Math 309 Spring 2021

Math 309 - Sections E & F - Spring 2021 - Linear Analysis

Contents	Systems of linear differential equations, Fourier series, and boundary value problems.
Instructor	Heather Lee (heathml@uw.edu )
Lecture time	MWF 10:30-11:20am (for Section E), 11:30am-12:20pm (for Section F). Zoom link posted on Canvas.
Office hours	Monday 5-6:30pm, Tuesday 1-2pm, and Friday 12:30-1pm. Use the Office Hour Zoom link posted on Canvas. Email me to make an appointment if you need to talk to me without other students present.
Grading	45% homework, 20% midterm exam, 35% final exam.
	Grading will not be curved, so as to eliminate competition between students. The grading standard will be set after I have looked at all the homeworks/exams and their rubrics carefully in order to determine a fair standard based on my judgement of their difficulties. Getting 60% in all three categories, homework, midterm, and final, automatically guarantees a pass (2.0); though the actual standard for passing might be lower.
Gradescope	www.gradescope.com; also accessible via Canvas.
Piazza	piazza.com; also accessible via Canvas.
Some registration dates	Last day of the unrestricted drop period (Apr 11) See the academic calendar for detailed dates on add/withdrawl Information on Extraordinary Circumstances Quarter (ECQ) Late Grading Options (Spring 2021 counts as an ECQ)

Homeworks |
Exams |
Lectures |
Other Resources |
Special Accommodations

Homeworks

Weekly assignments are generally due on Tuesday at 11:59pm, though there will be a few exceptions. I will post the problems about one week in advance on this webpage, and the exact same set of problems will also posted at the same time on Gradescope. You will be submitting your solutions on Gradescope following THIS INSTRUCTION. Late homeworks will not be accepted unless you have extenuating circumstances, see the special accommodations section.

In a given homework with N problems, I might select anywhere in the range of 0-N problem(s) for the grader to grade. You will not know which problems I would select before that homework is due. I will post solutions to all problems in Canvas after the due date.

What's covered in lecture should provide you enough tools to tackle these homework problems, but if you notice that the some homework problems are much harder than the basic examples presented in lectures or asking you to explore territories not completely covered in lectures, know that this is intentional as homework is a very important part of the learning process. Please always feel free to ask me for help when you are stuck.

Solutions should be presented using complete sentences, with grammatically correct English, that combine both words and precise mathematical expressions to articulate your line of reasoning. You don't need to feel extremely stressed out about English grammar, but your solution should show that you've put in a good effort as the ability to communicate your ideas clearly is a good skill to acquire no matter what your major is. Also, one good indicator of whether you've understood your solution properly is whether you are able to explain it to others. In your first draft of the solution, don't be afraid of writing down something that's wrong or something that could be right but you can't fully explain, but it does mean that you definitely need to think about it more until you are able to explain what you wrote.

Collaboration on homework is encouraged, but you need to write up the solutions in your own words that reflect your own understanding of the material. Simply copying other people's solutions would be doing yourself a disservice as well as compromising your academic integrity.

Do NOT post the following problem sets anywhere else on the internet.
Homework 0 (Due Tuesday, Mar 30, 9pm)

Homework 1 (pdf, tex) (Due Tuesday, Apr 6, 11:59pm)

Problems 1-6 are mostly a review of your prerequisite linear algebra knowledge and can be done before the start of this course. Problem 7 is doable after L3. Problems 8 is doable after L4. Homework 2 (pdf, tex) (Due Tuesday, Apr 13, 11:59pm)

This homework appears scarily long, but most of it is just for you to read. A couple of these might get followup questions in future homeworks. Problem 4 is doable after L3, problems 2, 3, 5, 6 should all be doable after L4 and the beginning of L5, problem 7 is doable after L6. Homework 3 (pdf, tex) (Due Tuesday, Apr 20, 11:59pm)

Problem 1 doesn't need any special knowledge from this class. Problems 2a,3a 4abc, 5ab,6a are doable after L7. Problems 2, 3, 4d are doable after L9. The rest of the problems, i.e. 4e, 5cd, 6bc are doable after L10. Homework 4 (pdf, tex) (Due Tuesday, Apr 27, 11:59pm)

Problem 1 is doable after L10. Problem 2 doesn't need any special knowledge from this class. Problems 3a, 4ab, 5a, 6a are doable after L11. Problem 3bc is doable after L12. The rest of the problems, i.e. 4c, 5b, 6b are doable after L13. Homework 5 (pdf, tex) (Due Monday, May 3, 11:59pm) Note the special exam week Monday due date.

Problem 1 is doable after L12. Problem 2 is doable after you finish doing HW4 Problem 3 (but it might be helpful to wait I read through this problem with you in L14). Problems 3ac and 4ac are doable after L14. The rest, i.e. problems 3bd and 4bd are doable after L15. Homework 6 (pdf, tex) (Due Tuesday, May 18, 11:59pm)

Problem 1 is doable after L3, L4. Problem 2 is doable after L8. Problem 3 is doable after L17. Problems 4 and 5 are doable after L18. Problems 6, 7a is doable after L19. Problems 7bc are doable after L20. Homework 7 (pdf, tex) (Due Tuesday, May 25, 11:59pm)

Problem 1 is doable after L17. Problem 2 is doable after L22. Problems 5 and 6 are doable after L23. Problems 3 and 4 are doable after L24. Homework 8 (pdf, tex) (Due Friday, June 4, 11:59pm)

Problem 5 doesn't require any special knowledge. Problem 4 is doable after L23/24. Problems 1 and 2 are doable after L25. Problem 3 is doable after L26.

Exams

Exams will be submitted on Gradescope. The exam will appear on Gradescope exactly at the starting time of the exam. The Gradescope format and the submission procedure for the exam will be exactly the same as that for the homework. Please leave yourself plenty of time for the submission process.

I will be checking my email during the exam time, so if you have any questions or if you experience any technical problems with the Gradescope submission, send me an email immediately, and you should get a response in real time (though there could be a tiny wait if many students are emailing me at the same time).

Due to the time pressure during exams, I will not require you to write solutions in complete sentences for exams, unlike the homeworks.

Allowed materials during the exam: you are allowed to use only scientific (no graphing) calculators (though I will design the exam so all the numbers on the exam should be computable by hand and it won't really be advantageous to have a calculator). Prior to the exam, you can write down a set of review notes (no page limit) to use during the exam. It cannot just be the entire lecture notes you took during class (or printed outs of them); it has to be something you write during the review process. No books and absolutely nothing online.

Past Exam Archive: past exams are NOT(!!) good indicators for what future exams will look like, though they are nonetheless useful practice (don't worry about doing all of them, just look at a couple).

Lectures

The textbook referenced is Boyce and DiPrima's Elementary Differential Equations and Boundary Value Problems (mostly Chapters 7 and 10). Getting a textbook is recommended but optional. The most important thing is to keep up with the lectures and not fall behind.

You can access an electronic version of this textbook on Canvas, starting from Mar 29 and free of charge until Apr 19, then it will cost $25. You must pay before Apr 19, after that you can no longer purchase the e-book. Use this U-Bookstore link for making the purchase (this link won't be activated until Mar 29).
After you make the purchase, first access it via the link on Canvas. Once you've used that link on the Canvas page, the e-book will go on your VitalSource bookshelf. You can read the book online, via Canvas or by directly logging into VitalSource Bookshelf. Or once you make the purchase, you can download and use the VitalSource reader. You can print up to 10 pages at a time as well. The downloaded version doesn't expire.
If you prefer a paper version, any edition of Elementary Differential Equations and Boundary Value Problems by Boyce and Diprima will do. Older versions are cheaper.

It is essential that you attend the lectures, not just read the notes. Recording of the lecture will be posted on Panopto afterwards (which are restricted to registered students and can be accessed from Canvas). I strongly recommend that you attend the real-time lectures and pay attention during them so you can ask questions and keep up with the pace of the class. Occasional minor mistakes/typos in the lectures are corrected in the notes after class, so make sure you check the notes that are posted here.

Screenshots or recordings of other students during active video participation sessions are strictly forbidden. Any student caught engaging in this behavior will be reported to the Student Conduct Office.

(Exam dates are set in stone, but other plans for future dates below are tentative.)

No.&Date	Topics and Comments	Notes
L1 Mon Mar 29	Topic: Logistics Math 307/308 review	307 review Worksheet Worksheet Solution
L2 Wed Mar 31	Topic: Math 308 review Textbook: 7.2, 7.3	307 review Worksheet Worksheet Solution
L3 Fri Apr 2	Topic: linear algebra review Intro. to system of linear differential equations Textbook: 7.1, 7.4	Notes for L3, L4(part a) Notes for L4(part b)
L4 Mon Apr 5	Topic: Intro. to systems of linear differential equations cont'd Textbook: 7.1, 7.4	Notes for L3, L4(part a) Notes for L4(part b)
L5 Wed Apr 7	Topic: Euler's method Textbook: 8.1 Additional Resource: Page 5 of this lecture note I wrote when teaching Math 307 has an example of Euler's method for a single first order equation.	Notes euler.jl The version below has that one extra plot of thetaL: eulerLecture.jl Sample plots: Plot1(h=0.1, N=100, not accurate enough) Plot2(h=0.01, N=1000) Plot3(h=0.01, N=10000)
L6 Fri Apr 9	Topic: Euler's method cont'd
L7 Mon Apr 12	Topic: Homogeneous 1st order systems with constant coefficients: diagonalizable matrix cont'd Textbook: 7.5, 7.7	Notes
L8 Wed Apr 14	Topic: Phase portraits for solutions of x'=Ax when A is diagonalizable with real eigenvalues Textbook: 7.5
L9 Fri Apr 16	Topic: Phase portraits for solutions of x'=Ax when A is diagonalizable with real eigenvalues Textbook: 7.5
L10 Mon Apr 19	Topic: Phase portraits for solutions of x'=Ax when A is diagonalizable with real eigenvalues cont'd Textbook: 7.6
L11 Wed Apr 21	Topic: Homogeneous 1st order system with constant coefficients: diagonalizable matrix with complex eigenvalues Textbook: 7.6	Notes
L12 Fri Apr 23	Topic: Homogeneous 1st order system with constant coefficients: diagonalizable matrix with complex eigenvalues cont'd Textbook: 7.6
L13 Mon Apr 26	Topic:Homogeneous 1st order system with constant coefficients: diagonalizable matrix with complex eigenvalues cont'd Textbook: 7.6
L14 Wed Apr 28	Topic: Homogeneous 1st order system with constant coefficients: non-diagonalizable matrix Textbook: 7.8	Notes
L15 Fri Apr 30	Topic: Homogeneous 1st order system with constant coefficients: non-diagonalizable matrix Textbook: 7.8	Notes
L16 Mon May 3	Midterm review
Wed May 5	Midterm exam during class time
L17 Fri May 7	Topic: x'=Ax where A is an nxn matrix Fourier series Textbook: 10.2-10.4	Notes (3x3 nondiagonalizable examples) Notes for L17(part 2), L18, L19, L20, L21(part 1) Graph of the partial sums for ex3 in L20 Notes for L21(part 2), L22(part 1) Fourier Series summary
L18 Mon May 10	Topic: Fourier series Textbook: 10.2-10.4
L19 Wed May 12	Topic: Fourier series Textbook: 10.2-10.4 Extra links: A series of videos introducing Michelson's Fourier machine, a mechanical device computing the Fourier series: video 1, video 2, video 3, video 4.
L20 Fri May 14	Topic: Fourier series Textbook: 10.2-10.4
L21 Mon May 17	Topic: Fourier series Half interval Fourier series Textbook: 10.4
L22 Wed May 19	Topic: Half interval Fourier series cont'd Fourier transforms Textbook: 10.4	See above for notes on L22(part 1) Notes for L22(part 2), L23(part 1) Notes for L23(part 2), L24, L25 Summary of heat equation with homogeneous boundary conditions
L23 Fri May 21	Topic: Fourier transforms The heat equation Textbook: 10.5
L24 Mon May 24	Topic: The heat equation Textbook: 10.1, 10.5
L25 Wed May 26	Topic: The heat equation Textbook: 10.5
L26 Fri Mar 28	Topic: The heat equation Textbook: 10.5, 10.6	Notes for L26(part 1) Notes for L26(part 2), L27(part 1) Notes for L27(part 2)
L27 Wed Jun 2	Topic: heat equation, wave equation, Laplace equation
L28 Fri Jun 4	Topic: Final exam review
	Final Exam: any 1hr50min (i.e. 110min) block during the time period of Mon Jun 7, 8:30am to Wed Jun 9, 4:30pm. I will be checking emails in real-time during Monday 8:30-10:20am and Wednesday 2:30-4:20pm.

Other Resources

UW CLUE is a space for students to connect and get support. They have tutors who are knowledgable in the content of Math 309. All are free of charge.

Desmos: a very nice online graphing calculator.

My lectures and notes for Math 307.

Julia:

Download the latest stable version at https://julialang.org/.
Follow this instruction, written by Per-Olof Persson, for installing Julia, running the initial tests, installing additional packages (for starters, install "PyPlot", "DifferentialEquations", "Juno", and "PyCall", and you can always install additional ones later when needed), and optionally for installing Atom and Juno. This instruction is written for PC Windows, but it's similar for MacOS.
Programming for Mathematical Applications is a very accessible set of lecture notes, mainly based on Julia. I would recommend that you at least try out Section 1.1 on Julia as a calculator. (If you are looking at the homepage for these notes, ignore any mentions of the cloud based Julia server based on Jupyter Notebooks.)

Special Accommodations

Homework:

as early as possible (1 hour before the due time at the latest)

Exams:

at least 1 week in advance

at least a day before the exam

Illness:

Disability accommodation:

UW DRS

Religious accommodations:

THIS PAGE

Friday, Apr 9, 5pm