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.

ANNOUNCEMENTS:

Final Exam: Wed., Dec. 11, 5:30 - 8:00pm.

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:

ReviewPlease come prepared with questions to ask, things you'd like me (the instructor) to go over and/or discuss.

Midterm Exam: TBA

Material on Exam: TBA

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

MAT 341

Lecture and RecitationFinal Exam: Friday Dec 11, 5:30-8:00pm, Place: TBA

LEC 2

MW

2:30pm- 3:50pm

Physics

P113

Xiuxiong Chen

Course Grader

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Willie Rush Lim

Instructor:Xiuxiong Chen

Office Location:4-100B Math Tower

Email:xiu@math.stonybrook.edu

Web site:http://www.math.sunysb.edu/~xiu/

Office hours:M 11:00am-1:00am

Grader:

R01:Willie Rush Lim

Email:Lim.Willie@stonybrook.edu

Office: Math Tower S-240A

Office hours:Tu 4:00pm-5:00pm (office), Tu 12:00-1:00pm,W 3:30pm-4:30pm (Math Learning Center)

## Course Text:

Boundary Value Problems and Partial Differential Equations, 6th Edition, by David L. Powers, Elsevier (Academic Press), 2010.## Homework:

There will be weekly HW assignments, generally due in class on Wednesday. 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.The grader for this course, Willie Rush Lim, will not accept late homework unless there is a valid reason (e.g. a medical reason).

## Grading Policy:

Grades will be computed according to the following percentages:

Homework

20%

Midterm, Date TBD, in class

30%

Final Exam: Friday Dec 11, 5:30-8:00pm, Place: TBA

50% (cumulative)

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

Week of

Topics

Problems Due

Due Date

Aug 26

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), 8Sept 11

Sept 2

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), 8Sept 11

Sept 9

1.4: Uniform convergence

1.5: Operations on Fourier Series-- -- Sept 16

1.9Fourier Integrals

2.1Heat Eqn:initial & bdry conds

1.5: 2, 3, 8

1.9: 1a, 3a, 3b

2.1: 2Sept 25 Sept 23

2.1Initial & bndy conds.

2.2Steady State solns

2.3Dirichlet conds.

2.2: 4, 5, 6

2.3: 5, 6, 7, 8Oct. 2nd

Sept 30

2.4Neumann boundary problem

2.7Sturm-Liouville problems

2.8Expansions in eigenfunctions

2.10Semi-infinite Domain

2.4: 2, 4, 5, 8, 9

2.7: 3(d),(e)Oct 7th Oct 7

2.11Infinite Domain

3.1The Wave Equation

3.2Soln of Wave Eqn

2.10: 1, 2, 4, 7

2.11: 5, 7Oct 16th Oct 14

3.3D'Alembert's Soln

3.4Generalities

3.2: 1, 2, 4, 5, 14

3.3: 8

--Oct 21st

Oct 21

3.6Unbounded domains

4.1The Potential Equation--

No HW due Oct 28th

Oct 28

Midterm (in class), Monday

4.2Potential in a Rectangle

4.3More on Rectangle problems

4.1:2, 10

4.2:5, 6

4.3:2a, 10Nov. 6th Nov 4

4.5Potential Eqn. in Disc

4.4General Features of Potential Eqn. (not all in text)

4.4:27, 28

4.5:2, 4, 9, 10Nov 13th

Nov 11

5.1-5.2PDE's in higher dimensions

5.32-d Heat Eqn in Rectangle

5.1: 2

5.2: 5

5.3: 5, 6, 7c, 11Nov 20th Nov 18

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, 25Nov 27th Dec 2