I just sent out an email with your final grade report including final exam grades, course averages,
and letter grades.
If you ever want to look over your final exam, please feel free to stop by my office. I tend to keep
them around for a year or more.
I hope you have a wonderful (what remains of the) summer! Most importantly, even though this class is
over, if you ever have any questions mathematical or otherwise, don't hesitate to stop by my office
or send me an email. I'd love to help if I can!
I don't plan to drop any quizzes, but I will drop the lowest homework.
This means that if you are at peace with your Homework 1-3 scores, you
can skip Homework #4 (.mw) (due Monday, August 7th).
I will replace a lowest test score with the final exam score - if it helps.
You may bring one page of notes - one side of a standard size piece of paper - to the final.
What to study? Our final covers Chapter 16 plus supplemental problems minus line integrals
with respect to arc length (i.e., 16.1). Also, we did not do "flux" type line integrals.
We did do "flux" surface integrals. You can ignore any flux line integral stuff.
Old final exams since Fall 2013 are good resources.
Even older finals contain relevant vector calculus problems, but also have irrelevant review
questions mixed in.
7/27
Don't forget that Homework #3 (.mw) is due next week
[Tuesday, August 1st]. I recommend getting that one done early. Not just because you
want to have plenty of time to study for Test #3, but also it should help you understand
triple integrals better!
Test #3 is Wednesday, August 2nd. It covers Chapter 15 as well as the handouts
on double Riemann sums and vector fields (I'll pass that one out soon).
I also recommend checking out my multiple integral Maple examples
which contain numerous examples of setting up triple integrals.
I will provide the change of coordinate formulas for rectangular to spherical coordinates:
• $x=\rho\cos(\theta)\sin(\varphi), y=\rho\sin(\theta)\sin(\varphi), z= \rho\cos(\varphi)$.
as well as the spherical coordinates Jacobian:
• $J = \rho^2\sin(\varphi)$.
and a double angle identity. If I give a center of mass or centroid problem, I will provide
formulas for mass and moments.
As usual, your best tool for studying is my old test. Here is our list of
relevant problems from Old Exams:
Spring 2012 up to Spring 2021
Spring 2021 Test #3: All of it except problem #3.
Test #3: all of it except...
Summer 2019 skip #1
Fall 2016 skip #1b
Spring 2016 skip #1b
Fall 2014 skip #1b & #1c
Fall 2013 skip #1b & #1c
Spring 2012 skip #7
Fall 2011
Test #3: 1-5
Spring 2011
Test #3: All of it except problem 3
Fall 2009
Test #3: All of it (includes a prob. dens. function problem)
Also, the Maple examples in Multiple Integrals [multiple_integrals.mw]
should be quite helpful for understanding the process of setting up triple integrals.
Don't forget that Homework #2 (.mw) is due next week
[Tuesday, July 25th].
Also, Test #2 is Wednesday, July 26th. Although we should finish its material
tomorrow. [So the stuff we cover early next week on integration will not be on Test #2.]
Reminders:
• Test #1 is Friday (July 14th).
• I plan to give you the same formulas as on the last few Test #1's.
• Homework #1 is due Monday (July 17th).
• We will tie up some loose end and review for our test tomorrow.
Test #1 covers the parts of sections 11.1, 11.2, 12.1-12.5, 13.1-13.5, & 16.1 we
discussed in class.
Our handout is worth checking out: Differential Geometry Summary (.pdf) [Source: (.tex)]
While old tests are a good resource for getting an idea of what kinds of things I like
to ask. Keep in mind that we switched textbooks several years ago so there are a few topics
that aren't as relevant and a few that are missing. For example, you won't find much
referencing torsion. Also, keep in mind that summer school tests are longer because
fall/spring tests are designed for 50min classes.
Studying old tests is helpful, but make sure you also look over your notes from class
and try lots of suggested homework problems.