• The final exam is graded now, solutions are here: final_sol.pdf, and you can pick up your final after the winter break. Your grade will be sent by email shortly. The average score was about 102/150 and a histogram of the grades is here
  
  

• The average class grade is C+. Your class grades will be sent shortly by email. A histogram of the grades for the class is here:
  
  

Solutions for the optional HW10 are here: pdehw010.pdf.

Here is a preliminary version of the formula sheet you will have for the exam: formulas.pdf.

• Midterm #3 was given back today. If you did not get yours, please come to my office. The solutions are here: exam3_sol.pdf. The average grade was about 78 and a histogram appears below:
  
  
• We also went over a practice final which is available here: final_practice.pdf with solutions here: final_practice_sol.pdf.
• Good luck on your final exam period!

• The final exam is next Monday 12/15 between 1pm-3pm in the usual classroom for the course.
  
  
  
  • Wed 12/10 lecture will be dedicated to solving a practice final and midterm 3.
  • The final is comprehensive: 1.1-1.2, 2.1-2.4, 3.1-3.8, 4.1-4.5 and 7.1-7.8.
  • No notes, books or calculators allowed. A note card is allowed but it must be single-sided, handwritten and no bigger than a letter-sized page.

• HW10 is a short optional and extra credit assignment due Friday 12/12 at 2pm:
  
  
  
  • 7.8: 2, 14, 18, 31, 50

• Midterm 3 should be graded by Tuesday 12/9. Please come by my office if you want to get it before Wed 12/10.

• The solutions for HW9 are here: pdehw009.pdf, apologies for the unnecessary delay.
• Lecture notes for today (inhomogeneous heat equation) are here: pde019.pdf.

• Today we went over the solutions to the practice midterm 3: exam3_practice_sol.pdf. Note that the in the real exam there could be problems on the Fourier cosine or sine transform, even if none were present in the practice exam.
• Notes for Monday’s lecture on generalized functions (distributions) are available here: pde018.pdf.
• The solution to HW8 is available here: pdehw008.pdf. The solution to HW9 will be posted on Friday.

• Midterm 3 will be on Wed Dec 3 in class. The change was requested by all present students. Topics covered are 4.4-4.5, 7.1-7.7, with more emphasis on 7.1-7.4. You should be getting HW9 back by next Monday.
• Here is a Practice Midterm 3: exam3_practice.pdf. It will be solved next Wednesday (11/26). The real exam is shorter and easier.
• Today we started section 7.8 (lecture notes will be available later)

• Lecture notes for Monday and Wednesday are here: pde017.pdf. These lectures cover sections 7.5, 7.6 and 7.7.
• Solutions to HW7 are available here: pdehw007.pdf.
• Should you need extra time for HW8 you can still turn it in on Friday. However you will not get it next Wednesday.
• HW9 is due Wed Nov 26 2008. Each problem is worth 10 points for 70 points total + 10 points for the extra credit problem 7.5.10.
  
  
  
  • 7.4: 2
  • 7.5: 8, 9 (no credit if copied from student’s manual).
  • 7.6: 4, 8
  • 7.7: 2, 11
  • Extra credit: 7.5.10

• HW8 is due Wed November 19 2008. Each problem is worth 10 points for 60 points total.
  
  
  
  • 7.2: 36, 43, 50
  • 7.3: 9, 18
  • 7.4: 3

• Lecture notes for Monday lecture and Wednesday are available here: pde015.pdf and pde016.pdf.

• HW7 is due on Nov 12 2008. Each problem is worth 10 points (total 70 pts).
  
  
  
  • 4.5: 3
  • 7.1: 2
  • 7.2: 4, 29, 20, 23, 27

• Lecture notes for today and Monday are here: pde014.pdf.
• Midterm #2 is graded and was given back today. If you did not get yours, please come see me after class. The solutions are here: exam2_sol.pdf. The average grade was about 69.5 and a histogram of appears below:
  
  

• The practice midterm 2 solutions are here: exam2_practice_sol.pdf.
• There is a typo in the expression for A_n in the solution to problem 4.2.10 of HW6. The factor of 2 should be in the numerator, as it is in the book.

• Here are the codes I showed last Wednesday for the wave equation on a circular membrane
  
  
  
  • e4_2_2.m — Radially symmetric initial conditions
  • e4_3_2.m — General initial conditions
  • Both codes need the first few zeros of Bessel functions, which are stored in the file bz.mat. If you are interested in generating these zeros I used the function besselzeros.m which can be found here (see precomp_besseljzeros.m).

• The solutions to HW6 are here: pdehw006.pdf.
• The class notes for Wednesday’s lecture are here: pde013.pdf. We did the Laplace equation on circular regions.
• The practice midterm 2 is here: exam2_practice.pdf. This exam will be solved in class next Monday Oct 27. If it looks long it is because there are a lot (too many?) explanations and hints. Each question should be straightforward to answer, and none requires lengthy calculations.

• Midterm 2 is next week on Wed October 29 during class.
  
  
  
  • Topics covered: 3.6-3.8, 4.1-4.3
  • A practice midterm will be posted around the end of the week.
  • The Mon Oct 27 class will be devoted to solving this practice exam.
  • All identities using Bessel functions will be provided (table similar to the back-cover table of your textbook). You are responsible for knowing trig identities, integration by parts etc…
  • No notes, books or calculators allowed. A note card is allowed but it must be single-sided, handwritten and no bigger than half a letter-sized page.

• Solutions for HW5 are here: pdehw005.pdf.
• You should get HW6 back next Monday. Solutions to HW6 will be posted on Friday. Any homework handed in after the solutions are posted will not get credit.
• Today we solved the wave equation on a circular membrane when the initial conditions are not radially symmetric. The lecture notes are here: pde012.pdf.

• Lecture notes for Wednesday’s lecture are available here: pde011.pdf.
• The office hours during the break are cancelled. I’ll be out of town but joinable by email though.

• HW6 is due Wed October 22. Each problem is 10 pts except for 4.2.10 which is 30 pts.(Total 70 pts)
  
  
  
  • 4.1: 2, 3 (hint: transform to polar coordinates and use the Laplacian in polar coordinates. See e.g. the solution to problem 4.1.1 in the student solutions manual).
  • 4.2: 2, 4, 10 (do not do the Matlab part for 4.2.2 and 4.2.4; problem 4.2.4 is very simple if you look at the solution to problem 4.2.5 in the student solutions manual)

• Solutions to HW4 are here: pdew004.pdf.
• Lecture notes will be posted tomorrow. We continued with circular membranes (section 4.2) with a detour to Bessel functions (sections 4.7-4.8).

Today we covered Section 4.1 on the Laplacian on different coordinate systems and we got started with the wave equation on circular regions (section 4.2). Lecture notes are here: pde010.pdf.

Here are some codes that may be useful for the extra credit Matlab part of HW5.

• An implementation of the 2D Wave Equation (example 3.7.1): e3_7_1.m.
• A implementation of the 2D Heat Equation (example 3.7.2): e3_7_2.m.

• HW5 is due Wed Oct 8. Each problem is worth 10 pts (total 50 pts +10 pts).
  
  
  
  • 3.7: 2, 13, 16. 2b is extra credit, worth 10 pts. A Matlab code you can modify will be provided later today.
  • 3.8: 2, 3

• We covered section 3.8 on the Laplace equation. Lecture notes are here: pde009.pdf.
• I also gave back midterm 1. The average was about 65.8/100. The histogram is here:
  
  
• Check out this cool Java applet demonstrating vibrating square membranes. You can pluck the membrane and see it vibrate.

• Solutions for the practice first midterm are here: exam1_practice_sol.pdf. I sent these to the class mailing list on 9/22, as a glitch in the Math dept. filesystem did not let me change anything to this website.
• Solutions for the first midterm are here: exam1_sol.pdf. You will have the graded midterms next Wed.
• Here is how your HW were graded. This will be indicated on your assignments from now on.
  
  
  
  • HW1: 70 pts total (10 pts each except 1.2.4 which counts for 20 points)
  • HW2: 70 pts (10 pts for each problem) + 30 pts for the Matlab part
  • HW3: 60 pts (10 pts for each problem) + 20 pts for Matlab part
  • HW4: 70 pts (10 pts for each problem)

• Today we covered section 3.7 on the 2D wave and heat equations. Lecture notes are here: pde008.pdf

The solutions to HW3 are available here: pdehw003.pdf.

• Here is practice midterm 1: exam1_practice.pdf. This exam is longer and harder than the real one, so don’t panic if it takes you more than one hour to complete. Solutions will be given on Monday in class.
• To help you study sections 3.4-3.5 for the exam, here are two typical exercises from that section, augmented with some other things that could be useful: pdehw004_bis.pdf.

• HW4 due October 1st 2008:
  
  
  
  • 3.4: 1, 4, 9 (for 3.4.9: only part concerning 3.4.1)
  • 3.5: 4, 14, 9
  • 3.6: 2

• Solutions for HW1 (pdehw001.pdf) and HW2 (pdehw002.pdf) are now available. Solutions to HW3 will be posted Friday at noon.
• Class notes for today’s lecture are here: pde007.pdf. We finished sections 3.5 and 3.6. I showed two Matlab demos:
  
  
  
  • e3_5_1.m, the 1D heat equation with homogeneous Dirichlet boundary conditions (ice bath on both ends of the rod)
  • e3_6_3.m, the 1D heat equation with homogeneous Dirichlet boundary condition on one end and Robin type boundary condition on the other. This one requires some advanced Matlab, and is posted only for those interested.

• In Monday’s lecture we covered sections 3.4 and 3.5. Notes are here: pde006.pdf.
• Midterm 1 is Wednesday September 24 in class. Some related announcements:
  
  
  
  • The previous lecture to the exam (Mon Sep 22) will be dedicated to do a practice exam which will be posted by the end of the week.
  • No notes, books or calculators allowed. A note card is allowed but it must be single-sided, handwritten and no bigger than half a letter-sized page.
  • Sections covered are: 1.1 – 1.2, 2.1 – 2.4, 3.1 – 3.5.
  • You should be getting HW1 and HW2 graded by next Wednesday. I expect HW3 to be graded by next Monday. In any case, solutions will be released shortly after Wednesday class, so that you can study for the exam.
  • HW4 will be posted tomorrow and due on Wed Oct 1st and it will be on sections 3.4 – 3.5. Since these sections are included in the exam, I will post solutions to closely related problems. As you may have noticed solving the 1D heat equation with Fourier series is actually easier than solving the 1D wave equation.

• HW3 is due on W September 17 and consists of:
  
  
  
  • 2.3: 2,7
  • 2.4: 6
  • 3.3: 2,3,4
  • For the computational part of section 3.3, you may use as a model the following example p_3_3_5.m, which shows the string in Problem 3.3.5 (the last exampel I showed today, up to a factor of 2). I will show this demo on Monday. Modifying this code should be straightforward once the coefficients b_n and b_n^* for the solution are known.

• We covered sections 3.2 and 3.3. Next time we will see some demos of vibrating strings and sections 3.4-3.5. Lecure notes are here: pde005.pdf.
• More endless fun with strings and this Java vibrating string applet.

We covered section 2.3 on the Fourier series with arbitrary period and the cosine and sine series. The notes are here: pde004.pdf.

The math department provides (free) tutoring for this class in the T. Benny Rushing Mathematics Center. Here are the tutors that are most likely to help you with Math 3150:

• Today we covered Fourier series (section 2.2). Lecture notes: pde003.pdf.
• The deadline for HW1 is extended to Mon Sept 8 in class. The reason is that there was some confusion on problem 1.2.4a. The change of variables (chain rule) is outlined in Example 3 p 4, and you need to apply it twice.
• HW2 is due on Wed Sept 10 in class
  
  
  
  • 2.1: 7, 9
  • 2.2: 7, 9, 10a, 11, 13
  • Some exercises ask you to plot Fourier series approximations. The easiest way to do this is to modify the Matlab code I showed in class: sawtooth.m. If you prefer you can use some other language (Mathematica, Maple, etc…). When asked to submit computer related work please include printout of code and plots. To allow some time for setting up your accounts, the computer related part can be submitted up to Wed Sept 17.

• To access Matlab read on:
  
  
  
  • All registered students to this class have an account in the computer lab. To login please follow these instructions. Please do make sure you can login as assignments will have some basic programming part. Contact me if you have problems with your initial login.
  • Matlab is not required but it is recommended, as sample code will be given in this language. Only basic Matlab knowledge is needed. You can also use Octave which is an open source alternative to Matlab, but I do not guarantee that the sample code I give will be Octave compatible.
  • The Math Department’s Computer lab is located between LCB and JWB in the T. Benny Rushing Mathematics Center, room 155C. Matlab may also be available on other campus computer labs.

• I also showed a java applet illustrating Fourier series, endless fun!

• We covered 2.1. Lecture notes are available here: pde002.pdf.
• HW1: due Sept 3 2008 in class
  
  
  
  • 1.1: 1, 11
  • 1.2: 4, 5a, 7, 16

• Homework policy:
  
  
  
  • No late homeworks will be accepted.
  • You can work in groups, but you should submit your own write up.
  • Extensions may be granted on a case by case basis, but you have to let me know before the homework is due, and homework given after solutions are posted will receive no credit.
  • If you need to, you can also give your homework electronically (scanned) or leave it in my mailbox. Please contact me before you use any of these alternative methods.

• Please check your UMail email, if you have not received an email from the class by tomorrow, contact me. Announcements will be available here and through the class mailing list (your UMail ‘unid@utah.edu’ email account was added automatically when you registered). If you do not use this account that often I recommend you forward your UMail with the uNID Account Tools.

Class notes for lecture 1 are available here: pde001.pdf. We covered essentially 1.1,1.2 and 3.1 in the book. Plan for lecture 2: finish 1.2, 2.1 and 2.2.

The author of the textbook provides a solutions manual. Homework problems that are copied from this manual will not have credit.