Math 214 Section 002 Fall '08

Prerequisites: MATH 213 or 215
Time and venue: TR 4:30-5:45pm Innovation Hall 207
Instructor: Maria Emelianenko
Email: memelian @
Office: 226A Science and Tech I
Office hours: TR 2-3pm

 Site contents:  Syllabus  Matlab  Announcements  Lecture notes  Schedule and homework  Links  Help info  Anonymous Feedback Form

[06/11/08]  Welcome! Our first meeting is on Tuesday, Aug. 26. The textbook we are going to use is "Elementary Differential Equations" by Boyce and DiPrima, 8th edition.
If you have time, please try to familiarize yourself with the material by reading the introduction and prepare for the fruitful work this semester. Hope it will be an enjoyable one!

[08/27/08]  The bookstore has been notified of a mistake with textbook order. If you have purchased a textbook by Polking instead of Di Prima, they should reimburse you for your purchase and you should be able to get the correct book as soon as the new order comes in in a couple of days. You can also purchase the Di Prima book online at to get it faster. For now, a copy of Di Prima book has been placed on reserve in the library (JC desk).

[08/28/08]  Please check the discussion board for questions regarding homework 1, including problem descriptions. Quiz 1 today is going to consist of a short portion on direction fields (see lecture notes for a typical problem) and a review of differentiation/integration (see a short Calculus review formula sheet in the links section below).

[09/02/08]  Office hours on Thursday Sept. 4th will be from 1-2pm instead of 2-3pm. Please take a note of this change!

[09/03/08]  The outdated page links to Integration and Partial Fractions tutorials have been updated (see the Links section below). You may want to check them out when working on your calculus review.

[09/08/08]  The Boyce-diPrima textbook is available at the Bookstore now, so feel free to stop by and get your copy!

[09/11/08]  The original solution set for Quiz3 had a typo in problem 1. The correct solution to the IVP should have read y = 1-sqrt(t^2+5) (see the corrected version online). Apologies for the confusion.

[09/12/08]  Please take a couple of minutes to let me know how things are going! A short class survey is available online in the Assessment section of Blackboard. You can also put your comments in the anonymous part of the discussion board if you wish, or use the Anonymous Feedback Form on this website.

[09/30/08]  Midterm I is this Thursday, October 2, during regular class session. Several Practice tests are available in the Supplementary material section of the Blackboard website. I will not be available on Thursday Oct 2 before the exam, so if you have questions, come see me on Wednesday 5-6pm (this replaces the Office hour on Thursday).

[10/09/08]  Answer key to Midterm I given in class had typos in answers for problems 5,6 and 9. If you haven't made the corrections in class, please check the file available online at Blackboard in the Content/Exam Solutions section.

[10/09/08]  Homework 6 is due today and its solutions will be discussed in class. There is NO CLASS on Tuesday Oct 14 due to Columbus day break (Monday classes are being taught on Tuesday). Quiz 6 is scheduled for Thursday Oct 16.

[11/26/08]  Homework 12 is due on Tuesday: assignment is ##1-12, Chapter 6.5. There is NO CLASS on Thursday Nov 27 due to Thanksgiving break. Quiz 11 is scheduled for Tuesday Dec. 2.

[12/03/08]  Don't forget the Final Exam is on Tuesday, Dec. 9, at 4:30-7:15pm in the same room as usual. Two practice exams are available: [Exam1][Exam1key][Exam2][Exam2key]. As usual, disregard questions on topics not covered in class.

Lecture notes
Lecture notes will be posted here as the course progresses. This and other material will also be available online at the Blackboard website (check the Course Content folder).
Reading assignments and selected homework problems will follow our main text: "Elementary Differential Equations" by Boyce and DiPrima, 8th edition, Wiley.

Lecture 1 [08/26/08]: [pdf]

Lecture 2 [08/28/08]: [pdf]

Lecture 3 [09/02/08]: [pdf]

Lecture 4 [09/04/08]: [pdf]

Lecture 5 [09/09/08]: [pdf]

Lecture 6 [09/11/08]: [pdf]

Lecture 7 [09/16/08]: [pdf]

Lecture 8 [09/18/08]: [pdf]

Lecture 9 [09/23/08]: [pdf]

Lecture 10 [09/25/08]: [pdf]

Lecture 11 [09/30/08]: [pdf]

Lecture 12 [10/07/08]: [pdf]

Lecture 13 [10/09/08]: [pdf]

Lecture 14 [10/16/08]: [pdf]

Lecture 15 [10/21/08]: [pdf]

Lecture 16 [10/23/08]: [pdf]

Lecture 17 [10/28/08]: [pdf]

Lecture 18 [10/30/08]: [pdf]

Lecture 19 [11/04/08]: [pdf]

Lecture 20 [11/06/08]: [pdf]

Lecture 21 [11/18/08]: [pdf]

Lecture 22 [11/25/08]: [pdf]

Lecture 23 [12/03/08]: [pdf]

Lecture 24 [12/05/08]: [pdf]

Your grade in this course will depend on your performance on two written in-class midterm exams, weekly in-class and online quizzes and a comprehensive final. Tentative weight of assessment components:
- Midterm I (Oct. 2, in class): 25%
- Midterm II (Nov. 20, in class): 25%
- Final exam (Dec. 9, 4:30-7:15pm): 25%
- Quizzes: 15%
- Participation: 10%

Letter grade will be determined as follows:
Score above 90% 80% 70% 60% otherwise
Letter grade A B C D F

Weekly practice problems will be given that will not count towards the final grade, unless specifically noted. I strongly encourage all participants to do these exercises in order to gain the necessary grasp of the material and perform well on exams and graded assingments. I will discuss solutions in class every week.
I expect all class participants to abide to the rules and regulations specified in the official GMU Honor code.

Tentative schedule
  Adobe reader needed to view .pdf files is available here

Please note that this schedule is subject to change. Make sure you check this site frequently for updates.

1 [08/26/08]
Chapter 1.1
Chapter 1.2
Quiz 1
2 [09/02/08]
Chapters 1.3, 2.1
HW1 due    [HW1 solution]
Chapters 2.1, 2.2
Quiz 2
3 [09/09/08]
Chapters 2.2, 2.3
HW2 due    [HW2 solution]
Chapters 2.2, 2.3
Quiz 3
4 [09/16/08]
Chapter 2.3
HW3 due    [HW3 solution]
Chapter 2.4
Quiz 4
5 [09/23/08]
Chapter 2.5
HW4 due    [HW4 solution]
Chapters 2.5, 3.1
Quiz 5
6 [09/30/08]
HW5 due    [HW5 solution]
Midterm I Review
Midterm Exam I
7 [10/07/08]
Exam I results and solutions
Chapter 3.2
HW6 due    [HW6 solution]
Chapter 3.3
8 [10/14/08]
Columbus Day break - no class
Quiz 6
Chapter 3.4
9 [10/21/08]
HW7 due    [HW7 solution]
Chapter 3.5
Quiz 7
Chapter 3.6
10 [10/28/08]
HW8 due    [HW8 solution]
Chapter 3.8
Quiz 8
Chapter 3.9
11 [11/04/08]
HW9 due    [HW9 solution]
Chapter 6.1
Quiz 9
Chapter 6.2
12 [11/11/08]
HW10 due    [HW10 solution]
Chapter 6.3
Quiz 10
Chapter 6.4
13 [11/18/08]
HW11 due    [HW11 solution]
Midterm II Review
Midterm Exam II
14 [11/25/08]

Thanksgiving break - no class
15 [12/02/08]
HW12 due    [HW12 solution]
Final Review
Help info and contacts
If you are looking for help, these are some of your options:
  • Try coming to my office hours.
  • If you have conflict with my office hours, talk to me after class or email me, I'll try to make an appointment for you at a different time.
  • Additional help is available in the Mathematics Tutoring Center, located in the Johnson Center room 344. Hours are posted on the Tutoring Center website.
If you have concerns or suggestions that you'd rather leave anonymous, please use the anonymous feedback form. I need to know what you think in order to make the learning process effective, so any feedback is valuable to me.

MATLAB is an interactive programming language for general scientific and technical computation with powerful graphics and library functions. We will be using MATLAB environment for some homework problems towards the end of the semester and I expect you to be able to get access to it. Here is some relevant information.
- Some guidelines for accessing and using MATLAB are available here:
- A standalone student version of the product is available from Mathworks website for a reasonable price.

Some MATLAB tutorials you might want to read:
Useful links
Every now and then I find interesting information on the web or in press. I'll be putting this stuff here, since it could help some of you to refresh things you might have forgotten or to aid with the general understanding of the course. If you find something useful yourself, please let me know, I'll be really happy to expand this list with your suggestions.

Basic math reference resources:
Partial fractions tutorial
Integration tutorial
Partial derivative examples
A concise Integral Table from Mathwords
Calculus review - formulae you have to remember!
Huge collection of Math related info at Wolfram Mathworld

Software tools available online:
ODE Software: powerful Dfield and PPlane Matlab tools (read instructions!)
DFDEMO: Direction field Java applet
One more direction field Java applet
Phase portrait generator (applet by Prof. Mansfield, PSU)
Studying ODE (applets for dir. fields, solving systems and more, by M. Rychlik)
Differential Equations and Initial Value Problems, applet
Systems of ODEs, applet
ODE solver Solutia (script for solving DE in standard form)

Course notes from different sources
ODE modules from Duke Univ. (TRY THESE!)
S.O.S. Math - nice short Differential Equations course online
S.O.S. Mathematics - CyberExam - sample exams online
Nagle's ODE book: Interactive Differential Equations supplement
1st Order ODEs (nice introductory notes by I. Blank, in .ps format)
Differential Equations Notes (good notes w/lots of examples by B. Ikenaga, in .ps format)
GATech DE course (great notes, by Jason Metcalfe)

Miscellaneous links
You might need to install current version of Ghostview to be able to view .ps files!

ODE Lecture Notes (handwritten notes, more advanced material, by M. Pemberton)
Advanced Differential Equations (extended source of notes on DE by S. Newhouse, in .ps format)
ODE course for Engineers (nice application examples, by J.R. White)
ODE notes (in .pdf, by Peter Wolenski, LSU)
Numerical Solution of ODEs (CSEP electronic book)
Numerical Solution of ODEs (Advanced course on theory of ODE, .ps file)
Numerical Methods (S. Dalziel)
Partial Differential Equations Notes (html notes on PDEs by A. Hood)
Course Notes: ODE, PDE etc (J. Labute at McGill, in .pdf)
Topics in Calculus (has some ODE notes too, by L. Lady)
ODE Notes and Exercises (Maple-based exercises, by P. Monk)
ODE course: lectures, problem sets, exams etc (by J.N. Kutz, U. Wash)
ODE Exams, Worksheets, ... (R.L. Devaney)
Mathematical Notes (.pdf notes on ODE by M. Malek, more theoretical)
PDE & Vector Calculus Lecture Notes (by W. Zakrzewski, Durham UK)
Complex Analysis and Differential Equations (by S.G. Rajeev, Rochester)
Difference Equations to Differential Equations (D. Sloughter)
Linear Methods ... (E.M. Harrell, J.V. Herod)
Hilbert Space Methods for PDEs (R.E. Showalter)
Topics in Integral and Differential Calculus (T. Kawasaki)
ODE Projects (A.C. Heinricher)
Maple Worksheet Repository
Graphical Tools (applets)
Taylor polynomial applets:   1, 2, 3, 4
Java Examples etc. (J. Feldman)
Damped Harmonic Motion, applet
Interactive Math Programs (calculus and DE applets from Dartmouth)
Kepler's Laws, applet
Fourier Synthesis, applet
The Lorenz Equations, applet
Nonlinear Klein-Gordon wave equation (applet by Paul Garrett)
Heat equation, applet
Java calculus, applets
MathServ DE Toolkit
Math Archives: ODEs, PDEs
Math Forum - Differential Equations (notes, problems, puzzles, discussions etc)
Differential Equations and more ( project)
ODE Project at BU
Sampler of applets (performance analysis, by Paul Garrett, UMN)
Famous Curves Applet Index (spirals, involutes and more)
Math Reference Tables