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

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) Homework 2 (pdf, tex) (Due Tuesday, Apr 13, 11:59pm) Homework 3 (pdf, tex) (Due Tuesday, Apr 20, 11:59pm) Homework 4 (pdf, tex) (Due Tuesday, Apr 27, 11:59pm) Homework 5 (pdf, tex) (Due Monday, May 3, 11:59pm) Note the special exam week Monday due date. Homework 6 (pdf, tex) (Due Tuesday, May 18, 11:59pm) Homework 7 (pdf, tex) (Due Tuesday, May 25, 11:59pm) Homework 8 (pdf, tex) (Due Friday, June 4, 11:59pm)

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. 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
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
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
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:
  • Special Accommodations

    Homework: Exams: Illness: Disability accommodation: Religious accommodations: