## Links to other webpages for Math 421

 General information || Syllabus & textbook problems || Students in the course ||| Course diary Laplace transforms Linear algebra Fourier series PDE's & BVP's

 Exam warning!Final exam in SEC 216 (the usual classroom) on Friday, December 16, from 8 AM to 11 AM Review sessions: Wednesday, December 14 at 4-6 PM in Hill 425 Laplace transforms & linear algebra. Thursday, December 15 at 4-6 PM in Hill 425 Fourier series, the wave/heat equations, & associated boundary value problems.

Things to do

 Laplacetransforms
 Linear algebraterms
 Fourier series formulas
 Soon: somefriendly pairs!

Other class material

Title
What is it?Handed out
or posted
The final exam The final exam, in a somewhat more compact form.
The misprint in the last problem (where b) and c) instead of a) and b) was written) has been corrected. There was no part a) asking for an essay describing how you feel about the heat equation. Here is a discussion of the grades and the grading and here is how course grades were determined.
Mr. O'Sullivan pointed out several small grading errors today (1/6/2006). Thankfully they did not affect the actual course grades of any student. I also altered problem #7 in the linked exam. In part e), the c) has been changed to reference d) which is what I wanted to ask.
12/21/2005
The formula sheet for the final exam Copies of this will be distributed with the final exam. 12/13/2005
Some two-dimensional PDE problems You may try these problems yourself. Answers to these questions and to some questions from the textbook are given here. 12/8/2005
A two-dimensional heat flow example Some pictures of a steady-state heat distribution on an idealized square plate in the plane. 12/8/2005
Review material for the final exam
There is almost too much material.
Review sessions: Wednesday, December 14 at 4-6 PM in Hill 425
Laplace transforms & linear algebra.
Thursday, December 15 at 4-6 PM in Hill 425
Fourier series, the wave/heat equations, & associated boundary value problems.
12/6/2005
Wave equation examples Two examples of initial data for the wave equation "evolving". Please see also here for some animated gifs of this data. 12/1/2005
One heat flow example An approximation to a boundary value problem for the heat equation is graphed for several small values of time. Some relevant Maple commands are also given. Please see also this page where there are more pictures 11/21/2005
11/21/2005
Exam 2 Exam 2, in a somewhat more compact form. The two small corrections needed in problem 2g) and in problem 8b) did not seem to cause difficulty. 11/21/2005
Review material for exam 2
A review session is scheduled for Wednesday, November 16, at 7 PM in Hill 525.
10/3/2005
Fourier series formula sheet for the second exam This is a draft of a Fourier series formula sheet for the second exam. Comments and corrections are invited.
This was the formula sheet handed out with the second exam.
11/8/2005
Block matrix problems Students can earn an extra 5 points on the second exam by solving these problems correctly and handing in the results before noon on Monday, November 14. 11/7/2005
Pictures of partial sums of some Fourier series, and the Maple instructions needed This was handed out in class to help understand the general behavior of Fourier series. 11/7/2005
An additional comment on problem 3a) has been written. Mr. O'Sullivan kindly showed the instructor a valid alternate method to compute the answer.
10/11/2005
Exam 1 Exam 1, in a somewhat more compact form. This even includes problem 2, I hope, which may be invulnerable to copying. 10/11/2005
The formula sheet used on the exam The formula sheet, including some RREF's, as was handed out on the exam. 10/11/2005
Review material for exam 1
A review session is scheduled for Sunday, October 9, at 4 PM in Hill 525.
10/3/2005
Draft version of a formula sheet for the first exam Here is a draft version of a formula sheet for the first exam. This sheet was used for the first exam in a fall, 2004, instantiation of this course. Students are encouraged to send comments and corrections. I am even willing to get suggestions for more entries to this sheet, although it is not clear to me that students are well served by too many formulas. For example, the Laplace transform of J0(t), a Bessel function, is 1/sqrt(s2+1). 9/27/2005
The entrance "exam" The purpose of this assignment is to give insight to students very early in the course about some of the methods to be used. Familiarity with all of the material tested here is necessary for success in this course. Also students can see how the instructor grades. Solutions are due at the beginning of class on Thursday, September 8.
A message to me about problem 6 and my response.
9/1/2005
Information sheet A sheet to be passed out on the first day of class. 9/1/2005
This instructor has taught the course twice previously and there are very detailed records available on the web. The fall 2004 instantiation of the course used the same textbook and covered approximately the same syllabus. The spring 2004 instantiation had a similar syllabus but a different text. In both cases, these items may be most useful for students: review problems, most with solutions; exams, most with solutions; and a detailed course diary with worked-out examples and useful links.