Instructor: Mette S Olufsen
Office: SAS 3216
Office Hours: By appointment via email.
Phone Number: 515-2678
Email address: firstname.lastname@example.org
This course provides an introduction to differential equations.
The course will cover methods for solving ordinary differential
equations including Laplace transforms, Phase plane analysis, and
numerical methods. Matrix techniques for systems of linear
ordinary differential equations.
of Differential Equations and Boundary Value Problems, Sixth
Edition. By: Nagle, Saff, Snider, Addison-Wesley, Copyright:
Pearson Education Inc.
Computer tools will be used including Matlab, Maple, and pplane
Format: During the course
weekly homework will be assigned. In addition, all students are
required to do a larger group project using differential equations
to solve an applied problem.
In addition to homework problems, two in-class tests and one
final will be given.
Evaluation criteria:The course will be graded
based on the work performed in homework (25%), tests (30%),
project (15), and final (30%).
Prerequisites: MA242 or (MA132 and MA231).
Students from MA132/MA231 should expect additional work to learn
how to solve linear systems of equations.
Homework: I encourage you to
work with others on the homework, but everybody must hand in
individual solutions. Homework requiring computer solutions
(e.g., Maple, Matlab, or pplane) can be done in groups. For
group homework only one solution is required with everybody's
name on it. Homework will only be graded if handed in on time.
1) Describe the project you have
chosen in a paragraph (Due Mond 10/28).
A: Question you plan to
how you plan to address the question
C: What do
you anticipate to learn about the problem
Example problems can be found throughout the book, after each
chapter a set of potential projects
with questions are outlined. However, in addition to answering the
questions specified in the book think
about A-C above.
2) Project HW 2 (Due Friday 11/22
- for comments Monday) or (Monday 11/25 - with email
A) Write up the introduction to your problem
and the questions you plan to address
B) Make a diagram for your model
C) Write up equations for your model
3) Final project
report(Due 12/13 before Final) and power point (Due after
report and power point should include: A)
Introduction (Why is the problem important and what do you expect
Problem formulation (What questions do you plan to ask and outline
your method of solution)
design (Diagram illustrating the flow in your model and derivation
Results (Solution of equations, simulations, graphs, etc.)
Discussion (Answer your questions, what are the limitations of the
model and how could they be addressed)
your report I expect that you include citations to literature
other than the text book.
no page-limitation for the written report, the main point is that
it should be thorough enough and contain a satisfactory answer to
be noted, that it is OK if your model cannot answer your question,
if that is the case try and discuss how it could be improved to
get a better answer.
Project presentations: Last two classes in December!
Friday Dec 13th 8-11AM in SAS 2106
Allowed: One sheet of notes written on both sides
Bring: Calculator, Paper to write on, Pencils, Erasers, Ruler
Given: Final + Table with Laplace transforms, from the back of the
Homework 1 (Wed 8/28/2013) 1)
Webwork: 0-Introduction 01
2) Webwork: 0-Introduction
3) Paper: Sec 1.2 # 23, 25,
3) Computer: Sec 1.3 #11,
13, 15 (use pplane or ISOCLINES.m). Note pplane does NOT give
you the isoclines you would have to draw these by hand.
4) Paper: From the notes
about modeling (pages 11-12), for every group provide examples
for each model type.
Homework 2 (Wed
2) Webwork: 2-Separable
3) Computer: Plot values
for the US population predicted using exponential p(t) =
p0 exp(kt) [solution to dp/dt = kp], and logistic growth p(t) =
M p0 / ( p0 + (M-p0) exp(-kMt) )
dp/dt = kp(M-p) ], as well as the actual growth from 1790
realistic values for p0, M, and k. Use http://www.census-charts.com/Population/pop-us-1790-2000.html
directional fields and flow fields (graph of dp/dt as a fct of
p) for both equations. Discuss results
4) Paper: Solve 3.2
problems 19 and 21
Homework 3 (Wed
Webwork: 1-First-order-equations 04-Linear-integrating-factor [NEW DUE DATE 9/18]
2) Paper: Section 3.3
3) Paper: Devise a problem
that discusses heating/cooling. Describe the problem, set up
equations, discuss time-scales.
7 (Fri 10/18/2013)
Show that for A = [ 2
and B = [1 0
1 2 3
the product A B is not equal to B A
2) Show that
that for A = [ 1 2
1 with the inverse matrix
inv(A) = [ 3/2 -1 1/2
1/2 0 -1/2
-3/2 1 1/2 ]
The product A
inv(A) = I (the identity matrix)
3) In class we
stated a theorem for matrices of
order n x n. For these the following
statements are equivalent
a) A is singular
(does not have an inverse)
b) The determinant
of A is 0
c) Ax = 0 has
d) The columns
(rows) of A for a linearly dependent
In class we
showed b) for the matrix A = [ 2
homework show a) that the matrix
does not have an inverse.
that c) that Ax = 0 has nontrivial
solutions (i.e., that you will get a
row of zeros if you try to calculate
And discuss how
you can show d.
8 (Mon 10/28/2013) 1) For
the Matrix A = [ 0
-5 -3 -7
Show that the
three general solutions are given by