Although I earned a BS degree in chemical engineering in 1999 and have taken multivariable calculus, Professor Jeffrey Chasnov’s Vector Calculus for Engineers[1] was a great challenging learning process.
I found the time needed to complete the course could be long or short. Initially, I started out as I do with all my courses and tried to solve all problems without looking at the solutions. Since the course is compressed, much is covered in a short period. There were new topics that I had to learn, and I was rusty on other topics. So, week 3 sent me a message. Don’t be afraid to learn from the solutions to meet the deadlines. This is very important for week 4, which was the most challenging week for me.
When learning from the solutions, one MUST figure out the missing steps to ensure competence on the weekly assessments. This takes knowledge of physics and mathematics for some problems, and just mathematics for other problems. In engineering, we were taught to always draw our system. I found this to be true in this course as well. At times, one cannot just memorize the equations given, and there are many great equations and tricks given, but one must take the extra step to figure out how the equations were derived. As a simple example, the last problem in the notes[1a] integrates the circle over dr and one must remember that s = r(theta) and ds = r d(theta) to get the problem fully. This is knowledge from trigonometry and basic calculus, and Professor Chasnov expects one to use known physics and mathematical relationships to solve problems. Obviously, this includes material learned in Vector Calculus for Engineers.
I found the time required to complete problems was longer than suggested, and I put in 6 hours a day on some days, but my average was near 4 hours a day. Most weekly assessments took me much longer than 45 minutes to complete. Week 4 took me 4.5 hours but note that I shot for 100% on each assessment on first attempt. Also, I have an illness that causes shaky hands so my writing can be bad. This is a huge factor in later weeks where much algebra is needed to solve the problems. Week 5 had excellent applications.
Overall, Professor Jeffrey Chasnov put together a very useful course for engineers, physicists, and people who want to learn vector calculus. He does expect familiarity with mathematics and physics, and I am happy I had refreshed my algebra, trigonometry, single variable calculus, and physics using Coursera. I also used MITx and MIT OCW. I now have more confidence going into my study of computational fluid dynamics (CFD) and fluid dynamics[2]
I earned an overall 96% in the 5 week course which means I solved 48 of the 50 weekly assessments problems. In college, I received similar grades in my calculus courses. I found that the course was challenging and on par with MITx calculus and physics courses and University of Pennsylvania Calculus Coursera courses.
References:
[1] https://www.coursera.org/learn/vector-calculus-engineers
[1a] Chasnov, Jeffrey R. Vector Calculus for Engineers: Lecture Notes for coursera. URL: https://www.math.hkust.edu.hk/~machas/vector-calculus-for-engineers.pdf
[2] Warsi, Z.U.A.. Fluid Dynamics (p. 2). Taylor and Francis CRC ebook account. Kindle Edition. Google Book: https://lnkd.in/gha_C-un
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