Everything here is subject to revision.
Changes will be announced in class and/or by email.
Please report any mistakes to
trolson@mtu.edu
Multivariable Calculus
MA3160, Section R10
T.Olson, Spring 2011
Link to the microscope :
A vector-field microscope
to visualize derivatives,
including a flow program that lets you see how polygons distort
under the flow of a vector field.
Divergence is seen as the
increase in area, while curl is seen as the rotation.
See handout for directions on using the microscope to
view divergence and curl.
Mathematical Sciences Instruction Page
Sign up for a MathLab section during the first week of class.
You can do this from your "home" computer or you can go to Fisher 331
and ask a Lab Consultant for help starting Thursday.
Calc.III MathLab Coordinator Questions about the labs (due dates, grades, registration, etc.)
should be addressed to the MathLab Calc.III coordinator,
Bill Laffin (calc3cc@mtu.edu).
For Chapter 17:
w17_1.nb contains
Mathematica commands which can be used to
generate parametric plots .
Download this to your account and then run it
locally using Mathematica. (old version)
Help in drawing parametric curves
is in sec4_8.nb. (old version)
Section 16.5 worksheet help:
Use sec16_5.nb to view the
3-D regions on integration on the section 16.5 worksheet.
Section 16.4:
The Mathematica commands Tami used to compute
integrals in polar coordinates
are in polar_integrate.nb.
(old version)
Homework help for the section 16.2 homework
(double integrals),
can be found in sec16_2new.nb.
(old version)
To check your answers to section 15.3 homework
(Lagrange multipliers),
use sec15_3.nb.
Use sec15_1.nb
to check your answers to section 15.1 homework.
A Mathematica notebook,
w15_1.nb, contains
Mathematica commands which can be used to
generate graphs for the Play-Doh worksheet (section 15.1).
It also has a cute little animation that shows how to deform
a Play-Doh bowl into a graph for problem 15.
To download this to your account, hold the Shift key while
you click the left mouse button.
Use partials.nb
to generate the graphics Tami used for
illustrating partial derivatives and
their relationship to cross-sections
(section 14.1).
Use sec12_5.nb
to generate the graphics Tami used for
graphing slices of functions of three variables (section 12.5).
Use ans12_3.nb
to generate pictures illustrating the answers to the
contours worksheet.
A Mathematica notebook,
graphs.nb, contains
Mathematica commands which can be used to
generate 3-D graphs of functions of two variables
(i.e., z=f(x,y)) and equations in 3 variables.
Download this to your account, then run it locally
using Mathematica.
This introduction to 3-D graphs is
a Mathematica notebook with simple instructions for
making all kinds of graphs which will be useful in this class.
Possibly useful calculus links
(These haven't been updated in a long time.)
(I count on my students to tell me if the links aren't working or if
there's a new link I should include.)
Practice quizzes from Terence Gaffney at Northeastern University
Visualize divergence and curl. See how a rectangle flows in a vector field ... divergence is the change in area and curl is the rotation
A vector-field microscope to visualize derivatives, along with a ``rectangle flow'' similar
to the previous link (but here you can enter any vector field you want!)
