This is an archived version of a class I taught at Kennesaw State University. For now, you can still find my course webpage on KSU's website, but I expect it to be taken down eventually. I think these are pretty okay, so I've decided to archive them on my personal webpage. If you spot any mistakes, please let me know.
I should probably explain what "Calculus IV" even means, to readers not familiar with the KSU calculus sequence. As I taught it, this is a course that starts from some basic knowledge of double and triple integrals and builds up the theory of line and surface integrals of scalar and vector fields, as well as the Stokes-type theorems about such integrals.
Most universities fit this into a single semester with the course that introduces multivariable calculus. I think that most students could benefit from more time with this material, but it's true that the paragraph above makes up slightly less than a semester's worth of content. Different instructors had different approaches to filling out the course; my choice was to sprinkle in an introduction to differential forms. In these notes, the content on differential forms can be skipped without too much confusion, but it may be of interest to someone who plans to eventually get into differential geometry.
D2L will be used to submit assignments (these will be posted both here and on D2L, for convenience) and to view grades. The syllabus will also be posted there.
During the scheduled office hours, you should feel free to show up with no notice if you have questions of any kind.
If you cannot make the scheduled office hours, begin by emailing me; if your questions are easy to answer by email, I will do that, and if not, we can find another time to meet. (Allow some time for me to check my email.).
There will be eight homework assignments, two midterm exams, and one final exam; the dates are marked below.
I will post the homework assignments here and on D2L; they are always due on Friday at 11:59pm, via D2L.
Exams will be given in person during our ordinary 75-minute class period.
A number like HHW 12.3 indicates material covered in Chapter 12, section 3 of the textbook. We are going through some difficult material slowly and carefully here, so every note like this applies to a set of 2-3 lectures at once.
The schedule below has links to lecture notes for every day of the semester, so that you can read ahead if you like. These will be updated as we go, and I will keep a log of the changes I make.
Note 9/27: Due to the day we missed on account of weather, we'll have one fewer lecture, and I've decided to skip lecture 15 (containing further examples and applications of Green's theorem) to fit in the rest of the material. To make life easier on my end, I will not change the numbers of lectures 16-28. If you are interested in the missed content, you can still read it here.
| Date | Topic covered | Textbook section | Homework |
| Tue 8/13 | Cylindrical integrals Lecture notes |
HHW 15.7 | |
| Thu 8/15 | Spherical integrals Lecture notes |
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| Tue 8/20 | Substitution in 2D Lecture notes |
HHW 15.8 | |
| Thu 8/22 | Substitution in 3D Lecture notes |
HW 1 due Friday | |
| Tue 8/27 | Parametric curves Lecture notes |
HHW 16.1 | |
| Thu 8/29 | Scalar line integrals Lecture notes |
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| Tue 9/3 | Vector fields Lecture notes |
HHW 16.2 | |
| Thu 9/5 | Vector line integrals Lecture notes |
HW 2 due Friday | |
| Tue 9/10 | Flux integrals Lecture notes |
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| Thu 9/12 | Path independence Lecture notes |
HHW 16.3 | |
| Tue 9/17 | Conservative or not? Lecture notes |
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| Thu 9/19 | Trouble with domains Lecture notes |
HW 3 due Friday | |
| Tue 9/24 | Exam 1 | ||
| Thu 9/26 | Canceled due to weather | ||
| Tue 10/1 | 2D curl and divergence Lecture notes |
HHW 16.4 | |
| Thu 10/3 | Green's theorem Lecture notes |
HW 4 due Friday | |
| Tue 10/8 | Parameterizing surfaces Lecture notes |
HHW 16.5 | |
| Thu 10/10 | Surface area Lecture notes |
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| Tue 10/15 | Area of implicit surfaces Lecture notes |
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| Thu 10/17 | Scalar surface integrals Lecture notes |
HHW 16.6 | HW 5 due Friday |
| Tue 10/22 | Vector surface integrals Lecture notes |
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| Thu 10/24 | More surface integrals Lecture notes |
HW 6 due Friday | |
| Tue 10/29 | Exam 2 | ||
| Thu 10/31 | Curl vector field Lecture notes |
HHW 16.7 | |
| Tue 11/5 | Intro to Stokes' theorem Lecture notes |
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| Thu 11/7 | Stokes' theorem examples Lecture notes |
HW 7 due Friday | |
| Tue 11/12 | Conservative fields Lecture notes |
HHW 16.8 | |
| Thu 11/14 | Divergence theorem Lecture notes |
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| Tue 11/19 | Divergence and curl Lecture notes |
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| Thu 11/21 | Unifying the theorems Lecture notes |
HW 8 due Friday | |
| Tue 12/3 | Final exam (1:00pm to 3:00pm) | ||