Differential Equations

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Syllabus -- Preview Questions -- Homework Exercises

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General Information:

Title: Differential Equations, 3rd Edition
(Note: this is not the most recent edition.)
Authors: Blanchard, Devaney, Hall
Publisher: Brooks-Cole
ISBN: 0495012653
Amazon.com

Course Philosophies:

We will follow three philosophies throughout this course:

You learn math by doing math.

Mathematics is not a spectator sport!

Athletes do not train for sports by just watching other people -- they must exercise and practice. Similarly, you can not learn mathematics by only listening to the lecture; you must actively and consistently participate in the learning process, both in and out of the classroom. You should be thinking about and working on exercises as often as possible, including problems that are not graded.

Most importantly, do not mislead yourself into believing that you understand this course just because it makes sense when someone else is talking during class. Try to reproduce the same results by yourself later on without the benefit of notes. Ask questions as soon as you have them! Visit during office hours to talk about material from class!
The answer is not the goal.

Mathematics is not just about getting "the right answer"; you must strive to be more than just a walking and talking calculator. The answer is important, but equally important is the process. You always need to show your work, you should be able to explain how the formulas are developed, and you should understand what the mathematics means.
You master math by teaching math.

You have not mastered a topic until you are able to explain it to someone else (including answering any questions someone may ask). You should work towards a level of confidence such that you can present each topic to the class at the board without needing to look at notes.

Grades:

Your final grade will be weighted as follows:

Homework:

In general, late assignments will not be accepted. The only exceptions to this rule are illness requiring medical attention documented by a doctor's note, or involvement in a traffic accident documented by a police report. Therefore, it is in your best interests to complete assignments as soon as possible, in case of unforeseen events.
Written assignments will be graded for style and content.

Style guidelines:

Content grading guidelines:

Full points only for a perfect solution (correct answer and correct work).
Half points will be given if no work is displayed, even if the answer is correct.
Partial credit will be given for correct setup and progress made towards solution.

Other Assignments:

Preview Questions:
These are designed to encourage you to review relevant material that will be needed for the next topic, and to read the textbook section corresponding to a lecture ahead of time. This will help you identify the main points and follow the lecture more easily. These questions will be posted on the course webpage, and will be graded mostly on effort. There will typically be two to five questions. Your answers must be written in complete sentences that rephrase the question being asked.
Warm-ups:
At the beginning of class, after homework is collected, a question or exercise (usually based on recent material) may be written on the board. You will have a short time (3 – 5 minutes) to write up a solution to the problem. If time permits, papers will be randomly redistributed, a solution will be presented at the board, and you will assign a grade out of 5 points using the content guidelines used for homework.

Exams:

Exams are always at least indirectly comprehensive, as mathematics naturally builds upon itself. Notes are usually not permitted. Calculators may or may not be permitted; details will be provided as the exam date approaches.

Resources:

The website CengageBrain.com has made freely available both the first chapter of the textbook (4th edition) as well as a set of applets that illustrate many topics from the book. For convenience, there are copies of both of these resources in the attachments section below.
Particularly useful applets:

Modeling Applications of Differential Equations
Applets: Mass-Spring, Forced Mass-Spring, Competing Species, Predator-Prey
Section 1.3: Slope Fields
Applets: HPG Solver, Target Practice
Section 1.4: Euler's Method
Applet: Euler's Method
Section 1.6: Equilibria and the Phase Line
Applet: Phase Lines
Section 2.1: Modeling via Systems
Applets: HPG System Solver, DE Sketchpad
Section 2.4: Euler's Method for Systems
Applet: Euler's Method for Systems
Section 3.2: Straight-Line Solutions
Applet: Matrix Fields
Section 3.7: The Trace-Determinant Plane
Applet: Linear Phase Portraits
Section 4.3: Undamped Forcing and Resonance
Applet: Beats and Resonance

When you're having difficulty understanding a new concept, it often helps to have the concept explained in a different way. Therefore, alternative, freely available learning materials are listed below:

Khan Academy: tutorial videos covering an enormous range of topics in mathematics and science, from high school to college level. Mathematics topics include Algebra, Geometry, Trigonometry, Probability, Statistics, Calculus (Differential, Integral, and Multivariable), Differential Equations, and Linear Algebra. An amazing resource.
Patrick - Just Math Tutorials: tutorial videos in mathematics. Topics include Algebra, Trigonometry, Probability and Statistics, Discrete Mathematics, Calculus (Differential, Integral, and Multivariable), Differential Equations, and Linear Algebra.
Brightstorm: tutorial videos in mathematics and science. Mathematics topics include Algebra, Geometry, Trigonometry, Precalculus, and Differential Calculus.
Paul's Online Math Notes: lecture notes (textbook-quality) and "cheat sheets" (summary/review/formula/fact sheets) for Algebra, Calculus (Differential, Integral, and Multivariable), Differential Equations, and Linear Algebra.

Additional Information:

Collaboration on work is permitted and encouraged. It is a great idea to talk about the problems with each other and try to solve them together. However, solutions must be written up independently and in your own words.
Students with disabilities are encouraged to speak to the professor about accommodations they may need to produce an accessible learning environment.