MATH 321 (Fall 2018)

Instructor's contact information

Michael Robinson
220 Don Myers Technology and Innovation Building
michaelr at american {dot} edu
Office hours:
My research website
Feel free to contact me with any and all questions (course-related or not)

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Course description
Homework assignments
Course schedule
Information about exams
Course policies

Course description

First order equations, linear equations of higher order, solutions in series, Laplace transforms, numerical methods, and applications to mechanics, electrical circuits, and biology.

Prerequisite (or concurrent): MATH-310 and MATH-313

The course textbook is Elementary Differential Equations and Boundary Value Problems, by Boyce and DiPrima. Any edition will do; I'm using the Sixth edition.

In this course, students will

  1. Classify differential equations based on the techniques for solving them
  2. Solve those differential equations that are amenable to elementary techniques
  3. Construct approximate solutions to arbitrary differential equations
  4. Apply differential equations and their solutions to mechanics, electrical circuits, and biology


Homeworks are posted on BlackBoard, though I usually remember to print out copies to distribute in class. They are to be submitted electronically as PDF files through BlackBoard. Please take the time to check your scans for legibility before uploading!

Homework 1 due September 17
Homework 2 due September 24
Homework 3 due October 8
Homework 4 due October 15
Homework 5 due November 5
Homework 6 due November 12
Homework 7 due November 26
Homework 8 due December 6

Course schedule

Unit 1: Solving first order equations

After this unit, you should be able to
  1. Classify differential equations by linearity and homogeneity and
  2. Solve first order ordinary differential equations by separation and by integrating factors.

August 27: 1.1, 2.1: Classification of differential equations
August 30: 2.2, 2.4: Consequences of linearity
September 6: 2.3: Separable equations
September 10: 2.5-2.7: Modeling with separable equations
September 13: 2.8: Exactness and integrating factors
September 17: 2.9: Homogeneous equations
September 20: 2.11: Existence and uniqueness of solutions

Unit 2: Solving higher order equations

After this unit, you should be able to
  1. Solve higher order ordinary differential equations with constant coefficients and
  2. Solve boundary value problems involving homogeneous and nonhomogenous equations.

September 24: 3.1: Homogeneous equations with constant coefficients
September 27: 3.2: Fundamental solutions of linear homogeneous equations
October 1: 3.3: Linear independence and the Wronskian
October 4: 3.4: Complex roots of the characteristic equation
October 8: 3.5: Repeated roots of the characteristic equation
October 11: 3.6: The method of undetermined coefficients

October 15: Review for Exam 1
October 18: Exam 1 in class

Unit 3: Solving by transformation

After this unit, you should be able to
  1. Use Laplace transforms to solve linear differential equations with non-constant coefficients and
  2. Express solutions to nonhomogeneous equations as convolutions.

October 22: 6.1: The Laplace transform
October 25: 6.2: Using Laplace transforms for initial value problems
October 29: 6.3: Step functions
November 1: 6.4: Discontinuous forcing functions
November 5: 6.5: Impulse functions
November 8: 6.6: The convolution integral

Unit 4: Solving approximately

After this unit, you should be able to
  1. Write power series solutions and
  2. Approximate solutions using Euler's and related methods.

November 12: 5.1-5.2: Power series
November 15: 5.3: Series near an ordinary point
November 19: 5.4: Regular singular points
November 26: 5.8: Bessel's equation
November 29: 8.1: Euler's method
December 3: 8.3: Improvements to Euler's method

December 6: Review for the final exam

Final exam: Thursday, December 13, 2018, 8:10am-10:40am

Course policies


For each exam, you will be permitted to bring one 3"x5" index card with handwritten notes on it. Electronic calculators will not be permitted. However, mechanical calculators (such as this or these) are fine.


Since the course is taught in a highly interactive manner, you are generally expected to attend and participate in all of the lectures. Please contact me in advance if you cannot attend, especially in the case of an exam.


The course grade will be determined as follows:
30% Homework
35% Exam 1
35% Final exam

Late homeworks will not be accepted, unless there is an official (University-approved) reason for doing so.

Academic dishonesty

Academic dishonesty is a serious offense. As a start, you should read and understand our University's policies.

There is to be no collaboration with other people using any means during an exam. Doing so risks starting academic dishonesty proceedings. However, you may ask me questions during an exam, which I may answer at my discretion.

You may collaborate with other students in this class on homeworks, but the work you turn in must be your own. You may not collaborate with others outside of the class on homeworks without my express permission. This prohibition extends to the use of online forums and paid tutoris. If you feel that you don't know how to proceed on an assignment, ask me for help!

At a minimum, honesty consists of presenting your ideas clearly and in your own words, possibly orally. On the other hand, the creation and writing of calculations, proofs, examples, or counterexamples is a creative process. Here are a few typical cases that are relevant for homework:

  1. If you create a calculation, example, counterexample, or proof for your work on your own, you need not notate it as such. (It is expected that you will rediscover standard examples, and these will not cause any concern.)
  2. If a colleague shows you an example, counterexample, or proof that you like, please credit that person by name in your write-up. You should expect that I may challenge you to explain your writing in your own words, possibly orally. If you cannot successfully defend your answer, no credit will be awarded to you.
  3. If you write a calculation, example, counterexample, or proof as part of a group, please credit all members of your group by name in your write-up. You should expect that I may challenge you to explain your writing in your own words, possibly orally. If you cannot successfully defend your answer, no credit will be awarded to you, even if other group members are able to defend the same answer.

The mathematics community has a unique perspective on academic honesty and priority. The mathematics community has strict social guidelines for assigning credit, which I expect you'll adhere to. Due to the canonicity of certain mathematical results and constructions, sometimes well-intentioned people end up in priority disputes when they independently discover something. If you have any questions on this matter, you are expected to consult me directly for advice.