Below is a list of my current, upcoming and previous teaching activities

Current Courses

I am currently not teaching any courses for the 2021-2022 academic year.

Previous Course Pages

Brown University

University of Maryland

Updated: Tuesday, July 8

MATH 246 - Ordinary Differential Equations
for Scientists and Engineers

News and Updates

  • Solutions to the Final exam are posted here.
  • The grade distribution for the Final is now posted here.
  • Solutions for Quiz 10 are now posted here
  • Information about the Final Exam, along with old Exams, practice problems and solutions, and a copy of the table for Laplace transforms is now included here.
  • Solutions to Quiz 9 are now posted.
  • The grade distribution for Exam 3 is now posted here. What a great improvement!
  • Solutions to Exam 3 are now posted here
  • A Description of Exam 3 along with some practice problems is listed here
  • The solutions for Quiz 8 are posted here.
  • The solutions for Quiz 7 are posted here.
  • The grade distribution for Exam 2 is now posted here.
  • Solutions to Exam 2 are now posted here.
  • There will be a review session for Exam 2 on Sunday at 3:00pm in the usual Room MATH 1308. Bring questions.
  • Solutions to Quiz 6 are posted here
  • Solutions to Quiz 5 are posted here
  • Solutions to Quiz 4 are posted here.
  • The grade distribution for Exam one is now shown here.
  • The rest of the MATLAB assignments are posted.
  • Solutions to the Exam 1 are now up here.
  • Some practice problems for Exam 1 are posted here.
  • Solutions to Quiz 3 are posted here.
  • Solutions to Quiz 2 are posted here.
  • The second MATLAB assignment is up.
  • Solutions to Quiz 1 are posted here.
  • Calculus Review Notes have now been added under the section Calculus Review Information.
  • The office hours are now listed under course information.
  • The first MATLAB Assignment is up and due on Friday 6/6.
  • The Course Schedule is up!

Course Information

Time: MTuWThF 11:00am - 12:20pm
Room: 1308 MATH
Section: 0102
Office Hours: MW 12:30-1:30pm, F 10:00-11:00am.
Instructor: Sam Punshon-Smith
Office: 3303 MATH
Email: punshs@math.umd.edu


An introduction to the basic methods of solving ordinary differential equations. Equations of first and second order, linear differential equations, Laplace transforms, numerical methods, and the qualitative theory of differential equations.

For a more detailed outline of the course topics, see the Course Schedule below.

Primary Materials Required

New Ordinary Differential Equations (NODE) Online Resource
by the NODE team

This is the Math department's new online textbook developed by C.D. Levermore and the NODE team at UMD. It is a free online text in interactive pdf form. Each chapter has both internal and external links to various resources to supplement the material in the text. To access this text, you will need to login with your UMD account

Warning Please note that the interactive pdf functionality does not work fully on all browsers/ pdf viewer combinations. All of the important information will still be there, but some of the links to the other chapters may not work. If this happens to you, it should be no problem to go back to list of chapters and navigate from there.

Differential Equations with MATLAB (HLOR)
by Hunt, Lipsman, Osborn, Rosenberg

This is supplementary text for working with MATLAB and differential equations. MATLAB problems and readings will be assigned out of this book. The book can be bought for about $20 used at the link provided.

Other Resources Not required

Elementary Differential Equations
by by Boyce and DiPrima (tenth edition)

This book was the standard reference at UMD until recently. It is also the default book used at many Universities. The presentation of the material is not far from that in "New Differential Equations".

Elementary Differential Equations with Boundary-Value Problems
by Edwards and Penny (sixth edition)

Also a very good reference used at many universities.

Paul's Online Notes Online Resource
by Paul Dawkins

These are a set of free online notes on differential equations. They cover some of the same, but not all, topics covered in "New Differential Equations". The equations are rendered in the browser, and may be difficult to read. However, a pdf of each section can be downloaded.

MIT Open Courseware Videos on ODEs Online Resource
by Arthur Mattuck

This is a collection of free online videos for MIT students. The videos cover most (but not all) of the topics covered in this course, but in a different order

Khan Academy videos on ODEs Online Resource

This is another collection of free online videos on ODEs. These lecture cover some of the material of the course, and many of the lecture vary in quality. The videos should be used as a supplement to the course and are not sufficient for a replacement of the text.

Quizzes and Solutions

The solutions to the Quizzes are posted below:

Quiz 1 Solutions

Quiz 2 Solutions

Quiz 3 Solutions

Quiz 4 Solutions

Quiz 5 Solutions

Quiz 6 Solutions

Quiz 7 Solutions

Quiz 8 Solutions

Quiz 9* Solutions (Quiz Not Given)

Quiz 9 Solutions

The phase diagrams in Quiz 9 were generated by the following MATLAB codes Clock_Spiral_Sink.m and Nodal_Source.m

Quiz 10 Solutions

Exams and Solutions

Exam 1

Practice Problems and Solutions

Exam 1 practice problems, and solutions. Courtesy of Dr. Levermore.

Exam Solutions

Solutions to Exam 1.


The distribution of scores for Exam 1 is shown in the following histogram:

Exam 2

Exam Description

Exam 2 will contain seven or eight problems and one extra credit problem. It will cover material from Chapters 1-8 in Part II as indicated in the course schedule. There may also be some questions on MATLAB as done in MATLAB assignments 2,3. The extra credit problem will be an application problem from Part I. Don't expect it to be the same as problem 3 from Exam 1.

Practice Problems and Solutions

Exam 2 Practice Problems, and solutions. Courtesy of Dr. Levermore's Fall 2013 course.

More Exam 2 Practice Problems, and solutions. Courtesy of Dr. Levermore's Fall 2012 course.

Exam Solutions

Solutions to Exam 2.


The distribution of scores for Exam 2 is shown in the following histogram:

Exam 3

Exam Description

Exam 3 will contain nine problems and be based on the material in Part II Ch9 (Laplace Transforms), Part II Ch 1-5 (Linear Systems) and any MATLAB covered in MATLAB assignments 3 and 4. Please take a look at the sections listed under the "sections" column of the website for the NODE text here, to see exactly which sections in each chapter are covered.

You may safely assume that I will not ask you to compute the eigenvalues of anything bigger then a 2 by 2 matrix. Any matrix larger than a 2 by 2 will be given the eigenpairs when needed.

Practice Problems and Solutions

Exam 3 Practice Problems, and solutions. Courtesy of Dr. Levermore's Fall 2013 course.

You may safely ignore problem 9.

More Exam 3 Practice Problems, and solutions. Courtesy of Dr. Levermore's Fall 2012 course.

You may safely ignore problem 6.

Exam Solutions

Solutions to Exam 3.


The distribution of scores for Exam 3 is shown in the following histogram:

Final Exam

Exam Description

The final exam will take place in the usual room MATH 1308, and will take 2 hours. The exam will be comprehensive (Parts I, II, III) and will be comprised of 10 or 11 problems. You will also be expected to know the MATLAB that you have used in any of your MATLAB assignments. The exam will be closed book and closed notes. Calculators will not be allow, and the questions will be made so that you do not need one.

Practice Exams

Please take a look at the following Final exams from previous years. No solutions have been provided.

Spring 2014 Final Exam, Fall 2013 Final Exam.

Here are also some practice problems with solutions:

Final Exam Practice Problems and solutions. Courtesy of Dr. Levermore.

Other Sample problems removed because they had the same questions.

Copy of the Laplace transform table on the exam.

Exam Solutions

Solutions to the Final Exam.


The distribution of scores for the Final is shown in the following histogram:

Tutoring Information

The math department has very good resources available for tutoring in various topics, including MATLAB. The schedule and list of tutors, organized by tutor, topic and room location is listed on the math department website. I strongly recommend making use of these resources if you are having trouble with the course material, or if you are simply looking for extra input.

Calculus Review Information

For those who would like a refresher on the calculus required for this course, please take a look at Dr. Levermore's calculus review notes.

A review of Trigonometric and Hyperbolic Functions

Limits and Differentiability: Basic Concepts and General Rules

Some Applications of Derivatives

Limits and Integrability: Basic Concepts and General Rules

More Basics of Integration

Techniques of Integration

MATLAB Information

The use of the MATLAB software package will be an important element in this course. You will use MATLAB to solve differential equations numerically and symbolically, to plot and visualize solutions and direction fields, analyzing behavior and mathematical properties of those solutions in both a quantitative and qualitative manor.

The use of MATLAB will be done entirely outside of the lecture. Students will be responsible for reading the appropriate sections in Differential Equations with MATLAB to complete the assignments. See Grading and assignments for more information on the MATLAB assignments.

MATLAB Software

MATLAB software is available from various sources on campus. The latest version R2014a can be downloaded by students for free from UMD's terpware website.

There are many computer lab locations around campus with access to MATLAB. The closest such location is in the math OWL Lab in MATH 0203. Other OWL locations around campus, along with their hours and software is located at the campus computer labs site.

MATLAB Assignment Schedule

  • MATLAB Assignment 1 Due Fri 6/6
    Read HLOR Ch 1-4
    Complete Problem set A (p49-52), problems 7bde, 8abd, 10, 11, 13
  • MATLAB Assignment 2 Due Fri 6/13
    Read HLOR Ch 5,6
    Complete Problem set B (p85-96), problems 2, 7, 14bc, 18
  • MATLAB Assignment 3 Due Fri 6/20
    Read HLOR Ch 8-10
    Complete Problem set C (p141-148), problems 6, 11bc, 13, 15
  • MATLAB Assignment 4 Due Fri 6/27
    Read HLOR Ch 11
    Complete Problem set D (p167-180), problems 7, 12, 13, 15
  • MATLAB Assignment 5 (Final Assignment) Due Fri 7/11
    Read HLOR Ch 13
    Complete Problem set E (p197-210), problems 12, 13b, 14b, 17

Submitting Your MATLAB Assignment

To complete a MATLAB assignment, you should create one m-file and create a MATLAB cell in the m-file for each problem in the order that they were assigned. The cells should be have the problem number clearly labeled at the beginning of the cell as a comment. Multi-part problems can be done in the same cell or multiple cells, as long as the problems are clearly labeled by comments. Error messages or faulty code will immediately receive a grade of 0

To submit your work, use the "publish to html" option in MATLAB. This option creates a nicely formatted version of your work, which can be viewed in MATLAB or any web-browser. You should print the html version of the work as displayed in MATLAB or the browser. Please be sure to type or write in pen at the top of the page, your name and the course name and number, and the assignment due date.

Assignments which are incorrectly formatted with receive zero credit. Do not submit an assignment that you are unsure. If you have any questions about how to submit the assignment, please send me an email or see me during office hours.

MATLAB Resources

Getting Started with MATLAB and Simulink Student Version
by Mathworks

This is an excellent free set of online tutorials given by Mathworks specifically for students learning MATLAB

Chapter 1 of Numerical Computing with MATLAB
by Cleve Moler

This chapter is available for free online for free as a pdf. The introduction is very broad and general.

Grading and Assignment Information


Suggested homework assignments for each day will be listed in the course schedule. These assignments will not be collected, but should serve as a guideline for the quizzes and exams later in the course.


There will be 10 in-class quizzes. The quizzes will be graded out of 10 points each with the lowest 2 grades dropped. The quiz problems will be based on the suggested homework, and solutions will be posted on this webpage.

MATLAB Assignments

There will be 5 MATLAB assignments throughout the class. Each assignment will be due on Friday of each week, excluding independence day, and will be graded out of 20 pts each. The assignments will be given out of Differential Equations with MATLAB with each assignment 1-5 being given out of the corresponding problem sets A-E in the text. No partial credit will be given on each problem with zero credit being given for MATLAB code or commands that produce error messages or faulty plots.


There will be 3 in-class exams worth 100 pts each and a in-class final on the last day worth 200 pts. The material covered by each exam is listed on the course schedule.

Note: In the event that you have score poorly on one of the in-class exams (15pts lower than the average of the other two), you will have the option to choose to replace that low score with the score on the final. Students who qualify will be asked to indicated their choice on their final exam before they submit it.

The break down and percentages are described in the following table:

Points Percentage
Quizzes 80 (8x10) 12%
MATLAB 100 (5x20) 15%
In Class Exams 300 (3x100) 44%
Final Exam 200 29%
Total 680 100%

Grades will be tentatively be assigned based on the following cutoffs. These cutoffs may be subject to change as the course progresses.

Points Percentage Grade
612-680 90%-100% A
544-611 80%-89% B
476-543 70%-79% C
408-475 60%-69% D
< 408 < 60% F

Grade modifiers (+-) may be added to grades within 15pts (~2%) of the boundary points. Eg: 89% = B+. I reserve the right to assign grade modifiers to student grades as I see fit.

Course Schedule

Below is a tentative course schedule. It contains an outline of course topics, reading assignments and suggested problems. It also contains important dates for exams, quizzes and assignments are due dates. The assigned readings are to be done before the lecture date listed.

Date Material Reading Suggested Homework
M 6/2 Classification and Course Overview
Part I Ch 1 1, 2, 3, 5, 7, 8, 10, 14
Tu 6/3 Linear Equations Part I Ch 2 1, 2, 4, 7, 10, 12, 15, 23
W 6/4 Quiz 1 - Ch 1-2
Seperable Equations
Part I Ch 3 2, 3, 4, 7, 13, 16, 19, 21
Th 6/5 General Theory
Graphical Methods
Part I Ch 4, 5 Ch4 5, 9 Ch5 2, 4, 6, 8, 15, 16
F 6/6 MATLAB Assignment 1 due
Quiz - Ch 3-5
Part I Ch 6 Ch6 1, 4, 8, 10, 12, 14, 15, 16
M 6/9 Numerical Methods Part I Ch 7 1, 2, 4, 7, 9, 10, 13, 14
Tu 6/10 Quiz - Ch 6,7
Exact Differential Forms and Integrating Factors
Part I Ch 8 2, 6, 8, 11, 14, 17, 18, 19
W 6/11 Exam I Part I Ch 1-8 --
Th 6/12 Introduction Part II Ch 1 Ch1 3, 4, 6, 8 Ch2 3, 4, 5, 6, 7
F 6/13 MATLAB Assignment 2 due
Homogeneous Equations: General Methods and Theory
Supplement: Linear Algebraic Systems and Determinants
Part II Ch 2, 3 Ch2 13, 14, 15, 16, 17, 18, 20 Ch3 1, 2, 3, 4
M 6/16 Quiz - Ch 1-3
Homogeneous Equations with Constant Coefficients
Part II Ch 4 Ch4 1, 2, 5, 7, 8, 10, 12, 16, 18, 21, 20
Tu 6/17 Nonhomogeneous Equations: General Method and Theory
Nonhomogeneous Equations with Constant Coefficients
Part II Ch 5, 6.1 Ch5 1, 3, 6, 7, 8, 10, 12, 14, 15, 19
W 6/18 Quiz - Ch 4, 5
Nonhomogeneous Equations with Constant Coefficients cont...
Part II Ch 6.1-6.4 Ch6 1, 3, 5, 7, 8, 9, 10, 11, 12, 15, 18, 19, 21, 22, 24, 26
Th 6/19 Nonhomogeneous Equations with Variable Coefficients Part II Ch 7 Ch7 1, 2, 3, 5, 7, 9, 12, 14, 16, 17, 18, 19
F 6/20 MATLAB Assignment 3 due
Quiz - Ch 6,7
Application: Mechanical Vibrations
Part II Ch 8 Ch8 1, 3, 5, 7, 9, 11, 15, 20, 23
M 6/23 Exam 2 Part II Ch 1-8 --
Tu 6/24 Laplace Transform Method Part II Ch 9
W 6/25 Laplace Transform Method cont... Part II Ch 9 Ch9 4, 5, 7, 8, 9 ,10, 12, 13, 14, 15, 16
Th 6/26 Quiz - Part II Ch 9
Linear Systems: General Methods and Theory
Part III Ch 1, 2.0 Ch1 1, 2, 5, 6
F 6/27 MATLAB Assignment 4 due
Supplement: Matrices and Vectors
Linear Systems: General Methods and Theory cont...
Part III Ch 3,2 Ch2 1, 2, 3, 4, 6, 7, 10, 11, 13, Ch3 8-13
M 6/30 Quiz - Ch 1-3
Linear Systems: Matrix Exponentials
Part III Ch 4 1, 3, 4, 9, 11, 13, 14 15, 18
Tu 7/1 Linear Systems: Eigen Methods Part III Ch 5 1-4, 7, 8, 10, 12, 14, 15, 19, 20
W 7/2 Quiz - Ch 4, 5 -- Cancelled
Catch Up
-- --
Th 7/3 Exam 3 Part II Ch 9, Part III Ch 1-5 --
F 7/4 Independence Day - No class -- --
M 7/7 Linear Planar Systems: Phase Portraits Part III Ch 6 Ch6 1, 3, 5, 7, 8, 14, 18, 19, 22, 23
Tu 7/8 Quiz - Ch 6
Autonomous Planar Systems: Integral Methods
Part III Ch 7 Ch7 1, 3, 5, 9, 10, 12, 15, 17, 20, 22, 23
W 7/9 Autonomous Planar Systems: Nonintegral Methods Part III Ch 8 Ch8 1, 3, 5, 6, 8, 11, 13, 16, 20
Th 7/10 Quiz - Ch 7, 8
Review and Catch up
F 7/11 Final Exam and Final MATLAB Assignment due Comprehensive --

Academic Integrity Policies

The University has a nationally recognized Code of Academic Integrity, administered by the Student Honor Council.
It is expected that all students will abide by this code during all assignments, quizzes, and examinations in this course.
A summary of the code can be found on Testudo.

The Student Honor Council proposed and the University Senate approved an Honor Pledge. Each student will be asked to hand write and sign the University of Maryland Honor Pledge on each examination.

This Pledge reads:

I pledge on my honor that I have not given or received any unauthorized assistance on this examination.

Visit the Student Honor Council webpage about the University of Maryland Honor Pledge.