Sections 13-16


Instructor: Gregor Kovacic
Office: Amos Eaton 419
Phone: 276-6908
Office hours: Click here.
E-mail: kovacg at rpi dot edu

Teaching Assistant: Anuj Shah
Office: Amos Eaton 317
Office hours: Tuesday, 4:00-5:30 PM, Wednesday, 5:00-6:30 PM
E-mail: shaha5 at rpi dot edu

Lectures: Tuesday, Wednesday, Friday, 2:00-2:50 PM, Ricketts 203
Recitations: Section 13: Monday, 10:00-10:50 AM, Low 4034
Section 14: Thursday, 10:00-10:50 AM, Low 4040
Section 15: Monday, 3:00-3:50 PM, Low 4040
Section 16: Thursday, 3:00-3:50 PM, Low 4040
Class Notes: 1st Order, 2nd Order, Fourier Series and Partial Differential Equations, 2X2 Systems, Laplace Transforms.

Text: Boyce and DiPrima, Elementary Differential Equations and Boundary Value Problems. Any edition will do.
(You can get old editions of this book at for as low as $1.)

Learning Objectives

To learn the basics of differential equations (as described in the outline and recommended problems) which are a crucial tool in higher-level scientific and engineering subjects. An additional benefit will be to improve mathematical manipulation, modeling, and reasoning skills.

Course Outline

The following table gives the sections that we will cover, and roughly the week these sections will be covered.
(The section numbers are from the 7th edition of the Boyce-DiPrima book.)

August 31 - September 4
1.1-1.3, 2.1
September 7-11 (no classes September 7)
2.2, 2.3
September 14-18
2.5, 3.1, 3.2
September 21-25
3.3, 3.4, 3.5
September 28 - October 2
3.6, 3.7
October 5-9
3.8, 3.9
October 12-16 (no classes October 12, Monday schedule on October 13)
5.5, 10.1
October 19-23
10.2, 10.3, 10.4
October 26-30
10.5, 10.6
November 2-6
10.7, 10.8
November 9-13
7.1, 7.2, 7.3
November 16-20
7.5, 7.6
November 23-27 (no classes November 24-27)
November 30 - December 4
9.2, 9.3
December 7-11
9.4, 9.5
December 16-18
December 21-22

Attendance Policy

There is no requirement to attend either class or recitations. This said, however, long-time experience shows that students who do not attend class and/or recitations usually do poorly in the course. Neither the instructor nor the teaching assistant are in any way responsible for briefing students who missed class on the missed material and/or announcements.


There will be three in class, 50-minutes-long exams, given most probably during the following weeks:

Exam 1 In class, Friday, September 25
Exam 2 In class, Tuesday, November 3
Exam 3 In class, Tuesday, December 8
Final Exam TBA, during the finals period.

There will also be an optional three-hour final exam during the finals period for those students who will not be happy with their previous grades. The rules for and implications of taking this final exam are explained below.

You are allowed one handwritten sheet (8.5 by 11 inches) of notes for each exam and the final. No other materials (books, notes) or electronic aids (calculators, clle phones, laptops, etc.) will be allowed.

Only students with notes from the Student Experience Office, (4th floor of Academy Hall, x8022) will be allowed to take makeup exams.

Here, you will find a number of old exams. The format of the exams and quizzes will likely be similar to this.


There will be approximately biweekly quizzes given during the recitations. They will closely follow the material presented in class, recitations, and on the suggested homework listed below.

The dates of the quizzes and their contents will be announced here.

No aids of any kind will be allowed on the quizzes.

There will be no makeup quizzes. The lowest quiz grade will be dropped automatically. For any additional missed quizzes you will need to bring a note from the Student Experience Office, 4th floor of Academy Hall, x8022. In case you do, the zero for that quiz grade will be dropped, and the average over all the other quizzes will be substituted for it.

Academic Integrity

Copying from fellow students' work or from unallowed aids during a quiz or an exam, as well as using electronic means to contact helpers outside the examination room, is a breach of academic integrity, and will not be tolerated. Standard Institute procedure for academic integrity breaches will be followed.

Suggested Homework

Suggested homework can be found at the URL

These homework problems are representative of the material tested on the quizzes and exams.

It is strongly recommended that you work through all the suggested homework problems. This is because mathematics is a skill acquired through practice, similar to playing an instrument or a sport. The only mathematics you will ever really master is the mathematics you will do yourself. Passive ability to understand lectures and recitations alone is no guarantee that you will be able to solve problems on the quizzes and/or exams.

Working on the suggested homework problems in groups or at least checking your solution methods with other students is highly recommended. While most of the problems are standard, they sometimes do require generating an idea, and this is always easier in a group.

To help you with your practice, here is a list of suggested problems from the 9th edition of the textbook. Here and here are two more lists of suggested problems, one from the 7th edition of the Boyce-DiPrima book, and one from the 7th and the 8th editions. Solutions to some of these practice problems are also available.

Here are also some video clips of Prof. Schmidt solving problems from the Boyce-DiPrima book.


If you have serious problems when trying to solve the suggested homework, you should seek tutoring from the Advising and Learning Assistance Center. Available times Monday through Thursday, 8:00-10:00 PM in DCC 345.


I am expecting to use the following grading rules: Each of the three exams will constitute 1/3 of your final grade.

The lowest exam grade will automatically be replaced by the quiz average if the latter is higher.

The percentages for grade cutoffs will be no stricter than

92-10090-9287-8982-8680-8277-79 72-7670-7267-6960-66< 60

and may end up being looser, but I won't know where exactly they will be until the very end.

At any given moment, you can compute your current grade as follows: Drop the lowest quiz grade, add the points you got for your remaining quizzes, and divide by the maximal possible number of points on those quizzes. (Each quiz will have that number printed in a prominent place.) This will give you your total quiz percentage so far. Then take the percentages on your exams so far. Drop the lowest exam percentage or the total quiz percentage so far, whichever is the lowest, and average the rest. Compare with the above table. This is the worst your grade can be at that time.

Grades should first be appealed to the instructor. Any further appeals should be directed through the office of the department head.

Optional Final Exam

If you are unhappy with the grade that you got from the exams and the quizzes, you can give it up, and instead take the optional final exam during the finals week. The grade on the final exam will supersede all the previous grades, so do not take the final exam unless you are absolutely sure that you will do better than during the semester.

The Optional Final Exam will be given during the finals period.

You are allowed one handwritten sheet (8.5 by 11 inches) of notes. No other materials (books, notes, calculators, etc.) are allowed.

Computational and Visualization Aides

Maple and Mathematica are useful tools for carrying out hard algebra, and for visualization. They can be particularly useful for plotting complicated graphs, direction fields, and vector fields. An even more useful tool is Matlab, which you can use for plotting and also numerical computations.

Sample Maple worksheets can be found here. Many more Maple links can be found here.

In the framework of Rensselaer's Project Links, a number of interactive learing modules have been developed. For us, the most interesting ones will the ones on differential equations, especially those on mechanical oscillations. Other modules of interest for this course include Fourier series, drag forces on solid objects, heat conduction, and chemical kinetics.

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