MAT 341: Applied Real Analysis

Welcome to MAT 341.

The aim of this course is to understand how certain partial differential equations arise (the heat equation and the wave equation, in dimensions one and two), and how to arrive at solutions to these equations by using Fourier series. The course begins with a discussion of Fourier series.

Homework for sections 2.4,2.5

You may hand in the homework for sections 2.4,2.5 on Tuesday 10/27, the week after the midterm.

Change in office hours

My usual Wednesday office hours (8:30am-9:30am) will not take place on 10/14 and on 10/21; instead I will have Monday office hours (8:30am-9:30am) on 10/12 and on 10/19.

Course instructor

Lowell Jones Office: Math Tower 2-111. Telephone: 632-8248.
Office hours: Tu,W,Th 8:30am-9:30am.

Course Grader

Zhiyu Tian, Office:Math Tower 2-116.
Office hours:Tuesday 6-8 pm in the MLC and Monday 4-5pm in 2-116.


Lec 01 Tu,Th 9:50am-11:10am SB Union 226 Jones


Boudary Value Problems and Partial Differential Equations, fifth edition, by David L. Powers


You should read the corresponding section of the text before attending each lecture.

Problem sets will be assigned weekly; check this webpage for the assigments. Each homework set is due during the first class of the following week (unless otherwises stipulated). Note that the solutions to some of the problems appear in the back of the text book. You should nonetheless try and solve these problems without recourse to the answer key, and should write the problem up carefully in your own words even if you have consulted the book for the final answer: always show your work.

The grader for this course, Zhiyu Tian, will not accept late homework unless there is a valid reason (e.g. a medical reason).

It is OK to discuss homework problems with other students. However, each student must write up the homework individually in his/her own words, rather than merely copying someone else's.

Solutions to homework

Solutions for HW in sections 1.5,1.6 can be found at solutions for 1.5,1.6

Solutions for HW in sections 1.9,1.11 can be found at solutions for 1.9,1.11

Solutions for HW in section 2.1 can be found at solutions for 2.1

Solutions for HW in sections 2.2,2.3 can be found at solutions for sections 2.2,2.3

Solutions for HW in sections 2.4,2.5,2.6 can be found at solutions for sections 2.4,2.5,2.6

Solutions for HW in sections 2.7,2.8,2.10 can be found at solutions for sections 2.7,2.8,2.10

Solutions for HW in sections 3.2,3.3 can be found at solutions for sections 3.2,3.3


There will be one midterm in class: on Thursday October 22, 2009. The final exam is scheduled for Thursday December 17, 2009 between 11:15am-1:45pm. The place of the final exam will be announced on this web site towards the end of the semester.

Make certain that you will be available at these times, as there will be no scheduled make-ups for these tests.

Please note that makeup exams are only given if a student misses an exam for unforseeable circumstances beyond the student's control. In particular, schedule conflicts are not an acceptable reason for missing an exam.

Review for Midterm and Practice Midterm with Hints

The midterm will cover the material in sections 1.1-1.6,,2.1-2.3 of our text book. Be sure to review the definitions and the statements of theorems, also review old homework problems.

A practice midterm can be found at practice midterm

Some hints to doing the problems on the practice midterm can be found at Hints for practice midterm problems

Results of Midterm

The class average for the midterm is 76%. Only your percentage grade on the midterm will be used in determining your final grade for the course. Roughly speaking you can translate your percentage grade on the midterm to a letter grade as follows: >89 is A or A-; >75 is B+,B or B-; >60 is C+ or C.

You can find the solutions to the midterm at solutions to the midterm You can pick up your exams in class on Tuesday October 27.

Final exam and practice final exam

The final exam will cover material in sections 2.1-2.5,2.10, 3.1-3.3,3.6,4.1-4.3,5.3. It will take place in room W-4550 of the main Library at 11:15am-1:45pm on December 17,2009.

A practice final exam can be found at Practice final .

Some solutions to the practice final can be found at Solutions to practice final .


20% Homework
30% Midterm
50% Final Exam


A very useful resource is the Math Learning Center (MLC) located in room S240-A of the mathematics building basement. The Math Learning Center is open M,Tu,Wed from 10:00am to 9:00pm, on Thur from 10:00am to 6:00pm, and on Fri from 10:00am to 2:00pm.

Another useful resource are your teacher and grader, whose office hours are listed above.


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 (DSS)at 632-6748 or at DSS will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential.

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 following website:


The following table will be filled in as the semester progresses. Always refer to it for each week's reading assignment and homework assignment. During this semester I shall try to cover (at a minimum) the following sections of our text book: 1.1-1.6,1.9,1.11; 2.1-2.11; 3.1-3.4,3.6; 4.1-4.5; 5.1,5.3-5.7.'s password: Linux 2.6.24-24-generic #1 SMP Wed Apr 15 15:54:25 UTC 2009 i686 The programs included with the Ubuntu system are free software; the exact distribution terms for each program are described in the individual files in /usr/share/doc/*/copyright. Ubuntu comes with ABSOLUTEL
Week Topic Notes Homework
8/31-9/4 1.1,1.2   1.1: verify 4.7-4.12 on page 439, verify table 1 on page 61,do problems 1 and 7 on pages 63 and 64 1.2:7,8,9
9/7-9/11 1.3,1.4   since some of you do not yet have the text, you may hand in the first assignment during our Thursday lecture this week 1.3: compute the Fourier series for the square wave function (see example 1 page 75); 2,3,5,7(hint: in problem 7 first compute the Fourier Series for the quadratic function A+Bx+Cx2) 1.4:2,3(b)(d)(e),5(a)(c)
9/14-9/18 1.5,1.6   1.5:3,5,6,8 1.6:2,4
9/21-9/25 1.9,1.11   the homework from sections 1.5 and 1.6 may be handed in on Thur. 9/21. (Hint for doing problem 2(a) in 1.6: review problem #7 in section 1.3.) 1.9:1(a)(b),2,5 1.11:1,3
9/28-10/2 2.1   no class on Tuesday, hand in homework assigned last week during Thursday class 2.1:1,2,4,5
10/5-10/9 2.2,2.3   2.2:1(need not find physical interpretation of this problem),6,7 2.3:4,5,6,9(a)(b)(c)
10/12-10/16 2.4,2.5   homework from last week may be handed in on Thursday; Wed. office hour is replaced by Monday office hour (8:30am-9:30am) 2.4:1(need not sketch graphs),5,8 2.5:3,7,10
10/19-10/23 2.6   midterm in class on Thursday 10/22/09, covering thru section 2.3; Wed. office hour is replaced by Monday office hour (8:30am-9:30am), you may hand in the homework for sections 2.4,2.5 next week on Tues. 10/27 2.6:6,7,10
10/26-10/30 2.7,2.8   2.7:2,3(b)(c)(d),4(in problem 3 do not sketch the graphs of the eigenfunctions) 2.8: 2,4 (in these two problems assume that the "regular Sturm-Liouville problem" is given by equations (1),(2),(3) on page 175, with l=0 and r=a)
11/2-11/6 2.7,2.8,2.10,2.11   hand in the homework from sections 2.7,2.8,2.10 on Thursday 11/12 2.10:1,2,4,7(in problem 7 you may assume that the limit of f(x) --- as x goes to positive infinity --- exists)
11/9-11/13 3.2,3.3   3.2:1,3,4,6,7 3.3:3,5,6,10
11/16-11/20 3.3,3.6   you may hand in the HW from sections 3.2,3.3 during the Thursday lecture of this week 3.6:1,2,7,8
11/23-11/27 3.1   no class on Thursday 11/26/09
11/30-12/4 4.2,4.3   you may hand in the homework for section 3.6 during the Tuesday lecture this week 4.2:4,6,7(b) 4.3:4,5,7
12/7-12/11 5.3   Thursday 12/10 is our last class meeting; you may hand in the homework for sections 4.2,4.3 on Thursday of this week; you do not have to hand in the homework for section 5.3 5.3:4,5,6,8