MATH 321 (Spring 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)

Quick Links

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.

Homework 1 due February 1
Homework 2 due February 12
Homework 3 due February 22
Homework 4 due March 5
Homework 5 due March 29
Homework 6 due April 9
Homework 7 due April 19
Homework 8 due April 30

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.

January 18: 1.1, 2.1: Classification of differential equations
January 22: 2.2, 2.4: Consequences of linearity
January 25: 2.3: Separable equations
January 29: 2.5-2.7: Modeling with separable equations
February 1: 2.8: Exactness and integrating factors
February 5: 2.9: Homogeneous equations
February 8: 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.

February 12: 3.1: Homogeneous equations with constant coefficients
February 15: 3.2: Fundamental solutions of linear homogeneous equations
February 19: 3.3: Linear independence and the Wronskian
February 22: 3.4: Complex roots of the characteristic equation
February 26: 3.5: Repeated roots of the characteristic equation
March 1: 3.6: The method of undetermined coefficients

March 5: Review for Exam 1
March 8: 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.

March 19: 6.1: The Laplace transform
March 22: 6.2: Using Laplace transforms for initial value problems
March 26: 6.3: Step functions
March 29: 6.4: Discontinuous forcing functions
April 2: 6.5: Impulse functions
April 5: 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.

April 9: 5.1-5.2: Power series
April 12: 5.3: Series near an ordinary point
April 16: 5.4: Regular singular points
April 19: 5.8: Bessel's equation
April 23: 8.1: Euler's method
April 26: 8.3: Improvements to Euler's method

April 30: Review for the final exam

Final exam: Monday May 7, 2018, 11:20am-1:50pm

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.