Math 302 Differential Equations with Applications
Fall 2017

Course Information

  • Jonas Lührmann
  • Email: luehrmann (at)
  • Office: Krieger 219
  • Office hours: WF 14:30-15:30
  • MWF 12:00 - 12:50 at Remsen 101
  • MWF 13:30 - 14:20 at Remsen 101
  • Elementary Differential Equations and Boundary Value Problems (10th Edition) William E. Boyce and Richard C. DiPrima

We will basically cover the material detailed in the official 110.302 Differential Equations Course Syllabus. However, the lectures will not follow the text verbatim and I strongly recommend to take notes in class.


There will be two midterm exams and a final exam:

  • 1st midterm exam: Monday, October 9, in class
  • 2nd midterm exam: Monday, November 13, in class
  • Final exam: Wednesday, December 13, 9:00-12:00

Exams are closed book, closed notes. There will be no make-up exams. For excused absences, the grade for a missed exam will be calculated based on your performance on all remaining exams. If you miss an exam, you will have to be cleared by the Director of Undergraduate Studies Richard Brown to be excused from the exam, a process that will include documentation and a valid excuse. Unexcused absences count as 0.

Grade Policy:

The course grade will be determined as follows:
  • Homework: 10%
  • Midterm exams: 25% each
  • Final exam: 40%

Homework based on the week's lectures will be posted as official in the course schedule below, usually sometime on Friday. That assignment will be due at the beginning of class the next Friday. Hand your homework set into the bin corresponding to your section. You will receive your graded homework back from your section teaching assistant the following week. No late homework will be accepted. If you absolutely cannot make it to class, arrange for someone else to hand it in for you. However, you may miss up to two homework assignments without grade penalty, as the lowest two homework scores will be dropped from the final grade calculation.

In order to master the material of the course, it is key that you do your homework. You should make every effort to solve the assigned problems using the concepts learned from the lectures and readings. You will be graded mostly on your ability to work problems on exams. If you have not practiced the techniques within the homework problems, you will have serious difficulties to work problems on exams. You are strongly encouraged to do your homework in groups. However, you must write up your solutions on your own. Copying is not acceptable.

You must staple your homework and write your name, your section number and the name of your teaching assistant clearly at the top. Write legibly. The grader might choose not to grade your homework if it is too messy. Your solutions to the assigned problems should be detailed enough so that the reader can follow your thought process.

Course Policy:

You are responsible for lecture notes, any course material handed out, and attendance in class. I will not formally record your attendance, but you are encouraged to come to lectures. By attending lectures you will get a sense of what I consider important and that should help you know what to focus on when you study for the exams.

No cell phones and no computers are allowed during the lecture, except for note taking.

Academic Support:

Besides attending the lectures and the recitation sections I encourage you to use the following opportunities for additional academic support:
  • Come to my office hours and to your section's teaching assistant's office hours.
  • Go to the math helproom in Krieger 213. The hours are 9:00-21:00 on Monday through Thursday and 9:00-17:00 on Friday. This free service is a very valuable way to get one-on-one help on the current material of the class from other students outside the course. It is staffed by graduate students and advanced undergraduates.
  • Participate in the PILOT learning program. It is a peer-led-team learning program. Students are organized into study teams consisting of 6-10 members who meet weekly to work problems together. A trained student leader acts as captain and facilitates the meetings.
Check out the following JHU webpage with information about academic support and tutoring.

Special Aid:
Students with disabilities who may need special arrangements within this course must first register with the Office of Academic Advising. I will need to have received confirmation from the Office of Academic Advising. To arrange for testing accomodations please remind me at least 7 days before each of the midterms or final exam by email.

JHU Ethics Statement:

The strength of the university depends on academic and personal integrity. In this course, you must be honest and truthful. Cheating is wrong. Cheating hurts our community by undermining academic integrity, creating mistrust, and fostering unfair competition. The university will punish cheaters with failure on an assignment, failure in a course, permanent transcript notation, suspension, and/or expulsion. Offenses may be reported to medical, law, or other professional or graduate schools when a cheater applies.

Violations can include cheating on exams, plagiarism, reuse of assignments without permission, improper use of the internet and electronic devices, unauthorized collaboration, alteration of graded assignments, forgery and falsification, lying, facilitating academic dishonesty, and unfair competition. Ignorance of these rules is not an excuse.

In this course, as in many math courses, working in groups to study particular problems and discuss theory is strongly encouraged. Your ability to talk mathematics is of particular importance to your general understanding of mathematics. You should collaborate with other students in this course on the general construction of homework assignment problems. However, you must write up the solutions to these homework problems individually and separately. If there is any question as to what this statement means, please ask the instructor.

ODE Applets:

On the following webpage you can find several Java applets that are helpful in understanding the behavior of solutions to ordinary differential equations (ODEs): Java Applets for ODEs (JOde). (Your browser must support Java for the applets to work) You may also want to check out the MIT Mathlets and you may want to use Wolfram Alpha to plot slope fields of ODEs (enter "slope field").


Section #
Office hours

T 13:30-14:20

Maryland 104

Caroline van Blargan

Th 13:00-15:00
Krieger 201


T 15:00-15:50

Hodson 210

Caroline van Blargan

Th 13:00-15:00
Krieger 201


Th 15:00-15:50

Shaffer 300

Emily Stoll

W 15:00-17:00
Krieger 207


Th 16:30-17:20

Shaffer 303

Emily Stoll

W 15:00-17:00
Krieger 207


Th 15:00-15:50

Hodson 203

Junghyun Min

W 17:00-19:00
Krieger 207


T 15:00-15:50

Maryland 217

Cuiqing Li

F 11:00-12:00
Krieger 211


Th 13:30-14:20

Maryland 104

Junghyun Min

W 17:00-19:00
Krieger 207


Th 15:00-15:50

Maryland 104

Hanveen Koh

W 11:00-12:00
Krieger 201


T 16:30-17:20

Hodson 301

Chris Chia

M 16:00-17:00
Krieger 207

Course Schedule

Here is a tentative schedule for the course. It will be updated as we go with lecture notes and homework assignments. The lecture notes are only meant to supplement your own note taking in class and your reading of the textbook. Solutions to selected homework problems will be provided. I strongly recommend to you to read the relevant sections of the textbook before and/or after each lecture.

Topics and Sections

Aug 31,
Sep 1

§1.1 Mathematical Models and Slope Fields
§1.2 Solutions to Some Differential Equations
§1.3 Classification of Differential Equations

Aug 31 Sep 1

Please become familiar with the organization of this course by carefully reading the syllabus on this webpage.

Do the following exercises from the textbook:
§1.1: 2, 4, 15-20
§1.2: 3, 7, 13, 15
§1.3: 1, 2, 4, 9, 17
(Use a computer to draw direction fields and print them out)

Selected Solutions

Sep 8

Sep 6, 8

§2.1 Linear Equations and Integrating Factors
§2.2 Separable Equations
§2.3 Modeling with First Order Equations

Sep 6 Sep 8

Do the following exercises:
§2.1: 10, 20, 22, 28, 30, 35
§2.2: 2, 5, 14, 22, 24, 29

Read section §2.3 from the textbook

Selected Solutions

Sep 15

Sep 11, 13, 15

§2.4 Linear vs. Nonlinear Equations
§2.5 Autonomous Equations and Population Dynamics
§2.5 Exercises: Bifurcation Theory and Diagrams

Sep 11 Sep 13 Sep 15

Do the following exercises:
§2.4: 4, 5, 13, 15, 26, 27
§2.5: 2, 4, 7, 9, 14, 16, 17, 26, 27

Selected Solutions

Sep 22

Sep 18, 20, 22

§2.6 Exact Equations and Integrating Factors
§2.8 Existence and Uniqueness Theorem
§3.1 Homogeneous Equations

Sep 18 Sep 20 Sep 22

Do the following exercises:
§2.6: 4, 5, 8, 12, 14, 16
§3.1: 5, 7, 14, 18, 20, 21, 24, 25

Sep 29

Sep 25, 27, 29

§3.2 The Wronskian
§3.3 Char. Eqn. Roots: Complex
§3.4 Char. Eqn. Roots: Repeated

Sep 25

Oct 2, 4, 6

§3.5 Nonhomogeneous Equations
§3.6 Variations of Parameters
§3.7 Mech. and Electr. Vibrations

Oct 9, 11, 13

1st midterm on Monday in class

§4.1 Higher Order Linear Equations
§4.2 Homogeneous Equations
§4.3 Undetermined Coefficients

Oct 16, 18

§7.1 Introduction to Systems
§7.2 Review of Matrices
§7.3 Linear Algebraic Equations

Note: Fall break on Friday, October 20

Oct 23, 25, 27

§7.4 First Order Linear Systems
§7.5 Homogeneous Linear Systems
§7.6 Complex Eigenvalues

Oct 30,
Nov 1, 3

§7.7 Fundamental Matrices
§7.8 Repeated Eigenvalues
§9.1 The Phase Plane

Nov 6, 8, 10

§9.2 Autonomous Systems and Stability
§9.3 Locally Linear Systems
§9.4 Competing Species

Nov 13, 15, 17

2nd midterm on Monday in class

§9.5 Predator-Prey Equations
§9.7 Periodic Solutions and Limit Cycles

Nov 20-26

Thanksgiving vacation

No homework

Nov 27, 29
Dec 1

§8.1 The Euler or Tangent Line Method
§8.2 Improvements to the Euler Method

Dec 4, 6, 8

§6.1 Definition of the Laplace Transform
§6.2 Solution of Initial Value Problems
§6.3 Step Functions
§6.4 Discontinuous Forcing Functions

Final exam:

Wednesday, December 13, 9:00-12:00


Thu, Aug 31: Welcome to Math302 Differential Equations! I wish you all the best for this fall term.