Professor Leonard – Calculus 3
14.7: Triple Integrals Over Regions with Cylindrical or Spherical Coordinates
14. 8: How to Change Variables in Multiple Integrals (Using the Jacobian)
15.1: Introduction to Vector Fields (and what makes them Conservative)
15.2: How to Find Divergence and Curl of Vector Fields
15.3: How to Compute Line Integrals (Over Non-Conservative V.Fields)
15.4 Line Integrals on Conservative Vector Fields (Independence of Path)
Thomas Textbook
15.7 Triple Integrals in Cylindrical & Spherical Coordinates
16.1 Line Integrals
16.2 Vector Fields & Line Integrals: Work, Circulation, & Flux
16.3 Path Independence, Conservative Fields, & Potential Functions
Time flies when you’re having fun. I do enjoy Calculus, and I do enjoy Professor Leonard. But I’ve been working on Calc for much of the last 1.5 years. I could see the light at the end of the tunnel, and I was psyched. So, by the looks of it I knocked out a monumental load of work in 2 or so weeks. While I’m not too modest to pat myself on the back every now and then, it’s not as impressive as it might look.
Firstly, there were a lot of lectures, many hours of lectures, that moved through the final subjects. In my opinion, it was all basically an examination of different flavors of double and triple integrals. There would be more than a single lecture watched before exercises would be tackled. Thus, the long list of lectures. That wore thin, especially given how long I’ve been studying Calc, and given how ready I was to move on to the next subject.
Although I’m not an Engineering or Physics major, I can clearly see how the specific applications of integration that I studied would be very pertinent to engineering and physics. Seeing that was cool. Additionally, I got to put my toe in the water of Vector Calculus, the logical progression/hybrid of Calculus and Linear Algebra. So much to study, so little time.
I’m not going to get into any of the weeds and explain the math I studied. I’d rather reflect on the completion of the course and the completion of the Calc 1/2/3 sequence.
Calculus has changed my life. For a very long time I saw Calculus as a reminder of my scholarly negligence, of the fact that I lost my way many years ago. That I fucked up. And I always felt that Calculus was a subject of such importance that I was cheating myself but not having learned it. So, I finally righted that wrong.
This sequence marks the start of my commitment to re-education, to changing my life, to self-realization through learning. I made a choice, and then have stuck with it. Nearly every day for the past 20 months I’ve studied math. And I’m seeing new opportunities and believing that I can experience life in ways that I’d given up believing were possible.
My mind feels more alert, quicker, stronger, and more curious. Learning something new like Calculus has opened me up to new fields of thought, to a broadening path forward, and a greater appreciation for the past. And I’ve taken up a passion for Bach. Wow, Bach – my partner in this journey. Classical music overall, but particularly Bach. That wouldn’t have been possible were it not for Calculus.
I am grateful for the great minds who discovered and explored this math before me. I’m grateful for the wonderful teachers. Professor Leonard – I’m very grateful. I’m grateful for the unique work I have with a wonderful organization in China that basically allows me to dedicate my days to study and still stay afloat. I’m grateful for Bach and the brilliant musicians who play him for me.
And I’m grateful for MIT, for making its OpenCourseWare available. For my path continues now to Probabilistic Systems Analysis and Applied Probability. I’ll see you there.