First launch of a V-2 rocket from Cape Canaveral (1950).
Music by Arvo Pärt (1997).
First launch of a V-2 from Cape Canaveral (1950). Compare [1] and [2].

Dif­fer­en­tial Equa­tions (110.302) Fall 2013

Instructor:Carl McTague
MWF12–12:50pm (sections 1–4) in Maryland 110
1:30–2:20pm (sections 5–8) in Remsen 101
Office Hours:W 2:30–4:30pm in Krieger 212
Text:Boyce & DiPrima, Elementary Differential Equations and Boundary Value Problems, 10th Ed., Wiley, 2012 (Amazon).


12 DecHere is the Dear Abby question from the final exam. (There is incidentally the most oblique of references to Buñuel’s Obscure Object of Desire (1977).)
8 DecWhere to take the final exam (at 9am on Weds 11 Dec): §§1–2 in Shaffer 101, §§3–5 in Maryland 110, §§6–8 in Hackerman B17.
15 NovWhere to take the 2nd Midterm Exam: §§1–2 in Gilman 132, §§3–4 in Maryland 110, §§5–8 in Remsen 101.
7 NovThe 2nd Midterm Exam on Fri 15 Nov will not cover §§5.4–6, Power Series Solutions at a Regular Singular Point.
6 Nov
Here is a flash animation of the phase portrait evolution of the linear system: $$\vec{x}'=\begin{pmatrix}\phantom{-}\alpha&2\\-2&0\end{pmatrix}\vec{x}$$ as α increases. Notice the degenerate node which appears for an instant (at α=±3) as the system transitions between nodes and spirals. Experiment with the animation yourself using Mathematica:
  StreamPlot[v,{x,-5,5},{y,-5,5}]],{a,-10,10,Appearance ->"Labeled"}]
20 OctOffice hours for Week 8 will be 2:30–4:30pm Mon 21 Oct rather than Weds 23 Oct.
22 SeptThe schedule now recognizes the existence of Thanksgiving.
13 SeptI have changed my office hours to try to accommodate more of you.
11 SeptSolutions to the first homework assignment have been posted below.
2 SeptPlease attend section this week. Your TA will review some calculus.
8 AugThe ISBN 978-1-119-92506-4 listed in ISIS is for a special paperback run of the text available exclusively at the JHU bookstore with “Johns Hopkins University” and the course number printed on the cover (here’s a photo of it). The first word of the title has been dropped and the “and” appears to have been accidentally changed to “with” (but a few pages in, the title returns to normal). The color graphs are reproduced in black & white. The content is otherwise identical to the standard 10th edition but the price ($120) is lower. Note though that reluctance by non-JHU students to buy a JHU-branded text is likely to reduce its resale value. The price at Amazon ($150) for the standard 10th edition hardback is significantly lower than the list price the bookstore quoted ($240) when the dept decided to order the special paperbacks. The dept ordered them simply to help you save money. I am presently investigating why the Amazon price is so low (there are Amazon comments about needing to pay Wiley $75 separately for “access codes”—I doubt we’ll be needing them and don’t think the special paperbacks have them either). The Kindle edition ($80) appears to be an exact digital replica of the printed book (essentially a DRM’d PDF). Could you pull off using the 9th edition? Here’s what the author says is new in the 10th: (1st page), (2nd page). I intend to assign problems from the 10th edition and will expect you to hand in solutions to them. If you use the 9th edition then it will be your responsibility to ensure that you hand in solutions to the correct problems.


LectureDateTopicReadingAssignmentDue Date
1Sept 4Introduction§1.1:
4, 8, 12, 22, 24.
2, 8, 13.
(1.1.4), (1.1.12)
26Geometric Methods§1.3:1, 5, 12, 18, 20.Sept 9
First Order ODE’s:
39Linear Equations—Integrating Factors§2.1:5, 6, 12, 13, 15, 17, 27.(solutions)
411Separable Equations§2.2:3, 4, 8, 12, 21, 23, 28.(2.1.5), (2.1.6)
513Substitution Method & Applications§2.3:
2, 4, 10, 13, 14.
3, 4, 10, 14, 23, 27, 28.
(2.1.12), (2.2.12)
Sept 16
616Autonomous Equations§2.5:3, 7, 10, 20, 24.(solutions)
718Exact Equations§2.6:1, 4, 6, 10, 22, 23, 32.
820Existence & Uniqueness§2.8:2, 4, 8.Sept 23
Second Order Linear ODE’s:
923Constant Coefficients, Real Roots§3.1:3, 5, 10, 12, 17, 22.(solutions)
1025The Wronskian§3.2:3, 4, 8, 14, 22, 38.
1127Constant Coefficients, Complex Roots§3.3:2, 5, 10, 18, 22, 25.Sept 30
1230Euler Equations, Reduction of Order§3.4:4, 12, 16, 21, 24, 31, 37.(solutions)
13Oct 2Method of Undetermined Coefficients§3.5:2, 10, 18, 29.
144Variation of Parameters§3.6:4, 7, 14, 19.Oct 7
Oct 9FIRST MIDTERM (lectures 1–14)
1611Higher Order Linear ODE’s§4.1:
8, 16.
7, 11, 12.

Oct 21
14Fall Break Day (last day to drop is 13 Oct)
Power Series Methods:
1715Power Series Solutions : Ordinary Point§5.1:
2, 11, 16.
2, 6.
2, 3, 10.

1816Power Series Solutions : Regular Singular Point§5.4:
5, 17, 21.
4, 6, 12.
1, 14, 19.
Oct 21
Laplace Transform:
1918Laplace Transform§6.1:5, 15, 19.Oct 28
2021Solving Initial Value Problems§6.2:3, 6, 12, 22, 29.(solutions)
2123Discontinuous Forcing§6.3:
12, 15, 22, 27.
5, 10, 15.
2225Impulse Functions, Convolution§6.5:
1, 5.
4, 9, 15.
Oct 28
Systems of Linear ODE’s:
2328Linear Systems§7.1:
2, 6, 8, 16.
2430Review of Linear Algebra§7.2:
8, 10, 16, 22, 25.
2, 10, 16, 20, 22, 26.
25Nov 1Constant Coefficient Linear Systems§7.5:2, 7, 14, 18, 25, 27.Nov 4
264Complex Eigenvalues§7.6:2, 8, 9, 14, 18.(solutions)
276Fundamental Matrices§7.7:3, 11, 16.
288Repeated Eigenvalues§7.8:1, 2, 7, 15.Nov 13
2911Nonhomogeneous Linear Systems§7.9:1, 5, 7.Nov 13
Nov 15SECOND MIDTERM (lectures 17–29)
Nonlinear ODE’s and Stability:
3118Geometry of Linear Systems§9.1:1, 2, 15.
3220Geometry of Linear Systems (cont’d)§9.1:20, 21.
3322Autonomous Systems§9.2:2, 10, 15, 19, 21.Nov 25
3425Locally Linear Systems§9.3:1, 5, 14, 20, 27.Dec 2
35Dec 2Applications§9.4:
2, 5, 10.
2, 9, 13.
not collected
(partial solutions)
364Periodic Solutions and Limit Cycles§9.7:1, 3, 10, 11.
386Euler’s Method§2.7:
2, 11, 15.
Dec 11FINAL EXAM (lectures 1–38)


TAemailtimeroomofficehourshelp roomhours (Krieger 213)
1Kauffman<kauffman>Tues1:30–2:20pmKrieger 302Fri 2–3pmin Krieger 200Mon5–7pm
2Kauffman<kauffman>Tues3–3:50pmKrieger 309Fri 2–3pmin Krieger 200Mon5–7pm
3Xing Wang<xwang>Thurs3–3:50pmAmes 234Weds 3–5pmin Krieger 201Thurs7–9pm
4Xing Wang<xwang>Thurs4:30–5:20pmKrieger 302Weds 3–5pmin Krieger 201Thurs7–9pm
5Biggs<rbiggs>Tues4:30–5:20pmKrieger 309Tues 3–4pmin Krieger 411Weds1–3pm
6Xinyang Wang<xwang92>Thurs1:30–2:20pmKrieger 205Thurs 2:20–3:30pmin Krieger 207Mon7–9pm
7Qian<yqian6>Thurs3–3:50pmKrieger 308Thurs 4–5pmin Krieger 207Thurs9–11am
8Tolliver<tolliver>Tues3–3:50pmKrieger 302Thurs 2–3pmin Krieger 201Mon1–3pm


We will cover Chapters 1–9 of the text. Key topics will include:

First order ODE’s (linear, separable, autonomous, exact), Second Order Linear ODE’s (with constant & nonconstant coefficients), Higher Order Linear ODE’s (with constant & nonconstant coefficients), Series Methods, The Laplace Transform, Systems of Linear ODE’s, and Stabilitity in Nonlinear ODE’s.

Grading: The grading scheme will be:

Homework 15%First Midterm Exam 25%Second Midterm Exam 25%Final Exam 35%

Your 2 lowest homework scores will not count toward your grade.

Homework: Your assignments will be posted above. They will be collected in lecture (generally on Mondays) and returned in section. Late homework will not be accepted. Your two lowest homework scores will not count toward your grade. You are encouraged to discuss homework problems with one another. However, each of you must write up your solutions independently, in your own words, without supervision or well-meaning influence from anyone else. Disputes regarding homework grading should be discussed with your TA.

Midterm Exams will be in class on Weds 9 Oct and Fri 15 Nov. Books, notes, phones & calculators are forbidden. You must bring your ID to the exam, and may be called upon to show it. If you do not have your ID and your TA cannot attest to your identity then you may not receive a grade for the exam. The first midterm is scheduled so that the grades will be available before the drop deadline (Dec 13). You have the one hour of section time to bring up grading errors or omissions on the midterms, once they have been returned to you. You may not take the exam home and bring it back for corrections.

The Final Exam will be 9am–12pm Weds 11 Dec. Further particulars nearer the time.

Absence: You are expected to attend class and take exams as scheduled. There will be no makeup exams. If you miss a midterm exam then you will get a zero for that exam. If you miss the final exam then you will automatically fail the course. In exceptional circumstances documented by a letter from your doctor or your academic supervisor, the remaining homework and final exam may be given correspondingly more weight to take up the slack.

Disability: Any student with a disability who may need accommodations in this class must obtain an accommodation letter from Student Disability Services, 385 Garland, (410) 516-4720,

Ethics: Don’t get it WRONG, like Kant! Seriously though, cheating & other forms of academic dishonesty are corrosive & harmful to our university:

The strength of the university depends on academic and personal integrity. In this course, you must be honest and truthful. Ethical violations include cheating on exams, plagiarism, reuse of assignments, improper use of the Internet and electronic devices, unauthorized collaboration, alteration of graded assignments, forgery and falsification, lying, facilitating academic dishonesty, and unfair competition.

Report any violations you witness to the instructor. You may consult the associate dean of student affairs and/or the chairman of the Ethics Board beforehand. See the guide on “Academic Ethics for Undergraduates” and the Ethics Board Web site for more information.

Copyright © 2013 by Carl McTague