MATH 202 MIDTERM 1
Please work out five of the given six problems and indicate which problem you
are omitting. Credit will be based on the steps that you show towards the final
answer. Show your work.
PROBLEM 1 Please answer the following true or false. I
Surface Integrals
Surface Integrals for Parametric Surfaces
In the last section, we learned how to find the surface area for parametric surfaces. We cut the
region in the uv-plane into tiny rectangles and added up the area of the corresponding tiny
parall
Parametric Surfaces
Definition of a Parametric Surface
We have now seen many kinds of functions. When we talked about parametric curves, we
defined them as functions from R to R2 (plane curves) or R to R3 (space curves). Because each
of these has its doma
Math 202 Practice Final
Please work out each of the given problems. Credit will be based on the steps that you
show towards the final answer. Show your Work
Problem 1 Please answer the following true or false. If false, explain why or provide a counter
ex
Stokes' Theorem
Stokes' Theorem
The divergence theorem is used to find a surface integral over a closed surface and Green's
theorem is use to find a line integral that encloses a surface (region) in the xy-plane. The
theorem of the day, Stokes' theorem re
Math 202 Practice Midterm 3
Please work out each of the given problems. Credit will be based on the steps that you show
towards the final answer. Show your work.
Problem 1 Please answer the following true or false. If false, explain why or provide a count
MATH 202 PRACTICE MIDTERM 2
Please work out each of the given problems. Credit will be based on the steps that you
show towards the final answer. Show your work.
PROBLEM 1 Please answer the following true or false. If false, explain why or provide a
count
MATH 202
VECTOR CALCULUS
Monday and Wednesday 1:30 to 2:35
Tuesday and Thursday 1:00 to 2:05
Rooms Mondays: G1 Tuesdays, Wednesdays, and Thursdays G2A
Instructor Larry Green
Phone Number Office: 541-4660 Extension 341
Internet
e-mail:[email protected]
WWW:
Green's Theorem
A Little Topology
Before stating the big theorem of the day, we first need to present a few topological ideas.
Consider a closed curve C in R2 defined by
r(t) = x(t)i + y(t)j
a < t <b
We say C is simple if it does not intersect itself. A c
Divergence Theorem
The Divergence Theorem
When we looked at Greens Theorem, we saw that there was a relationship between a region and
the curve that encloses it. This gave us the relationship between the line integral and the double
integral. Moving to th
Line Integrals
Definition of a Line Integral
By this time you should be used to the construction of an integral. We break a geometrical figure
into tiny pieces, multiply the size of the piece by the function value on that piece and add up all
the products
Vector Fields
Definition and Examples of Vector Fields
We have now seen many types of functions. They are characterized by the domain and the
range. Below is a list of some of the functions that we have encountered so far.
Domain
R
R
R2
R
Range
R
R2
R
Vec
Conservative Vector Fields and Independence of Path
The Fundamental Theorem of Line Integrals
Consider the force field representing the wind shown below
You are a pilot attempting to minimize the work your engines need to do. Does it matter which
path you