220 Don Myers Technology and Innovation Building

michaelr at american {dot} edu

Office hours:

- Mondays 1-2pm,
- Tuesdays 10am-2pm,
- Wednesdays 10am-11am,
- Thursdays 10am-11am,
- or by appointment (please contact me 24 hours in advance to make arrangements).

My research website http://www.drmichaelrobinson.net/

Feel free to contact me with any and all questions (course-related or not)

Homework assignments

Course schedule

Information about exams

Course policies

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

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

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

- Classify differential equations by linearity and homogeneity and
- 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

- Solve higher order ordinary differential equations with constant coefficients and
- 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**

- Use Laplace transforms to solve linear differential equations with non-constant coefficients and
- 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

- Write power series solutions and
- 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 **

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.

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:

- 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.)
- 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.
- 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.