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, Sections R06 and R05
T.Olson, Spring 2009
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.
Course Information
Getting Help:
If you can't get your questions answered during the
"activity" part of class time, try these resources:
-
The Math Learning Center in Fisher 128
* Beginning ??? *
- Walk-in hours:
Sunday 7pm-9pm
M-Th 10am-5pm and 7-9pm
Fri. 10am-noon
- Regular appointments: Sign up -- it's free!
- Tami's office hours: Tu/Th 9-11am, and Fri 2-3pm
in Fisher 310
- Send email to trolson
(ask a specific question, or schedule an appointment
to meet with me.)
- Use your lab TA and fellow students
Study Help
Preparing for Tests
Labs
- Help for computing divergence and curl
(sections 20.1, 20.3)
can be found in sec20_1.nb.
- Integration help for the section 19.2 homework,
can be found in sec19_2.nb.
- Help in computing line integrals for secion 18.2
is in sec18_2.nb.
- 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.
- Homework help for the section 16.3 homework
(triple integrals),
can be found in sec16_3new.nb.
- Section 16.4:
The Mathematica commands Tami used to compute
integrals in polar coordinates
are in polar_integrate.nb.
- Homework help for the section 16.2 homework
(double integrals),
can be found in sec16_2new.nb.
- 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.)
Possibly useful study links
Calculator links:
(Not all links have been tested -- let me know if some aren't working.)
(And let me know which ones are useful!)
trolson@mtu.edu