; 2), 5).
Section 6.4 -- The Maximum Principle and Uniqueness for the Dirichlet Problem
Problems for self-study (not for grading): Problems 1), 2), 3).
© 2009 Alina Stancu