Ordinary Differential Equations - Math 325 - Spring 2009


Irina Mitrea, 225 Kerchof Hall, im3p@virginia.edu, Phone: 928-2787.

Teaching Assistant:

Justin Webster, Annex 2 Kerchof Hall, jtw3k@virginia.edu, Phone: 982-2785

General description:

Introduces the methods, theory, and applications of differential equations. Includes first-order, second and higher-order linear equations, series solutions, linear systems of first-order differential equations, and the associated matrix theory. May include numerical methods, non-linear systems, boundary value problems, and additional applications.

Prerequisite: MATH 132 or its equivalent.


William E. Boyce and Richard C. DiPrima, Elementary Differential Equations and Boundary Value Problems, nine-th edition.

Course web page:



Homework 1 (due at the discussion on Wednesday, January 28):
Section 2.1 (pages 39-41): Problems 13, 14, 17, 19, 31, 32
Section 2.2 (pages 47-50): Problems 1,2,3,4,5,6,7,8,25
Homework 2 (due during lecture Thursday, February 5th):
Section 2.5 (pages 88-94): Problems 7, 9, 10, 16
Section 2.6 (pages 99-101): Problems 1,2,3,4,5,6,7,8,15,22, 27
Homework 3 (due during lecture Thursday, February 12th):
Section 2.8 (pages 118-121): Problems 14, 15, 16,
Section 2.4 (pages 75-77): Problems 3,7, 13, 22, 23, 24,
Homework 4 (due during lecture Thursday, February 26th):
Section 3.1 (pages 144-145): Problems 3,6,7,12,15, 21
Section 3.2 (pages 155-157): Problems 2,6, 11, 14, 17, 21, 23, 28
Linear Independence Problems (attached to the email)
Homework 5 (due during lecture Thursday, March 12th):
Section 3.3 (pages 163-166): Problems 3,6,7,9,14,19,22,27,33,34,41
Section 3.4 (pages 171-174): Problems 3,5,8,13,14,18,19,24,27,32,38,39
Homework 6 (due during lecture Thursday, March 19th):
Section 3.5 (pages 183-185): Problems 3,7,11,15,18,19(a),23(a),25(a)
Section 3.6 (pages 189-191): Problems 3,4,9,10,13,15,17,19,20
Homework 7 (due during lecture Thursday, April 2nd):
Section 4.1 (pages 224-226): Problems 3,6,8,10,18
Section 4.2 (pages 231-234): Problems 11,13,14,17,20,23,24
Section 7.1 (pages 359-363): Problems 1,4,5,15,16
Homework 8 (due during lecture Tuesday, April 14th):
Section 7.2 (pages 371-373): Problems 6,7,12,17,24,26
Section 7.3 (pages 383-385): Problems 3,7,9,11,13,14,18,22,25,31
Section 7.4 (pages 389-390): Problems 4,5,6,7
Homework 9 (suggested problems -- they will not be graded):
Section 7.5 (pages 398-401): Problems 9,12,13,15,18
Section 7.6 (pages 409-413): Problems 2(a), 5(a), 6(a), 7,8,9,10
Section 7.7 (pages 420-422): Problems 1,3,4,6,9,10,11,12,16

Help at the Math Tutoring Center:



Prelim 1: Thursday, February 12th; Section 1 from 9:30 am to 10:45am; Section 2 from 11:00 am to 12:15pm
Prelim 2: Tuesday, March 17th; Section 1 from 9:30 am to 10:45am; Section 2 from 11:00 am to 12:15pm
Prelim 3: Thursday, April 16th; Section 1 from 9:30 am to 10:45am; Section 2 from 11:00 am to 12:15pm
Final Exam: Section 1 - May 1st, 14:00pm - 17:00pm; Section 2 - April 30th, 9:00 am to 12:00 noon

Notes, textbooks and calculators are not allowed during prelims and the final examination.


Section 1 - TR 9:30 am - 10:45 am, CLK 102
Section 2 - TR 11:00 am - 12:15 pm, CAB 222


Section 1- Wednesdays, 17:00 pm - 17:50 pm, CLK 101
Section 1- Wednesdays, 8:00 am - 8:50 am, CLK 101

Office Hours:

Irina Mitrea, 225 Kerchof Hall, TR 2:00 - 2:50 pm (or by appointment).
Justin Webster, Wednesdays from 9:00 - 10:30 am and Thursdays from 11:00 - 12:00 noon


Prelims count 15% each, the final 25%, the collective patterns of learning and attitudes in Math 325 count for 10% of the final score and the remaining 20% is apportioned among homework, quizzes and class participation. 1% bonus point is awarded for each participation in extracurricular mathematical activities such as the Math Club, the University of Virginia Undergraduate Lecture Series, the IMA lecture series.


There will be a short quiz every Wednesday, unless otherwise announced. It will be returned to you on Tuesday.


To be handed in at the Wednesday discussion meeting. Do all problems assigned. Part will be graded and returned to you the next week. Please be sure that your work is legible.

No late homework will be accepted. You may work cooperatively on assignments provided

You write up the solution yourself.
You put a note on your homework indicating the names of anyone you worked with.

Incomplete :

An incomplete will be given only in those rare circumstances where a student has completed all but a small portion of the course with a grade C or better and a severe, unexpected event prevents him/her from completing the course. In particular, if you get behind in the course you cannot ``bail out" by taking an incomplete.

Attendance and absences :

You are responsible for the material covered in class, whether you attend or not. You are also responsible for the announcements made during class; these may include changes in the syllabus.

Academic honesty is fundamental to the activities and principles of a University. Any effort to gain an advantage not given to all students is dishonest whether or not the effort is successful. When in doubt about plagiarism or collaboration, consult the course instructor.

If you need accommodations because of a disability , if you have emergency medical information to share with me, or if you need special arrangements in case the building must be evacuated, please inform me immediately. Please see me after class, or at my office.

Words of advice: I encourage you to ask questions about the HW. Keep up with the latest materials covered; experience shows that, otherwise, you are likely to get poor grades on the exams. If you miss a class, make sure you get the notes from someone else who attended it. The professor will not assist any absentee to find out what happened in his/her absence. Hard work and regular attendance will get you through this course.