Math 391 1XC - Summer 2020

Course Syllabus and Course Learning Outcomes

• Math 391 1XC Syllabus - Course syllabus. Contains grading policy, requirements, assignments and other important info.

• CLO - The course learning outcomes for the class.

Video Recordings of Lectures

Click here for video recordings of the lectures posted on YouTube.

Office Hours

Office hours will be held on Tuesdays and Thursdays from 12pm to 1pm via Zoom. If you'd like to see me during office hours, email me and I will send you the link.

Quiz and Quiz Answer Keys

• Quiz 1 Blank

• Quiz 1 Answers

• All other quizzes and their answers can be found in your Gradescope account.

Reviews for Tests

Test 1 Review

FOLLOW THE ADVICE/INSTRUCTIONS!

The most important assessment metric is what you can do correctly by yourself. If you did not get a problem correct entirely by yourself, assume you don't understand that problem. Whether you get help from looking at a written solution, or an answer, or a hint from another human, or by watching virtual Jhevon on YouTube, any help you get indicates that there's something you don't understand. Strive to be able to do a problem correctly all by yourself. When you can get several problems for some topic correct, back to back, while almost being bored, then you can say you understand that topic. At all times, prioritize what you can do on your own.

I am not saying don't get help (you should!), but don't confuse the help for your own understanding. I will give you instructions on how/when to get help in this section. Be sure to distinguish between what you originally did vs what you got help with. Use a different writing color, or use a different paper all together. You need to save your original work, and don't copy the help you got from somewhere else in the same place as your original work. Your original attempt must be kept in its original form. Do not contaminate this. Any time you get help, write it somewhere else or write it in a different color ink, etc.

Don't practice the same problems over and over. It is easy to confuse "understanding" with "remembering". If you need more practice on a certain problem type, consult your textbook for new problems.

A. Do some preliminary studying, as I've been describing in class and have been suggesting by quizzes (know general formulas, methods, concepts, etc.) This should not take you too long, assuming you've been studying for quizzes. But take some time to really sharpen up on these. Work out all the kinks, so you can recall a fact quickly and accurately, by rote, on command.

B. Save all the scrap paper that you use for studying. Distinguish between anything that you did on your own, and anything that you got help with from any other source. That way, when getting help or assessments from me, or a tutor, we would be able to see what you understand written on the paper and thus would be able to help you better.

C. Below you will see problem sets to complete, taken from past finals. Do one problem set at a time, in its entirety, under test conditions. The time you should take will be indicated. Do not go beyond this. If you run out of time before you complete a problem, write "ran out of time" in the space where you'd normally write the solution. You may do the solution afterwards (somewhere else, or with a different color ink) just to see that you could do it if you had not ran out of time. After each set, assess how you did, using any source--but a tutor or teacher is best.

D. Pay attention to the type of problems you're really good and/or fast at doing. These should be the problems that you do FIRST on the actual test. Do not do a test in order. Do what is easiest first. This builds momentum, confidence, and ensures that you don't lose points by running out of time when you could have done a problem. A slight variation on this is to start by doing the test in order, but the moment you realize you're stuck, just move on quickly and come back later.

E. Go here to access the final exams mentioned. Do the indicated problems giving yourself about 10 minutes per full problem. After each set, fill in the gaps with your notes, or the help of a tutor, etc. Then, once confident you understand, move on to the next set. The goal is, by the time you get through all problem sets, all your major gaps would have been filled. But you must do the work by yourself first, BEFORE getting help. It's OK if you leave something blank or half done at the first run through. Just fill in the gap afterwards, and again, make sure you don't confuse your original attempt (or lack thereof) with the help that you get! Keep these separate! You (or I) will need this to assess (and fix) your weaknesses later.

• Sp 2005: 1, 2, 3, 4, 7 (L), 10(a) (R), 10(b), 11.
• Fa 2005: 1 (B), 2, 4(b) (L), 5 (R) (and find the Wronskian), 6, 8, 9, 12, 13(a) (B), 13(b).
• Sp 2006: 1, 2, 3, 4, 5 (R), 9, 10, 11 (L), 12, 14.
• Fa 2006: 1, 2(a), 3(a), 4, 8, 9, 11 (R), 12 (they told you it's homogeneous. That's way too nice. I won't give you such info. Ignore the singular points part).
• Sp 2011: 1, 2, 3(a) (R), 3(b), 5, 6, 7 (hint: use an appropriate substitution--we'll look at a different way to solve this kind of problem in chapter 4), 8(a), 8(b) (L).
• Fa 2011: 1, 2(a), 29b) (R), 3(a) (B), 3(b), 5, 6, 7 (B), 8(a), 8(b) (L).

KEY:

• (R) = I'll give you one homogeneous solution and ask you to find a second using Reduction of Order

• (L) = Do NOT use the Laplace transform, but rather a technique from chapter 3

• (B) = A problem of this type may show up as a bonus problem

It has been brought to my attention that some of the finals above have been removed. You can access such files below:

• Math 391 Spring 2005 Dept Final
• Math 391 Fall 2005 Dept Final
• Math 391 Spring 2006 Dept Final

Do NOT look at the Spring 2017 final on the Main Math 391 page. We'll use that final to help us review at the end of the semester!

More Practice!!!

Below are my old test 1 and 2 from the last time I taught this course in Spring 2015. I give less tests now, so your test will cover material from both of these tests. You can take these under test conditions as described below. Print out both without looking at the problems(!), or when you've scheduled a time to take them, pull them up on a screen but don't scroll down until you're ready to begin.

Click on the link to access the tests, and do the following problems in one sitting. Use test conditions and STOP when the time is up!

• Jhevon's Test 1 from Spring 2015 - Take 1 hour - do the following problems:

1(g) both parts, 2, 3, 4, 5, Bonus problem 1, Bonus problem 3 (a function of y will make this exact).

• Jhevon's Test 2 form Spring 2015 - Take 1 hour - do the following problems:

1, 2, 4, 5

A bonus section for your test might look like the bonus of test 2, particularly problem 4. I'll ask about solving a SOLDE with undetermined coefficients, ask you to guess the solution of some SOLDE or HOLDE (Higher order linear ODE) under the undetermined coefficients method.

When you're done. Review the solutions and assess yourself. Remember what I said above, if you read a solution and it seems "obvious", but you were not able to do it when you were taking the test, it means it is actually not obvious and your brain is tricking you. Go over the topic and make sure you understand it.

• Jhevon's Test 1 Spring 2015 Solutions
• Jhevon's Test 2 Spring 2015 Solutions

Bonus round!

Here's a Mock Test. Do this after completing the above. How'd you do?

Hopefully you did good and know that you did good. I won't be providing solutions for this.

Test 2 Review

(A) Follow the instructions from the test 1 review.

The topics you will want to study are:

• Undetermined coefficients
• Higher order linear ODEs with constant coefficients, including roots of unity for a complex number
• Second order Euler equations; know about all cases
• Know how to find the singular points of an ODE and classify them as regular or irregular
• Finding series solutions to ODEs at ordinary points and regular singular points
• Know how to define a Laplace Transform, compute the Laplace Transform of a function, and use Laplace transforms to solve linear ODEs (You will be provided with a table of Laplace Transforms for the test)
• Know how to define a Fourier Series for a function and compute the appropriate Fourier series for a given function.
• Bonus will cover solving in the heat equation and separation of variables for PDEs. I might also ask you to compute some random inverse Laplace Transforms.

(B) Go here to access the finals mentioned, and do the indicated problems.

• Sp 2005: 5, 6, 7, 8, 9, 10.
• Fa 2005: 1, 3, 4, 5, 7, 10, 11, 13.
• Sp 2006: 5, 6, 7, 8, 10 (*), 11, 13.
• Fa 2006: 2(b), 5, 6, 7, 10, 11, 12(b).
• Sp 2011: 3(a), 4, 7, 8(b), 9, 10.
• Fa 2011: 2(b), 3(a), 4, 7, 8(b), 9, 10.

(*) - Do not use reduction of order! And pretend that you were NOT given one solution. For bonus: problems may be asked from any topic done throughout the semester.

(C)

More Practice!!!

Below are my old test 3 and 4 from the last time I taught this course in Spring 2015. Print out both without looking at the problems(!), or when you've scheduled a time to take them, pull them up on a screen but don't scroll down until you're ready to begin. Take them under test conditions.

Click on the link to access the tests, and do the following problems in one sitting. Use test conditions and STOP when the time is up! Take both tests in their entirety, and give yourself 1 hour and 15 minutes each.

• Jhevon's Test 3 from Spring 2015

• Jhevon's Test 4 form Spring 2015

When you're done. Review the solutions and assess yourself. Remember what I said above, if you read a solution and it seems "obvious", but you were not able to do it when you were taking the test, it means it is actually not obvious and your brain is tricking you. Go over the topic and make sure you understand it.

• Jhevon's Test 3 Spring 2015 Solutions
• Jhevon's Test 4 Spring 2015 Solutions

For even extra practice(!), go over tests 1 and 2 and do all the problems I told you not to do back then.

(D)

Bonus round!!!

Here is a mock test 2 to practice. Give yourself 1 hour and 30 minutes for this.

Mock Test 2 - Do this after completing the above.

Hopefully you did good and know that you did good. I won't be providing solutions for this.

Final Exam Review

Here's how to prep for the final:

(You should have done already, but if not, take a bit of time to do this now). Go over old quizzes (which you can find above) and tests for the class (which you can find below). Make sure you understand how to do each problem including the strategy for each problem type.

Once done, go here and do the spring 2017 final exam. Do it in its entirety under test conditions. The only other thing I will give you is a short Laplace transforms table (that does not include the equation for how to find the Laplace transform of a derivative).

You can check your work with the solutions here. DO NOT LOOK AT THE SOLUTIONS FILE UNTIL AFTER YOU TAKE THE FINAL YOURSELF UNDER TEST CONDITIONS!!!

You may next want to do the spring 2011 final in its entirety also. There are posted solutions for that.

For more practice, here's the Spring 2019 Final.

You can go over the quizzes and tests for our class. And even look up some ODE multiple choice practice problems to do under timed conditions.

Your final will be multiple choice, but going through long form finals and doing a lot of long form practice can teach you a lot of concepts if you're paying attention. So get to it.

Good luck.

Blank Tests and Solutions

• These were done online through Gradescope this semester. You will have access to the tests and the answers in your Gradescope account.

Announcements

• Remember to let me know your preferred email if I don't already have it.
• Test 1 will be on June 25th.
• Test 2 will be on July 16th.
• The final exam will be on Thursday, July 23 at 5:00pm to 7:15pm.