Vector Calculus for Engineers

Although I earned a BS degree in chemical engineering in 1999 and have taken multivariable calculus, Professor Jeffrey Chasnov’s Vector Calculus for Engineers 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 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

A great refresher course if you already know vector calculus and would like to take a cursory glance to brush up the concepts. I didn't have the in-depth knowledge of the topic but tackling it on your own can at first seem daunting. It had been something of a personal challenge for me. This course seemed to offer a practical grasp of the topics in four weeks. I figured if I could manage this, I will be able to gather enough courage to independently study the topic in more detail. Thanks to the incredible instructor, Professor Chasnov, the material didn't seem too hard. But I should mention that I am a physics major and I was already comfortable with working with vectors and had a good enough grasp on Calculus 2. My only complaint was with problems in lecture 41 which I personally thought could have done with an additional video on how to apply the theorems to Navier Stokes equation. I think I was looking a bit more information for the physical meaning behind the problem and how the theorems exactly help us. Something you can find out online... but that would require putting in additional hours, if you are up for it. I certainly had to work a lot more than what the course suggests is the time required to complete a given week.

All in all, I would definitely recommend this course to anyone who wants to get a working understanding of using multivariable calculus.

I can only deliver a mixed review. The course presents a generous amount of material, and all the basics are covered, but the presentation, especially in the final week, is perfunctory at best, grinding through derivations and leaving many steps for the student simply to "look up". Therefore, I recommend the course only as a review for anyone who already knows the material; trying to learn the details for the first time from this rushed and compressed presentation is likely to be frustrating, if not discouraging.

This is a likely related to Coursera's pressure to cram course contents into 4-week lumps as much as of anything else. That said, the lectures are well-organized trips through the standard derivations of results in Cartesian and spherical coordinate systems, but the motivation of the utility of scalar and vector products as projections and volumes is left behind once it has been given that perfunctory treatment in the early lectures. The course makes no attempt to get beyond dimension that can treated with analytic geometry of planes and 3-space; we do see the fluxes on cube faces and on the boundary of spheres; sadly, these treatments are too rushed. Vector calculus is a rich and beautiful subject, but don't come here to try to learn it for the first time.

This is an axcellent course with illustrative examples and relevant calculation algorythms, it is a complex introduction to vector calculus, however, it is not for the faint of heart. Unless you have a very solid foundation in mathematics (unlike me), be prepared to seek out supplementary materials and self-educate. This course is best taken after matrix algebra and differential equation courses of the same lecturer. It helps to already be familiar with Kronicker delta and Levi-Civita symbol, their identities and, most importantly, the rules on how to contract them ( there is an excellent video on YouTube from PHYSICS ⚛ universaldenker․org). It helps to do as many exercxises as possible on the theorems from last week, especially the Stokes' Theorem. This is a well-rounded introduction to the topic, be prepared to work with spherical coordinates!