MAT 341 Applied Real Analysis

Fall 2006

SUNY at Stony Brook

Department of Mathematics
Stony Brook University

This course is an introduction to three basic linear partial differential equations of mathematical physics, namely the heat equation, the wave equation and the potential equation, which play a fundamential role in mathematics and physical sciences. We will cover the basics of Fourier series and integrals and will use the method of separation of variables to solve the boundary value problems for these equations.


Textbook: Boundary Value Problems and Partial Differential Equations, Fifth Edition, by David L. Powers, Elsevier Academic Press, 2006.

Schedule: TuTh 9:50-11:10 am, Physics P113.

Prerequisites: Grade C or higher in the following: MAT 203 or AMS 261; MAT 303 or AMS 361: working knowledge of calculus and ordinary differentail equations with ability to perform basic algebraic computations with elementary and trigonometric functions.

Instructor: Leon Takhtajan, Math Tower 5-111, Phone: 632-8287, email: leontak@math.sunysb.edu
Office hours: Tu & Wed 4-5 pm, in 5-111, and by appointment.

Grader: Ritwik Mukherjee, Math. Tower 2-117, e-mail: ritwik@math.sunysb.edu
Office hours: Wed 5:30--6:30 pm in 2-117, Thu 11:30--1:30 in MLC.

Grading: Your course grade will be based on your examination performance and homework, weighted as follows:

Midterm I 20%
Midterm II 20% 
Final Exam 30%
Homework 30%

Reading assignments: It is fundamental to read corresponding sections in the textbook before the class. Independent reading is a crucial part of the learning process and it will greatly increase your comprehension of the lectures and enable you to ask useful questions in class. Furthermore, the lecturer will not always be able to cover all of the subject material for which you will be responsible. Also note that mathematical texts are not meant to be read like novels: very often you will come across passages that must be read several times before they make sense to you.

Homework: Studying mathematics makes no sense without regular practice. Only by solving homework problems, both routine and more challenging, one can master the material in this class. You will be required to do all the homework assignments. The homework for a given week is due next week's Tuesday in class. Late homework will be not accepted, no exceptions,

Exams:

Course description (tentative) & Homework assignments:

Week Sections
Notes Homework assignments
9/1-9/10 Review of Chapter 0
   0.1: 1-6; 0.2: 2,4,16; 0.3: 3; 0.4: 1,2; Misc. exercises: 2,4
9/11-9/17 Sections 1.1-1.3   1.1: 2,5; 1.2: 1,2,7,8,10; 1.3: 2,3,8.
9/18-9/24 Sections 1.5, 1.9 and 1.10   1.5: 8,9,10; 1.9: 2,3,6; 1.10: 2,3,4,6.
9/25-10/1 Sections 2.1-2.3   2.1: 2; 2.2: 2,5,6,7; 2.3: 5,6,8.
10/2-10/8 Sections 2.4, 2.5, 2.7 and 2.8   2.4: 2,8; 2.5: 3,4,7,10; 2.7: 3 (no need to sketch solutions), 4; Misc. Ex. on p. 207: 8,10.
10/9-10/15 Sections 2.10, 2.11   2.10: 1,2,5,8; 2.11: 2,4,5,8,9; Extra Credit: Misc. Ex. on p. 209: 20,21,22.
10/16-10/22 Sections 3.1-3.3 Midterm I, October 19 3.2: 3,4,5,7,14,15,16.
10/23-10/29 Sections 3.3, 3.6   3.3: 4,8,12; 3.6: 2,3,4; Misc. Ex. on. p. 247-248: 4,5,6,7; Extra Credit on p. 249-251: 16,26.
10/30-11/5 Sections 4.1, 4.2, 4.3   4.1: 1,2,4,5,6; 4.2: 2,6; 4.3: 1,2,6,10. Answers to even numbered problems
11/6-11/12 Sections 4.4, 4.5   4.4: 4,5,10,11,12,14,15; Extra Credit: 16.
11/13-11/19 Sections 5.1-5.3 Midterm II, November 16 4.5: 1,6,9; Misc. Ex. on p. 285-294: 15,16; 5.2: 1,2; 5.3: 7,8.
11/20-11/26 Sections 5.4, 5.5 The homework due Th., Nov. 30 5.4: 6,8; 5.5: 1,4,6; Extra Credit: 8,10.
11/27-12/3 Sections 5.5, 5.8 The homework due Th., Dec. 7 5.8: 1,2,4,5,6,7.
12/4-12/10 Sections 6.1, 6.2 The homework due Th., Dec. 14 6.1: 2,3,4,5,8; 6.2: 2,4,5,8.
12/11-12/17 Section 6.3 The homework due Fr., Dec. 15 Extra Credit HW 6.3: 2,3,4.
12/18-12/24 Finals week Final Exam, December 21

DSS advisory. If you have a physical, psychological, medical, or learning disability that may affect your course work, please contact Disability Support Services (DSS) office: ECC (Educational Communications Center) Building, room 128, telephone (631) 632-6748/TDD. DSS will determine with you what accommodations are necessary and appropriate. Arrangements should be made early in the semester (before the first exam) so that your needs can be accommodated. All information and documentation of disability is confidential. Students requiring emergency evacuation are encouraged to discuss their needs with their professors and DSS. For procedures and information, go to the following web site http://www.ehs.sunysb.edu and search Fire safety and Evacuation and Disabilities.