Math 2130 (Summer 2025) Homepage

News & Announcements

8/06
I just sent out an email with your final grade report.

If want to look over your final exam, please feel free to stop by my office. I usually keep them around for at least a couple of years.

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!

8/01
Reminders:
• The Final Exam is Tuesday (August 5th).
• Our last quiz is Monday. It covers 6.2, 6.3, & 6.5.
   [In particular, the quiz covers work type line ints., conservative vector fields/fund. thm.
    of line ints., & curl/divergence.]
Homework #4 (.mw) is due Monday (August 4th) at 1pm.

Grading/Final Exam Notes:
  • 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.
  • 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 6 plus supplemental problems minus line integrals with respect to arc length (i.e., half of 6.2). 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.

Schedule for last classes:
  • Friday (8/1): Discuss surface integrals, orientation, flux integrals,
                       & Stokes/divergence theorems. [Finish 6.6 and cover 6.7 & 6.8]
  • Monday (8/4): Questions then last quiz. Then finish reviewing for the final.
                       Homework #4 is due no later than 1pm.
  • Tuesday (8/5): Final Exam 8am-10:10ish.

7/29
Upcoming Final Handouts:
Divergence, Curl, and Forms [Source: (.tex)]
• Supplemental Vector Calculus Problems [Source: (.tex)]
The Big Theorems [Source: (.tex)]
Verify Stokes' Example [Source: (.tex)]

Lost Supplemental Line Integral Notes

7/25
Reminders:
Test #3 is Wednesday (July 30th).
• I plan to give you the same formulas as on the last few Test #3's.
Homework #3 (.mw) is due Tuesday (July 29th).

As mentioned before, I strongly recommend getting Homework #3 done early. Not just because you want to have plenty of time to study for Test #3, but also because it should help you understand triple integrals better!

Test #3 will cover Chapter 5 plus sections 2.7 & 6.1 as well as the handouts on double Riemann sums and vector fields (we'll discuss the vector field stuff on Monday).

Relevant handouts: Example Handouts: 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
    • Test #3: all of it except...
      • Spring 2021 skip #3
      • 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)
    • Final Exam: 3 (a prob. den. function problem)
  • Fall 2007
    • Exam #2: 3-6
  • Spring 2007
    • Exam #2: 3,4,6,8
    • Final Exam: 5-7
  • Spring 2006
    • Exam #2: 1-4
  • Fall 2005
    • Exam #2: 4-7
7/24
Reminder:
Homework #3 (.mw) is due Tuesday (July 29th).

Upcoming Handouts:
Spherical Cap Example [Maple: (.mw)]
• Also, the Maple examples in Multiple Integrals [multiple_integrals.mw]
    should be quite helpful for understanding the process of setting up triple integrals.
Examples of centroids handout [Source: (.tex)]
Vector Fields [Source: (.tex)]

7/21
Handouts from today:
• Double Riemann Sums Supplemental Homework [Source: (.tex)]
Triple Integral Example [Maple: (.mw)]
Triple Integral Example [Maple: (.mw)]

Reminders:
Test #2 is Wednesday (July 23rd).
• I plan to give you the same formulas as on the last few Test #2's.
Homework #2 (.mw) is due Tuesday (July 22nd).
Homework #3 (.mw) is due Tuesday (July 29th).

Test #2 will cover Sections 4.1-4.8 (& 2.6) as well as our handouts on...
Quadratic Approximations [Answers (.mw) or (.html)]
Differentiability [Source: (.tex)]

For the most part, all Test #2's are relevant except that some contain a problem on Riemann sums - these can be skipped for now.

Relevant old tests/test problems:
  • Spring 2011 up to Spring 2021
    • Test #2: all of it except...
      • Summer 2016 skip #2
      • Spring 2012 skip #7
      • Fall 2011 skip #10 (both sections)
  • Fall 2009
    • Test #2 Section 101: 2,3,4,5,7,8
    • Test #2 Section 102: 2,3,4,5,6b,7,8
  • Fall 2007
    • Exam #1: 6,7,8
    • Exam #2: 1,2
  • Spring 2007
    • Exam #1: 1,4,6,8,9
    • Exam #2: 1,5
    • Sample Final: 3,4
  • Spring 2006
    • Exam #1: 4,5,6,7
  • Fall 2005
    • Exam #1: 1,3,4,5,8
    • Exam #2: 2,3

7/18
Supplement (as we discuss the 2nd derivative test):
Taylor Polynomials [Source: (.tex)] and accompanying Taylor Polynomials Sage demo.

7/14
Homework #1 (.mw) is due today tomorrow.
   [Found a mistake - it's fixed - we'll extend the due date a day. My bad!]
Homework #2 (.mw) is due Tuesday, July 22nd.

Links to upcoming handouts:
7/09
Handout:
Differential Geometry Summary [Source: (.tex)]

Reminders:
Test #1 is Friday (July 11th).
• I plan to give you the same formulas as on the last few Test #1's.
Homework #1 (.mw) is due Monday (July 14th).

Test #1 covers the parts of sections 1.1, 1.2, 2.1-2.5, 3.1-3.4, & 6.2 we discussed in class.
Since we have been running a bit behind and didn't get in a full discussion about torsion, you may skip problems about 'torsion'. I plan to discuss line integrals with respect to arc length (this is part of section 6.2) tomorrow before review. I may ask you to set up such an integral, but I won't ask a corresponding center of mass / centroid question.

Old tests can be found here.

Studying old tests is helpful, but make sure you also look over your notes from class and try lots of suggested homework problems.

Relevant old tests/test problems:
  • Spring 2012 up to Spring 2021
    • Test #1: all of it.
  • Fall 2011
    • Test #1: all of it.
    • Test #3: 6
  • Spring 2011
    • Test #1: all of it.
    • Final Exam: 1ab, 2, 5
  • Fall 2009
    • Test #1 Section 101: 1, 2, 3a, 3c, 5b, 6
    • Test #1 Section 102: 1, 2, 3, 5, 7b, 7c, 8
    • Test #2 Sections 101 & 102: 1
    • Final Exam Sections 101 & 102: 1, 4
  • Rutgers Spring 2007
    • Exam #1: 2, 3, 5, 7
    • Exam #2: 2
    • Sample Final Exam: 1, 2
  • Rutgers Fall 2005
    • Exam #1: 2, 6, 7, 9
    • Exam #2: 9
  • [Honors Class] Rutgers Fall 2007
    • Exam #1: 1, 2, 3, 4, 5a
    • Exam #2: 7
  • [Honors Class] Rutgers Spring 2006
    • Exam #1: 1, 2, 3a, 3b, 6a
    • Exam #2: 8

7/07
Here's a Maple Summary Sheet [Source: (.tex)] and a Introduction to Maple (.mw) worksheet.

Don't forget that Homework #1 (.mw) is due Monday, July 14th.


6/18
Updates! Syllabus, tentative schedule, & suggested homework pages posted.

Note: We just switched textbooks (to OpenStax Calculus), so the schedule is possible more tentative than in the past. Also, I have yet to pick out suggested homework problems.

Maple homework assignments
Homework #1 (.mw) is due Monday, July 14th.
Homework #2 (.mw) is due Tuesday, July 22nd.
Homework #3 (.mw) is due Tuesday, July 29th.
Homework #4 (.mw) is due Monday, August 4th.

I have many many examples of how to use Maple on my Maple examples page.
We will have an introduction to Maple before the first assignment is due.

To do: Update homework.

1/01
Summer 2025 Session 2 MAT 2130 (Calculus III)
meets MTWRF 8:00am-10:10pm in Walker Hall 314.
Syllabus, tenative schedule, etc. to be posted this upcoming summer.

Q: Can I take this online?
A: Mostly, but not entirely. Please contact me, cookwj@appstate.edu, for further information.