This is essentially the third semester calculus course commonly taught as a 4 hour course in most US universities. It covers, vectors, 3D coordinate geometry, Calculus of Paths, Partial Derivatives, Multivariate Integration, Line and Surface Integrals, Green's, Stokes' and the Divergence Theorem. A more complete list of topics is evident from browsing the Course Planner or the list of lectures below. Note, the videos given in the playlist below are somewhat minimalistic. I really think if you are self-studying you might do better to use one of my previous years of Calculus III from my Math 231 course at Liberty University. That course had 5 days of lecture a week and so much more time to unwrap the idea. See for example:

and you can find much more at my Math 231 course website.

To be honest, when teaching online, it is really hard to add quality. In contrast, the real time interaction with students in Math 231 just leads to better quality overall in my estimation. Online is just not as good, it is just a reality we should admit.

The Syllabus and Course Planner

I wrote a text of sorts for this course based on my previous course notes from Math 231. I had intended to add a chapter on differential forms, but sadly I did not find time this semester.

If I am using printed notes they are fairly close to the notes above, but usually the page numbers differ slightly since the 2020 notes are an edit over those which I had printed on hand to make videos. I usually make a comment at the beginning of each lecture where I use such notes.

- Lectures 1,2 and 3: Vectors, Dot and Cross Products, Planes
- Lectures 4 and 5: Curves and Surfaces
- Lecture 6: Curvelinear Coordinates
- Lecture 7: Calculus of Paths
- Lecture 9: Geometry of Curves
- Lecture 10: Physics of Motion
- Lecture 11: Integral of function along a curve.
- Lecture 13: Directional Derivatives
- Lecture 14: level curves and gradients
- Lecture 15: Partial Derivatives
- Lecture 16: General Derivative, Jacobian Matrix
- Lecture 17: Chain Rules
- Lecture 18: Tangent Spaces
- Lecture 19: Differentials and Constrained Differentiation
- Lecture 20:
- Lecture 21: Lagrange Multipliers
- Lecture : Multivariate Taylor Expansions
- Lecture 23: 2nd Derivative Test
- Lecture 24: Closed Set Test
- Lecture 25: Double Integrals
- Lecture 26: Cartesian Triple Integrals
- Lecture 27a: Changing Variables for Multivariate Integration
- Lecture 27b: Changing Variables for Multivariate Integration
- Lecture 28: Geometry and Algebra of Volume Elements
- Lecture 29: Vector Fields
- Lecture 30: Gradient, Divergence and Curl
- Lecture 31: Line Integrals
- Lecture 32: Conservative Vector Fields
- Lecture 33: Green's Theorem
- Lecture 34: Deformation Theorem
- Lecture 35: Surface Integrals
- Lecture 36: Stokes' Theorm
- Lecture 37: Divergence Theorem
- I also asked the students to watch a couple lectures on Differential Forms from Math 231 of past years (they're on the playlist)

Note: these were recycled from Math 231 in the Fall 2017 Semester.

- Mission 1
- Mission 1 Solution
- Mission 2
- Mission 2 Solution
- Mission 3
- Mission 3 Solution
- Mission 4
- Mission 4 Solution
- Mission 5
- Mission 5 Solution
- Mission 6
- Mission 6 Solution
- Mission 7
- Mission 7 Solution
- Mission 8
- Mission 8 Solution

- Test 1
- Solution of Test 1
- Test 2
- Solution of Test 2
- Test 3
- Part A Solution of Test 3
- Part B Solution of Test 3

Final Exam: Back to my Home

Last Modified: 12-17-2020