This course is an introduction to Fourier Series and to their use and application in solving partial differential equations (PDE's). The course focuses on the heat equation, the wave equation and the potential or Laplace equation. These are the three main and fundamental types of PDE's. They are important in many applications and illustrate important properties of PDE's in general.
It will probably benefit you a lot to read the correspondings sections of the text before each lecture. There is a lot of material in the text that can't be covered in class, and you will need to read and understand this on your own. Always feel free to ask questions to your instructor and grader.
Final Exam: Friday, Dec. 13, 11:15 - 1:45pm in Humanities 1003
Here is a Practice Final
This Final Exam is OPEN BOOK. You may use the text for the course, and any notes you may have from lectures or other sources. This means you won't have to memorize the numerous formulas.
The Final will have at least 5 but less than 10 problems. The exam will cover topics discussed over the full semester, but with some emphasis on Chapters 4 and 5 of the text. See below for sections which were not covered, and so will not be on the exam.
Last week of classes:
Review Please come prepared with questions to ask, things you'd like me (the instructor) to go over and/or discuss.
Midterm Exam: Tuesday, Oct 22, 10-11:20am, in class.
Midterm Review: Class on Thursday, Oct 17.
Material on Exam: Chapters 1, 2, 3 of the text.
If you know you cannot make this Midterm date (out of town, etc) please send me an email and we'll make arrangements.
Topics in text you may skip:
Ch. 1.6, 1.7, 1.8, 1.10, 1.11.
Ch. 2.1, 2.5, 2.6, 2.9.
Ch. 3.1, most of 3.4, 3.5, most of 3.6
Ch. 5.1, 5.2, 5.4 - 5.8
Here is a Practice Midterm: Practice Midterm
You may ignore Prob. 5 (a),(c).
Also, Prob. 5 (and 6) on this exam is useful.
Lecture and Recitation
Final Exam: Friday Dec 13, 11:15am-1:45pm, Place: Humanities 1003
Instructor: Michael Anderson
Office Location: 4-110 Math Tower
Email: anderson at math.sunysb.edu
Web site: http://www.math.sunysb.edu/~anderson
Office hours: M/W 1:30-3pm & by appointment in 4-110 Math Tower
R01: Apratim Chakraborty
Email: apratim at math dot sunysb dot edu
Office: Math Tower S-240G
Office hours: M, 12-1pm (office), W, 2-4pm (Math Learning Center)
Boundary Value Problems and Partial Differential Equations, 6th Edition, by David L. Powers, Elsevier (Academic Press), 2010.
There will be weekly HW assignments, generally due in class on Tuesdays. Check the course schedule below for the assignments.
Note that solutions to some of the problems are at the back of the textbook. You should nonetheless try and solve these problems without recourse to the answer key and should write up the solution carefully in your own words, even if you consulted the book for the final answer. You must always show your work to receive credit.
It is OK to discuss HW problems with other students. However, each student must write up homework solutions individually in his/her own words, rather than merely copying from someone else.
Grades will be computed according to the following percentages:
Midterm, Date TBD, in class
Final Exam, Friday, Dec 13, 11:15am-1:45pm, Place: Humanities 1003
No make-up exams will be given. If a midterm exam is missed because of a serious (documented) illness or emergency, your semester grade will be determined on the basis of other work done in the course. Exams missed for other reasons will be counted as failures.
Resources: If you have questions regarding the course material at any time during the semester, you are encouraged to visit your instructor or TA during office hours, or make a separate appointment if necessary. Your instructors will also reply to email, within reason. Another excellent source of help is the Mathematics Learning Center (S240A in the Math Building - basement level), which is staffed by advanced math majors, graduate students and faculty daily. For a schedule of their hours, check their website.
Americans with Disabilities Act:If you have a physical, psychological, medical, or learning disability that may impact on your ability to carry out assigned course work, please contact Disability Support Services at (631) 632-6748 DSS . DSS office: EEC (Educational Communications Center) Building, Room 128. DSS will review your concerns and determine, with you, what accommodations, if any, are necessary and appropriate. All information and documentation is confidential. Arrangements should be made early in the semester so that your needs can be accommodated.
Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and DSS. For procedures and information go to the DSS website above.
Academic Integrity: Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another persons work as your own is always wrong. Faculty are required to report any suspected instances of academic dishonesty to the Academic Judiciary. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website here.
Critical Incident Management: Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of University Community Standards any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits the students' ability to learn. Further information about most academic matters can be found in the Undergraduate Bulletin, the Undergraduate Class Handbook and the Faculty-Employee Handbook.
Schedule of Topics
1.1: Periodic Functions, Fourier Series
1.2: Half Range expansions, even/odd
1.3: Convergence theorems
1.1: 1(b), 7
1.2: 1(a), 4, 8, 10(d), 11(d)
1.3: 2(d), 8
1.4: Uniform convergence
1.5: Operations on Fourier Series
1.9 Fourier Integrals
2.1 Heat Eqn:initial & bdry conds
1.5: 2, 3, 8
1.9 : 1a, 3a, 3b
2.1 Initial & bndy conds.
2.2 Steady State solns
2.3 Dirichlet conds.
2.2: 4, 5, 6
2.3: 5, 6, 7, 8
2.4 Neumann boundary problem
2.7 Sturm-Liouville problems
2.8 Expansions in eigenfunctions
2.4: 2, 4, 5, 8, 9
2.10 Semi-infinite Domain
2.11 Infinite Domain
3.1 The Wave Equation
2.10: 1, 2, 4, 7
2.11: 5, 7
3.2 Soln of Wave Eqn
3.3 D'Alembert's Soln
3.2: 1, 2, 4, 5, 14
3.6 Unbounded domains
Midterm Review (Thursday)
No HW due Oct 22
Midterm, Tuesday Oct 22, In class
No HW due Oct 29
4.1 The Potential Equation
4.2 Potential in a Rectangle
4.3 More on Rectangle problems
4.1: 2, 10
4.2: 5, 6
4.3: 2a, 10
4.5 Potential Eqn. in Disc
4.4 General Features of Potential Eqn. (not all in text)
4.4: 27, 28
4.5: 2, 4, 9, 10
5.1-5.2 PDE's in higher dimensions
5.3 2-d Heat Eqn in Rectangle
5.3: 5, 6, 7c, 11
5.9: Spherical Coords; Legendre Polys
5.10: Applications of Legendre Polys
5.9: 11, 12
5.10: 1, 2
Misc. Ex.p.371ff: 19, 25
See above for Time & Place of Final Exam