Fiona Lyons
Math 201
EulersMethod
Foreachdifferentialequation,writedowntherecursiveformulaassociatedwithEulers
Method. Also indicate whether or not you know how to find an analytic (exact) solution.
dy
dt
3y
dP
dt
0.25 P
dy
dx
7x
dy
dt
t3 y2
dP
dt
cP( M
Fiona Lyons
Math 201
10.23.2012
Math 201 Calculus I Text Reading Questions
Section 4.2
Answe r these quest i ons as you r e ad your t ext .
1. (4.2.1) What is the name of the function obtained by differentiating a given function
twice? What are the notat
Uzair Burmi
Fiona Lyons
Calculus I
Section 3.1 Worksheet
1. What do the initials IVP stand for?
IVP stands for 'initial value problem.'
2. What two things make up an IVP?
An IVP is made up of a differential equation and an initial value.
3. Solve each of
Fiona Lyons
Math 201
10.23.2012
Math 201 Calculus I Text Reading Questions
Section 4.2
Answe r these quest i ons as you r e ad your t ext .
1. (4.2.1) What is the name of the function obtained by differentiating a given function
twice? What are the notat
Fiona Lyons
Math 201 Calculus I Text Reading Questions
Section 4.5
1. (4.5.1) In the first experiment, what question is being asked?
2. (4.5.1) What law from physics will we use to answer this question?
3. (4.5.1) What two new formulas do the authors say
Math 201 Calculus I
Text Reading Questions
Answer these questions as you read your text. Type your answers into this sheet and
upload the document into Blackboard.
Chapter Introduction:
1. What derivative rules will we learn in this chapter? What else wil
Math 201 Calculus I
Text Reading Questions
Answer these questions as you read your text.
Section 2.6
1. (2.6.1) What do we want to learn about the data from the two Case Studies?
We want to learn and find out if the population in both studies is represent
9/09
Vincent Yu
DAS Reading Assignment
This article was written by David A. Smith, one of the authors of our textbook. The
essay is addressed to math professors, but you may find it interesting. As you read,
answer the questions below. Please type your an
Sections 1.5 and 2.1 Reading Questions
Section 1.5 The Algebra of Functions
1. (1.5.1) What kinds of algebraic operations can you do with functions?
Addition, subtraction, multiplication, division, extracti on of roots, and absolute
value are the kinds of
Math 201 Calculus I
Text Reading Questions
Answer these questions as you read your text. Bring your answers to with you to class
next time. We will discuss these sections together in class. I will collect your answers to
the reading questions at the end o
A GUIDE TO WRITING IN MATHEMATICS CLASSES AT
HOOD COLLEGE
Adapted from a Guide by Dr. Annalisa Crannell of Franklin & Marshall College 1994
WHY SHOULD YOU HAVE TO WRITE PAPERS IN A MATH CLASS?
For most of your life, the only kind of writing you have done
Ten guidelines for students doing group work in mathematics
Anne E. Brown
Department of Mathematics and Computer Science
Indiana University South Bend
1.Move into your groups quickly, sit close together, use first names, and get right to
work. Do not enga
SUGGESTED OUTLINE FOR A TEAM
REPORT
ADAPTED FROM DIFFERENTIAL EQUATIONS LABORATORY WORKBOOK BY BORRELLI,
COLEMAN, AND BOYCE
Authors, date, course number, title. (You may use the checklist for
your title page.)
TITLE PAGE.
Background, details of the proble
Uzair Burmi
Fiona Lyons
Chapter 3: Solutions to Initial Value Problems
1. Show that = 2 is a solution of the equation
3 10 =
by plugging in the value 2 for t.
2. Show that = 1 is a solution of the equation
tan(ln ) = 0
by substituting the value 1 for x.
*exercises 2, 3, and 4 are at the end of the document.
Fiona Lyons
Math 201 Calculus I Text Reading Questions
Section 2.5
1. (2.5.1) What assumptions are we making about population growth on this page?
We assume that populations grow at a rate proportiona
M A T H 201 C A L C U L U S I
W O R K S H E E T : S E C T I O N 2.5
Recall:
If
dP
dt
k P with P (0)
P0 , then P (t ) _.
1. In a certain population of fruit flies, the rate of growth is proportional to the population and
the constant of proportionality is
Fiona Lyons
Logarithms and Plotting Data Part II
If you have two variables, say x and y, and you plot y vs. x and get a straight line, then y
is a _ function of x.
If, on the other hand, you plot ln y vs. x (or plot y vs. x in a semilog plot) and get a
s
Fiona Lyons
Math 201 Calculus I Text Reading Questions
Answer these questions as you read your text.
Section 2.6
1. (2.6.1) What do we want to learn about the data from the two Case Studies?
We want to know whether or not populations grow exponentially.
2
Fiona Lyons
M A T H 201 C A L C U L U S I
F A L L I N G B O D Y PR O B L E MS
1. Suppose you are standing on a balcony and toss a water balloon off the balcony
towards an unsuspecting pedestrian below. When the balloon leaves your hand, it is
twenty feet
SettingupIVPs
Directions: For each situation given, set up an IVP. You do not need to solve it.
1. A patch of mold grows at a rate that is proportional to the amount present. Let be the size of the
mold (in grams), and let be the length of time (in days)
Names
Average and instantaneous rates of change
Working with a partner, fill out this worksheet in Notability and submit to your
instructor. Although each pair will submit only one filled-in worksheet, you should
complete and keep a copy for yourself.
Be
MATH 201 Homework: The Derivative
Fiona Lyons
Name _
1. If = 3 , what is
ds
dt
? [You may use the formula we discovered last week.]
3t^2-3 t^2
t- t
What is the (instantaneous) rate of change in when = 0? when = 1?
Sketch a graph of , and then sketch on i
Circular functions and differential equations
Find:
sin
sin(2)
sin(3)
sin(5)
sin(),wherekisanyconstant
sin(),wheretheGreekletter('omega')standsforaconstant
Show that, in general,
sin() = sin().
Explain why the function () = sin() is a solution of the di
Fiona Lyons
Math 201
10.23.2012
Math 201 Calculus I Text Reading Questions
Section 4.2
Answe r these quest i ons as you r e ad your t ext .
1. (4.2.1) What is the name of the function obtained by differentiating a given function
twice? What are the notat
Fiona Lyons
Math 201 Calculus I Text Reading Questions
Section 4.5
1. (4.5.1) In the first experiment, what question is being asked?
2. (4.5.1) What law from physics will we use to answer this question?
3. (4.5.1) What two new formulas do the authors say
Fiona Lyons
8.28.2012
Math 201
Math 201 Calculus I Text Reading Questions
Section 1.3 Terminology
1.3.1 Relations and Functions
What is a relation?
A relation is a pairing of the values of one varying quantity with values of another
varying quantity.
Is
Fiona Lyons
8/12
MATH 201 CALCULUS I
SECTION 1.5: INVERSES
1. Graphical: In both of the problems below, does the function whose graph is given have an
inverse function? If so, then check YES and draw the graph of the inverse function on the
same set of co