MTH 3410 - Calculus III
Your Name
Exam 1
Your Signature
Problem
Total Points
1
10
2
10
3
10
4
10
5
10
Total
Fall 2009
50
Score
This exam is closed book. You may use one handwritten 3 5 card of notes.
Calculators are not allowed.
In order to receive cre
MTH 3410
Your Name
Final Exam
Your Signature
Problem
Total Points
1
10
2
10
3
10
4
10
5
10
6
10
Total
Autumn 2010
60
Score
This exam is closed book. You can use one handwritten 8.511 page of notes for reference.
In order to receive credit, you must show
MTH 3410
Your Name
Final Exam
Your Signature
Problem
Total Points
1
10
2
10
3
10
4
10
5
10
6
10
Total
Autumn 2009
60
Score
This exam is closed book. You can use three handwritten 35 note cards for reference.
In order to receive credit, you must show you
MTH 3410 - Calculus III
Your Name
Exam 2
Your Signature
Problem
Total Points
1
12
2
12
3
12
4
14
Total
Fall 2010
50
Score
This exam is closed book. You may use one handwritten 3 5 card of notes.
Calculators are not allowed.
In order to receive credit,
MTH 3410 - Calculus III
Your Name
Exam 1
Your Signature
Problem
Total Points
1
10
2
10
3
10
4
10
5
10
Total
Fall 2010
50
Score
This exam is closed book. You may use one handwritten 3 5 card of notes.
Calculators are not allowed.
In order to receive cre
MTH 3410 - Calculus III
Your Name
Exam 2
Your Signature
Problem
Total Points
1
12
2
12
3
12
4
14
Total
Fall 2009
50
Score
This exam is closed book. You may use one handwritten 3 5 card of notes.
Calculators are not allowed.
In order to receive credit,
Basic Vector Algebra
Before we start messing with vectors, we need to tell Maple to be able to handle them. At their core,
vectors are a kind of matrix, and manipulating them is essentially linear algebra, so we must type in (make
sure to capitalize where
Space Curves
Recall in class we made a vector-valued function representing the intersection between the two surfaces
x2 + y 2 = 4
z = x2
The function we obtained was
r(t) = 2 sin ti + 2 cos tj + 4 sin2 tk
Lets use Maple to plot the surfaces and the space
Line Integrals
This lab will show you a way you can evaluate line integrals in Maple. You will nd two kinds of line
integrals, one of a scalar eld integrated with respect to arc length, and one of a vector eld along a curve.
First, consider the integral
x
Vector Fields
Lets plot some vector elds!
with(plots);
First of all, lets look at the vector eld I plotted in class yesterday.
fieldplot([y,x],x=-2.2,y=-2.2);
Notice how the vectors nearest the origin are the smallest, but they get larger the further out
Multiple Integrals
Multiple integrals in Maple are ultimately done in the same way as single integrals, only like everything
else in vector calculus, theyre bigger and more complicated. So todays lab will largely be a review of
integrating with Maple.
Con
A preview of partial derivatives and tangent planes
Today were going to do a number of new things, but tie them together with some graphs like weve done
previously. First things rst, we need a couple of packages. Type in:
with(plots):
with(LinearAlgebra):
Maxima and Minima
Today we will classify some critical points and nd the maxima and minima of a function on a restricted
domain, as we will do in class tomorrow. This involves nding the zeros of the rst derivatives (the critical
points), then examining th