Sections 17-20


Instructor: Gregor Kovacic
Office: Amos Eaton 420
Phone: 276-6908
Office hours: Click here.
E-mail: kovacg at rpi dot edu

Teaching Assistant: Stefan Schonsheck
Office: Amos Eaton 317
Office hours: Monday 10-11:30 AM, Wednesday 12:30-2 PM.
E-mail: schons at rpi dot edu

Lectures: Monday, Thursday, 2:00-3:20 PM, Low 4050
Recitations: Section 17: Tuesday, 8:00-8:50 AM, Sage 3101
Section 18: Friday, 8:00-8:50 AM, Amos Eaton 216
Section 19: Tuesday, 2:00-2:50 PM, Low 3130
Section 20: Friday, 2:00-2:50 PM, Amos Eaton 215
Class Notes: 1st Order, 2nd Order, Laplace Transforms, 2X2 Systems, Fourier Series and Partial Differential Equations.
The daily build of the classroom notes is here.

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.)

Course Outline

The following table gives the sections that we will cover, and roughly the weeks these sections will be covered. Not every word of every section will be covered.
(The section numbers are from the 10th edition of the Boyce-DiPrima book.)

August 31 - September 4
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, 5.4, 6.1
October 12-16 (no classes October 12, Monday schedule on October 13)
6.2, 6.3, 6.4, 6.5
October 19-23
7.1,7.2, 7.3
October 26-30
7.5, 7.6
November 2-6
9.1, 10.1
November 9-13
10.2, 10.3
November 16-20
10.4, 10.5
November 23-27 (no classes November 24-27)
November 30 - December 4
December 7-11

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 exams, given most probably during the following times:

Exam 1 In class, October 8.
Exam 2 In class, expected first or second week of November.
Exam 3 In class, expected first or second week of December.

There will be no final exam in this class, so make sure you do well on the exams and quizzes (see below). You are allowed one handwritten sheet (8.5 by 11 inches) of notes for each exam. No other materials (books, notes) or electronic aids (calculators, cell 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.

Exam grades should first be appealed to the instructor. You have 5 business days from the day the exam in question was handed back in class/recitation to appeal its grade. The fact that you were not in class/recitation on that day is not an excuse for an extension. No appeals will be granted by the instructor after that period. Any further appeals should be directed through the office of the department head.


There will be approximately weekly quizzes given during the recitations. They will closely follow the material presented in class, recitations, the suggested homework and the lists of problems listed below.

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

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

There will be no makeup quizzes whatsoever. 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.

Quiz grades should first be appealed to the TA. You have 5 business days from the day the quiz in question was handed back in the recitation to appeal its grade. The fact that you were not in the recitation on that day is not an excuse for an extension. No appeals will be granted by the TA after that period. Any further appeals should be directed to the instructor, and, if those fail, through the office of the department head.

Academic Integrity

Student-teacher relationships are built on trust. Acts, which violate this trust, undermine the educational process. The Rensselaer Handbook of Student Rights and Responsibilities defines various forms of Academic Dishonesty and you should make yourself familiar with these.

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. If caught, you will earn 0 points for that quiz or exam. If caught again, you will be sent to the Dean of Students with the recommendation that you be expelled from the class with a failing grade. It is also strictly forbidden to resubmitt a quiz or a test for regrading with changed answers. Such behavior will be considered the highest breach of academic integrity. It will definitely land you in the office of the Dean of Students with the recommendation that you be expelled from the class with a failing grade.

Standard Institute procedure for academic integrity breaches will be followed.

Suggested Homework

Some suggested homework problems and their solutions can be found at the URL

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

It is strongly recommended that you work at least through all these 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 and other suggested 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.

Here, here, and here are some of the same problems, and some different ones, in the HTML format. Here are some of their solutions.

Here are some more typed problems.

Here, you will find a number of old exams that you can use as practice problems.

To help you yet more with your practice, here is a list of suggested problems from the 10th edition of the textbook.

Here is another list of suggested problems, this one 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. These lists are a bit outdated, and contain problems from chapter 9 that we won't cover, but don't contain problems from chapter 6 that we will cover.


If you have serious problems when trying to solve the suggested homework or problems from any of the other lists above, you should seek tutoring from the Advising and Learning Assistance Center. Such problems may include: (i) you don't know how to even start the homework problems; (ii) you do not even know how to formulate a specific question to ask at the office hour; (iii) you went to the office hour three times in a row with substantial questions. Neither the instructor or the teaching assistant can provide tutoring during their office hours.


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.

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. In my opininon, if you are trying to learn one of then, Mathematica is more convenient for simple symbolic manipulation and plotting of the type that could help you in this class. An even more useful tool is Matlab, which you can use for plotting and also numerical computations.

None of these aids are allowed during quizzes and exams.

Back to Gregor Kovacic's Home Page