Homework 8, due November 21, 2016.

[goodwine]

Reading: Chapter 5, sections 1-3 and subsections 5.5.1-5.5.4. Chapter 11, sections 1-3.

Exercises: 5.1 (but make the -2t coefficient +2t), 5.5, 5.7-5.10 and 11.1 (part 2 only).

Project: (submit separately from your homework) It is now 2022 and you work for Tesla on suspension systems and vehicle dynamics. Elon has to decide whether to invest $2,000,000 in a suspension redesign project and need assurance the project is in technically competent hands.

Submit a one page description of the manner in which you validated the program you are using for the suspension design project. The one page should not take long to write. The work to make the one page compelling might take a long time. If you want non-imaginary motivation, this is where you prove to yourself that the program you are using for 15% of your grade is working correctly. If what you submitted with the last homework is incorrect do not base it on that, but rather on the correct version.

You should not say "I tried a, b and c." You should say "I tried a, and expected the result a' and that is what happened" and/or "I tried a for various frequencies, and the magnitude of the response for those frequencies was b, c, d, and e which correspond to points b', c', d' and e' on this graph, which is the closed form solution" or "if I do this, I expect the response to be like Fig 22 in book xyz, and here is the plot and it looks like Fig 22 in book xyx."

[goodwine]

For problems 5.7-5.10, do you want us to go through the whole process to find a0, a1, and a(n+1), or can we just use the given recurrence relations in the book?

No, work them out too. Unfortunately, Chapter 5 was the only chapter in the book where I didn't have a chance to use a preprint for teaching, so it wasn't debugged by some students, so there are a few more typos than normal.

[goodwine]

Hello professor, this is Mendel Moise. I am in your differential equation class. I have a question on the homework. If you are taking the derivative of a series that starts at n = 1, does the derivative and second derivative starts at n = 2, n = 3, or does it stay at n = 1 for all 3? This come up in exercise 5.8 when we have to determine a series solution for the chebychev equation, and in section 5.2 it says to assume a solution that starts at n = 1.

I think that's probably a typo and should start at zero.

[jfulnecky]

At the beginning of the instruction for Chapter 5 problems, it states "for any exercise that requires a series solution... Plot your solution for different numbers of terms in the partial sum." All the problems individually state to plot the solution except for 5.7 which only states that we need to find a solution to Airy's equation. Do we need to plot our solutions for 5.7?

[goodwine]

At the beginning of the instruction for Chapter 5 problems, it states "for any exercise that requires a series solution... Plot your solution for different numbers of terms in the partial sum." All the problems individually state to plot the solution except for 5.7 which only states that we need to find a solution to Airy's equation. Do we need to plot our solutions for 5.7?

I would say no, it is not required. However, at this point I suppose it would be very easy to do and a good way to check if your answer is correct.

[mjunker1]

Would you be able to post the codes from class starting from the beginning of chapter 5?

[goodwine]

Would you be able to post the codes from class starting from the beginning of chapter 5?

Yes, submit code, but if a problem is a simple modification from an earlier problem, you can just state that instead of printing out a program with a very trivial change.