Math
210
Spring
2011
Prof.
Donnay
Class
Materials and Assignments
Wk, Class#, Date 
Class
Material 
Assignment 
Wk
1: Class 1 W
1/19 
Introduction to Course. Problems Facing the World. Intro Differential Equations program.

For Friday Jan 21 at noon: 
Fill in Student
Information Survey Take Precourse Self Assessment and
Review For next class: Read the course syllabus. What is the Òspecial eventÓ
about? For Monday 1/24. Write about one of
the programs on the CD. Post your write up (1 to 2 paragraphs in the
Discussion Board of Blackboard). NOTE: EXTENSION OF THIS ASSIGNMENT
TILL WEDNESDAY. On Monday from 6 – 8pm, the math computer lab Rm. 349 will
be open. The DETools software is on the computers there. 
C2
M
2/24 
Pfaff
data set on atmosphere taken from Tom PfaffÕs website.
Question set for CO_{2} data. Excel
instructions on curve fitting (PC version, Mac version).
Differential Equations
and exponential functions worksheet. 
Wed Jan 26^{th}. a.
Write up neatly (complete
sentences, clearly define what your variables stand for and what your units
are) and hand in the CO_{2} assignment. b.
Post your write up about the
DETools module to Discussion Board in Blackboard by noon Wed. c.
Hand in the completed Differential Equations
and exponential functions worksheet. d.

C3
W
2/26 
Examine DETools Modules: Predator
– Prey, Chemical Oscillation (terms: Initial value, circular/periodic
behavior, parameters, tipping point = bifurcation value). Solving initial value problem for
basic population model dP/dt = kP using Ôguess and checkÕ method: P(t) = c e^{kt}.
ÒGoodÓ choice of variables.
Strengths and weakness of model (worksheet) as
applied to US population modeling.
The modeling cycle: simple assumption, translate in DE, solve DE using
initial data, predict new values, check to see if predictions are accurate,
revise model (if needed) by taking more factors into account. Translating basic assumption about
model (as given in a word statement) into a D.E. (worksheet).. 
For Monday Jan 28^{th}: Do
(as much as you can) the worksheet
on translation; we will go over this in your groups on Monday and work further
on it. For Wed Feb 2: Homeworks Assignment. You will need the Pfaff module on Global Temperature. The data on
temperature is contained in the same excel
file that we used for the CO_{2} levels. Note: use the
temperature data that starts in 1950. Correction:
the problems from Sect 1.1 should be #6, 10, 11, 12ab. The problems listed on the
HW sheet, # 4, 8, 9, 10ab were from the wrong edition of the text. If you have
already done the original problems, that is fine. If you have not yet done
the problems, please do the new set of problems. 
C4 M
1/31 
Modeling: translate statement into DE
(worksheet). Logistic Model derivation. Computational exploration
worksheet for logistic equation. Calculating and plotting slope fields
worksheet. 

C5
W
2/2 
Sect 1.3: Review of slope fields
given by f(t,y). Autonomous DE when slope field is f(y); slopes are constant
for fixed y, varying t. Nonautonomous DE when slope field of form f(t) or
f(t,y); i.e. slope field depends on t. When slope field =f(t), slopes constant
for fixed t as y varies. Decide f
type ={f(y), f(t), f(t,y)} for S1.3 #15(iviii). Meaning of solution
of DE via slope fields. Slope yÕ(t) of solution curve must match up with
slope of slope field for y(t) to be a solution. (handout). Separation of Variables technique. 
For
Monday Feb 7^{th}: Do the first problem from the HW set. For
Wed Feb 9^{th}: Do HW Wk 3. Pfaff
Modules: Do one of: World
Oil Consumption Ozone
Hole World
Population The
data table is on the Pfaff web site.
Next to the data table is a word document that gives you the instructions of
what you should do with the data. 
C6 M 2/7 
Separation of variables worksheet; plotting
exponentials; what
to do when you do not know what to do worksheet to solve modeling problem
about mixing. 
For Wed Feb 9^{th}: do quiz 1 
C7 W 2/9 
Sect 1.5 Existence and Uniqueness. 
For Mon Feb 14 and Wed Feb 16: 
C8 M 2/14 
Applications of Uniqueness theorem. Sect 1.4 Euler Method: worksheet. Excel spreadsheet
for Euler Method (version 1,
version 2, instructions). 
For Wed Feb 16^{th}; Quiz 2 
C9 W 2/16 
Partial derivative calculations. Qualitative analysis of DE
worksheet, phase line. Sect 1.6 
Note that there are two problems due
on Mon Feb 21; the rest are due on Wed Feb 23. 
C10 M 2/21 
Phase line: Linearization Theorem S
1.6. Introduction to S. 1.8: y_{g} = y_{h} + y_{p}
. 
For Wed Feb 23^{rd}: Quiz 3 Guidelines for redoing Quiz 2 
C11 W 2/23 
Using phase line analysis to study fishing problem. Sect 1.8: Theorems: Linear
combination of solutions of homogeneous equation are solutions. Difference of
particular solutions to nonhomogeneous equation is a solution to homogeneous
equation. 
HW
Wk 6: Most due on Wed but a bit is due on Monday. Here are the DE Challenge Problems.
Do two out of the three. 
C12 M 2/28 
Sect 1.8: How to find a particular
solution to linear nonhomongeneous DE: Educated guess (Method of Undetermined
Coefficient for constant coefficient DE). Sect 1.7: Bifurcation diagram for
Logistic Map with Harvesting. Calculate phase line for
various c values. 
For Wed March 2: Quiz 4 
C13 W 3/2 
Sect. 1.7. Calculating equilibrium
solutions using general formula. Visual method of determing bifurcations.
Finance problems. Intro to DE systems using DE Tools. 
HW
Wk 7: This will be due on Monday March 14^{th}. It will be
returned by Wed March 16^{th} so you can have it to study for the
Take Home Exam. Quick write (to be included in the hw).
What was one thing that your found interesting about our work on the
Bifurcation diagram? What is one question you have about bifurcations? 
C14 M 3/14 
Discussion
of midterm exam structure (List of topics, What makes a good
answer). Systems of DEs: vector fields (worksheet1),
parametric equations; geometric interpretation. Equilibrium solutions.
Analytic solutions of system. 
For
Wed 3/16. Post questions and potential exam problems to Blackboard Discussion
board. Do What
makes a good answer worksheet.

C15 W 3/16 
Review for midterm. 
Take home Midterm given out. Due at
the start of class on Monday 3/21. 
C 18 M 3/21 
Parametric Equation of line; Graphing
parametric equations vs (t, x(t)) graph. Equilibrium solutions. Physics
problems and associated 2^{nd} order DE. Connection with system. Sect
2.1, 2.2. Mathematica
to find Eigenvalues, Eigenvectors of matrix. 
For Friday 3/25: Worksheet on parametric equations. Textbook
problems. For Monday 3/28Worksheet: Relation between type of
equilibrium solution and eigenvalues. 
C 19 W 3/23 
Harmonic (S. 2.2) and Damped Harmonic
Oscillator (S. 2.3). Decoupled and Partially Coupled Systems (S. 2.3).
EulerÕs Method for Systems (S. 2.4) 
For Wed March 30, HW Wk 9. 
C20 M 3/28 
Course project information.
Vector spaces (hand
out); Conjectures about relationship between eigenvalues and type of
equilibrium; Linear map from R^{2 } > R^{2} given by matrix A; geometric meaning of
eigenvector, eigenvalues (woksheet,
graph paper). 
Quiz
for Wed March 30. 
C21 W 3/30 
Matrix is linear, linear combination
of solutions of a linear system is a solution. Straight line solutions with
eigenvectors, eigenvalues. General solution. 
For Monday April 4; post write up
about project to Blackboard discussion board. For Wed April 6, HW Wk 10. 
C22 M 4/4 
Complex numbers. Polar form. EulerÕs
formula. Practice drawing phase diagrams with for linear systems with real
eigenvalues. Complex eigenvalues give rise to spiral motions. Mathematica can
solve
systems of equations. 
Quiz
for Wed April 6^{th}. 
C23 W 4/6 
Determining the bending for
attractors/repellors. Complex eigenvalues give rise to real solutions. 
HW
Wk 11 including complex number
calculations. Read Project
Guidelines. 


Instructions for reassessement
of topics from midterm. To help organize the reassessment process, you should
fill in this reassessment sheet
and hand in to Professor Donnay when you hand in your preparatory work. 
C24 M 
Calculations of eigenvalues/vectors.
Nonlinear cases. 
Quiz
due Wed April 13^{th}. 
C25 W 4/13 
Nonlinear system analysis: find
linear approximation matrix near equilibrium point (Sect 5.1). 
HW
Wk 12 due Wed April 20^{th}. 
C26 M 4/18 
Jacobian matrix of partial
derivatives. Putting linear pieces together to make nonlinear system. Phase
portrait for diagonal matrix. 
Quiz
due Wed April 20^{th}. 
C27 W 4/20 
Numerical methods: Euler, Improved
Euler, RungeKutta (Sect 7.17.3). Numerical
solutions with Mathematica. (pdf
version) 
HW Wk 13: due Wed April 27^{th}.
Sect. 7.2 #1  Do both Euler and
Improved Euler for this example. Also solve for the exact value of the integral.
Compare. 


