Spring 2023: Differential Equations II (Math 332)


Instructor Dr. Armin Straub
MSPB 313
(251) 460-7262 (please use e-mail whenever possible)
Office hours MWF, 9-11am, or by appointment
Lecture MWF, 2:30-3:20pm, in MSPB 350
Midterm exams The tentative dates for our two midterm exams are:
Friday, February 17
Friday, March 31
Final exam Monday, May 1 — 3:30pm-5:30pm
Online grades Homework Scores
Exams: USAonline (Canvas)
Syllabus syllabus.pdf

Lecture sketches and homework

To help you study for this class, I am posting lecture sketches. These are not a substitute for your personal lecture notes or coming to class (for instance, some details and motivation are not included in the sketches). I hope that they are useful to you for revisiting the material and for preparing for exams.

Date Sketch Homework
01/09 lecture01.pdf Homework Set 1: Problems 1-6 (due 1/23)
01/11 lecture02.pdf Homework Set 1: Problems 7-8 (due 1/23)
01/13 lecture03.pdf Homework Set 1: Problem 9 (due 1/23)
01/18 lecture04.pdf Homework Set 2: Problems 1-3 (due 1/30)
01/20 lecture05.pdf Homework Set 2: Problem 4 (due 1/30)
01/23 lecture06.pdf Homework Set 2: Problems 5-6 (due 1/30)
01/25 lecture07.pdf Homework Set 3: Problems 1-3 (due 2/6)
01/27 lecture08.pdf Homework Set 3: Problems 4-5 (due 2/6)
01/30 lecture09.pdf Homework Set 3: Problems 6-7 (due 2/6)
02/01 lecture10.pdf Homework Set 4: Problem 1 (due 2/13)
02/03 lecture11.pdf Homework Set 4: Problems 2-3 (due 2/13)
02/06 lecture12.pdf Homework Set 4: Problem 4 (due 2/13)
02/08 lecture13.pdf work through Example 62
02/10 lecture14.pdf Homework Set 5: Problems 1-3 (due 2/17)
02/13 lecture15.pdf work through Example 68
02/15 review get ready for the midterm exam on 2/17 (Friday)
exam practice problems (as well as solutions) are posted below
02/20 lecture16.pdf Homework Set 6: Problems 1-2 (due 3/3)
02/22 lecture17.pdf Homework Set 6: Problems 3-4 (due 3/3)
02/24 lecture18.pdf Homework Set 6: Problem 5 (due 3/3)
02/27 lecture19.pdf Homework Set 7: Problems 1-2 (due 3/17)
03/01 lecture20.pdf Homework Set 7: Problems 3-4 (due 3/17)
03/03 lecture21.pdf Homework Set 7: Problems 5-6 (due 3/17)
03/13 lecture22.pdf Homework Set 8: Problem 1 (due 3/29)
03/15 lecture23.pdf work through Example 98
03/17 lecture24.pdf Homework Set 8: Problems 2-3 (due 3/29)
03/20 lecture25.pdf Homework Set 8: Problem 4 (due 3/29)
03/22 lecture26.pdf Homework Set 8: Problems 5-6 (due 3/29)
03/24 lecture27.pdf Homework Set 9: Problems 1-3 (due 3/31)
03/27 lecture28.pdf work through exam practice problems
03/29 review get ready for the midterm exam on 3/31 (Friday)
exam practice problems (as well as solutions) are posted below
04/03 lecture29.pdf Homework Set 10: Problem 1 (due 4/17)
04/05 lecture30.pdf Homework Set 10: Problem 2 (due 4/17)
04/07 lecture31.pdf work through Examples 135, 136
04/10 lecture32.pdf Homework Set 10: Problems 3-4 (due 4/17)
04/12 lecture33.pdf Homework Set 11: Problem 1 (due 4/26)
04/14 lecture34.pdf Homework Set 11: Problem 2 (due 4/26)
04/17 review / fill in gaps revisit Example 114
04/19 lecture35.pdf Homework Set 11: complete! (due 4/26)
04/21 lecture36.pdf work through Examples 142, 143, 144
04/24 lecture37.pdf finish all homework
04/26 review get ready for the final exam on 5/1 (Monday)
exam practice problems (as well as solutions) are posted below
04/28 review retake old midterm exams
lectures-all.pdf (all lecture sketches in one big file)

About the homework

  • Homework problems are posted for each unit. Homework is submitted online, and you have an unlimited number of attempts. Only the best score is used for your grade.

    Most problems have a random component (which allows you to continue practicing throughout the semester without putting your scores at risk).

  • Aim to complete the problems well before the posted due date.

    A 15% penalty applies if homework is submitted late.

  • Collect a bonus point for each mathematical typo you find in the lecture notes (that is not yet fixed online), or by reporting mistakes in the homework system. Each bonus point is worth 1% towards a midterm exam.

    The homework system is written by myself in the hope that you find it beneficial. Please help make it as useful as possible by letting me know about any issues!

Exams and practice material

The following material will help you prepare for the exams.


For more involved calculations, we will explore the open-source free computer algebra system Sage.

If you just want to run a handful quick computations (without saving your work), you can use the text box below.

An easy way to use Sage more seriously is This free cloud service does not require you to make an account or to install anything: after choosing Use CoCalc Anonymously, select View Your CoCalc Projects... (at the bottom of the page), create a project (choose any name for it), followed by New and Sage worksheet and start computing. (To save your work for later, you can create a free account.)

Here are some other things to try:

  • Sage can solve (symbolically!) simple initial value problems. For instance, to solve Example 18 in Lecture 4:
    y = function('y')(x)
    desolve(diff(y,x,2) - diff(y,x) - 2*y == 0, y, ics=[0,4,5])
  • Sage is happy to compute eigenvalues and eigenvectors. For instance, to solve Example 52 in Lecture 10:
    A = matrix([[8,-10],[5,-7]])
  • Sage can even compute general powers of a matrix. For instance, to solve Example 61 in Lecture 13:
    n = var('n')
    M = matrix([[0,1],[2,1]])
  • Similarly, Sage can compute matrix exponentials. For instance, to solve Example 66 in Lecture 14:
    M = matrix([[8,-10],[5,-7]])
    (Note that x is predefined as a symbolic variable in Sage; that's why we don't need x = var('x') as in the case of n above.)
  • Using matrix exponentials, we can easily solve inhomogeneous systems of differential equations. For instance, to solve Example 77 in Lecture 17:
    t = var('t')
    A = matrix([[1,2],[-1,4]])
    y = exp(A*x)*vector([1,2]) + exp(A*x)*integrate(exp(-A*t)*vector([0,2*e^t]), t,0,x)