Below is a list of my current, upcoming and previous teaching activities
I am currently not teaching any courses for the 2021-2022 academic year.
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.
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.
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.
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".
Also a very good reference used at many universities.
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.
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
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.
The solutions to the Quizzes are posted below:Clock_Spiral_Sink.m and Nodal_Source.m
The distribution of scores for Exam 1 is shown in the following histogram:
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.
The distribution of scores for Exam 2 is shown in the following histogram:
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.
You may safely ignore problem 9.
You may safely ignore problem 6.
The distribution of scores for Exam 3 is shown in the following histogram:
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.
Please take a look at the following Final exams from previous years. No solutions have been provided.
Here are also some practice problems with solutions:
Other Sample problems removed because they had the same questions.
The distribution of scores for the Final is shown in the following histogram:
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.
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 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.
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.
This is an excellent free set of online tutorials given by Mathworks specifically for students learning MATLAB
This chapter is available for free online for free as a pdf. The introduction is very broad and general.
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.
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:
|In Class Exams||300 (3x100)||44%|
Grades will be tentatively be assigned based on the following cutoffs. These cutoffs may be subject to change as the course progresses.
|< 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.
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.
|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
|Part I Ch 3||2, 3, 4, 7, 13, 16, 19, 21|
|Th 6/5|| General Theory
|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
|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||--|
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.