MAP2302
Lab 0: Ready, Set, Go!
Last Updated:
Monday, January 8, 2007 at 13:08
Goal
This very short "warm-up" lab consists of two (unrelated) parts.
Its goal is to make you familiar with
the character of the course and
the textbook, tools, and resources for the course.
Get To Know Your Book and Resources
- Read the Note to the Student in the
textbook (page xiii).
- Read carefully Sections 1.1 and 1.2.
- Read the brief summary
by Dr. Devaney (one of the textbook authors) of how this course
may differ from your other "traditional" math courses.
- Read the syllabus for policies.
- Review the guidelines for
Success in Mathematics.
- Browse the rest of the course resources.
Summarize the reading and your answers to the following open-ended questions
in a short essay (a couple of paragraphs, less than a page long).
Have you had a similar course (not necessarily in math),
where critical thinking and hands-on experience were at its core?
How does this course appear to be different from your other math classes?
What possible difficulties do you think you may encounter?
How do you plan to overcome them and succeed in the course?
How do you expect this course to benefit your studies at the Honors College?
What is your best skill in math?
What math skill of yours needs most work and improvement?
Get To Know Your Tools
Install DETools from the CD in the back pocket of the book to your home computer
(open the file README on the CD and follow the instructions).
Open FirstOrderExamples (the last tool in the first column) and play with the first four examples:
y'=-y2,
y'=cos(t),
y'=y(1-y),
y'=-2ty2.
Drag the starting point with your mouse to obtain various solutions to each differential equation.
Note: If you cannot get the book and the CD-ROM by the due date,
complete the assignment with the first 4 examples in the
IDE Solution Tool (IDE Lab 1b) instead;
the instructions below will not match these examples,
but do something similar and meaningful.
For each example, sketch by hand 3 different solutions (one coordinate system per example).
If they appear to be parallel translates of each other, say so.
In addition:
- y' = -y2:
Looking at the shape of the graphs, guess a solution.
Confirm your guess by plugging it in the DE.
- y' = cos(t): Same as above.
- y' = y(1-y):
Describe (in words) the behavior of the solutions
starting at y(0)<1, y(0)=1, and y(0)>1.
- y' = -2ty2:
- Looking at the shape of the solution through (0,2), guess a formula for it.
Check your guess by plugging it in the DE.
Chances are, your guess was wrong -- that is OK, my first guess was wrong too!
Note: you do not need to compute a solution for this case;
just make an honest guess and check it
(we will learn how to find exact solutions next class).
Moral: you can't always judge a function by its graph.
- There appear to be two sets of initial conditions:
for some, the solution has a vertical asymptote;
for some, the solution is a smooth function defined for all t.
Give three examples for each of the two types of initial conditions.
- (Extra credit)
Experimenting further with the tool,
try to find the "boundary" between the two sets of initial conditions
(describe the relation between t0 and y0).
In other words, tell me where in the ty-plane
I need to click in order to get a solution with no asymptote.
Report
After reviewing and heeding
the HC Project Report guidelines
listed in the Learning Resources for this course,
submit your brief (not to exceed 3 pages)
typed (or carefully hand-written in print) report for this lab
by the due date listed on the
course main page.
Collaboration
You should complete this project by yourself.
As usual, the Honor
Code applies to all graded work.
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Eugene Belogay
mailto: ebelogay@fau.edu