MATH 110
Don Lawrence
Study Guide for Exam I
The exam will cover homeworks 1 through 4; calculators
will
be allowed.
I try to make study guides complete, but there is no guarantee – I might think of something later
that I forgot to include.
Also look at homeworks, quizzes, handouts, labs, and class notes.
Topics
•
Modeling (building a DE or IVP)
o
Define your functions and variables
o
Constant rate of change (
47
=
′
y
)
o
Proportional rate of change (
y
y
47
.
=
′
), including interest compounded continuously,
unconstrained population growth, etc.
o
Jointly proportional rate of change (
kAB
y
=
′
)
o
Newton’s law of cooling
o
Constrained population growth
o
SIR
o
Approximate a constant
k
in an IVP
•
Extract information from an IVP or DE
o
Tangent line and linear approximation, given any presentation of the data (slope and point)
that allows you to find a tangent line (most likely given an IVP, but see also problems 8 and
11 on Homework #2)
o
Euler’s method
On an IVP
On a system of IVPs
Know how to use Excel to do Euler’s method
Successive approximation
•
Stop when consecutive approximations are the same, rounded to a specified
number of digits; use the latter of the two as your approximation
•
Why successive approximation is better than a single approximation
Error in Euler is approximately proportional to
t
∆
(♣)
Richardson extrapolation
•
Understand how to derive the formula, starting with fact ♣
•
Be able to apply it given a list of successive approximations
o
Know that a max or min of a function happens when its derivative is zero; use this fact to
extract from a DE information about where maxes/mins happen (e.g., where an epidemic
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 Fall '06
 staff
 Math, Numerical Analysis, IVP, Euler, slope field, Wellium

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