Back to Vector Calculus for Engineers

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1,125 ratings

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311 reviews

Vector Calculus for Engineers covers both basic theory and applications. In the first week we learn about scalar and vector fields, in the second week about differentiating fields, in the third week about multidimensional integration and curvilinear coordinate systems. The fourth week covers line and surface integrals, and the fifth week covers the fundamental theorems of vector calculus, including the gradient theorem, the divergence theorem and Stokes’ theorem. These theorems are needed in core engineering subjects such as Electromagnetism and Fluid Mechanics.
Instead of Vector Calculus, some universities might call this course Multivariable or Multivariate Calculus or Calculus 3. Two semesters of single variable calculus (differentiation and integration) are a prerequisite.
The course is organized into 53 short lecture videos, with a few problems to solve following each video. And after each substantial topic, there is a short practice quiz. Solutions to the problems and practice quizzes can be found in instructor-provided lecture notes. There are a total of five weeks to the course, and at the end of each week there is an assessed quiz.
Download the lecture notes:
http://www.math.ust.hk/~machas/vector-calculus-for-engineers.pdf
Watch the promotional video:
https://youtu.be/qUseabHb6Vk...

DK

May 22, 2020

i have completed Three courses of Professor Jeffrey. I'm so happy that i learnt a lot from him. Thanks to our professor Jeffrey and thanks to The Hong Kong University of Science and Technology.

BB

May 14, 2021

Professor Chasnov is a great instructor. I strongly recommend this course (and others from his). Thank you so much for making such great quality content available for everyone no matter where.

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By Chris H

•Nov 5, 2021

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

By Stephan L

•Feb 17, 2020

Well designed and implemented. Lecturer presents the material well and the notes are a model of what MOOC course notes should be like. Lot's of practice problems with sample solutions to work on which for a technical course like this is the only way you'll learn the material. My thanks to Professor Chasnov for putting in the work to create this.

By Ravikumar B

•May 4, 2020

This course is very well organized and well explained. I am very much thankful to Prof Jeffrey R. Chasnov for his fruitful videos which help us to update our knowledge in this area.

By Smita N M

•May 24, 2020

The course was very systematically designed. It gave us practice problems once the concept is covered. But 4th module was a bit tough. The professor taught it excellently.

By Vaishnavi A

•May 13, 2020

This course is very helpful . The instructor Sir were very clear in their explanations . The knowledge he gave is very useful . Overall course design is also great.

By Hrishabh S

•May 25, 2020

Really good instructor. Explains every concept patiently and clearly in a lucid language. The course really strengthened my calculus foundations. Loved it!

By BALIJA S S

•Jan 30, 2020

teaching is very extraordinary. I wish to have some more assignments, but it is quite well.

By Allaev S

•Jun 4, 2021

Professor Chasnov, Thank you very much for such awesome courses. You helped my career very much! I changed the direction of my career a little bit (from construction to the engineering seismology), but new area is related to vectors, matrices and differential equations and I didn't expected that I will need all this math knowledge, but after finishing all your math courses, my understanding of problems become very clear. It took around 3 and a half month to finish your Matrix, Vector and Partial derivative courses. Now I am going to start your Matlab Course, which I think will be also very beneficial! Regarding Vector Calculus course, last 2 Reading problems regarding Navi-Stokes and Maxwell equation were too tough to solve, but all other problems and exams were really good explained.

For future learners, I would like to clarify that this course is only a base knowledge and some of areas are explained too promptly. To get solid knowledge, you should solve additional problems from other sources and also use some other books as well during your studies. But I didn't find any better courses related to Matrices, Vectors and Differential equations, than the ones that is being taught by Professor Chasnov.

By George G

•Jul 15, 2020

Some parts were more difficult. The introduction to Levi-Civita Tensor and Kronecker delta I found to be a completely new area and took a bit of work to get a hold on it. I thought the practice exercises were very useful and would like to see more of them. The course was quite packed with material and one had to be prepared to devote time to it. The chance to successfully work out a puzzle or two was an attraction to me. I found the use of cylindrical co-ordinates etc quite tricky and would have appreciated more on the basic notions, maybe via practice problems. Some of the answers for the w4 assessment came from the practice exercises and this made it a bit trivial. Overall I got to like the material but it did need perseverance. I would have like to have see more discussions about tricky bits on the forum but it not seem to happen. I suspect the time for the course is maybe a bit short. Thanks for the chance to explore and puzzle out some new concepts. Keep up the good work.

By SMJ

•Jun 15, 2020

In my humble opinion every engineer should take this course. The instructor is highly organized and presents the concepts in a facile manner. I have become a fan of his creative teaching methodology. I hope he keeps benefiting all by offering courses in some other useful topics like partial differential equations, integral transforms, complex variables, tensors, ... Thank you tons Professor Chasnov. I wish the BEST comes your way for such dedicated service to the world community! God bless you.

By David C

•Aug 7, 2021

This course is an excellent exploration of vector calculus. The educator presented the material in sufficient detail with examples to enhance the learning experience. Practice through problems and quizzes allowed the learner to gain understanding of the topics covered. I would recommend this course to those students interested in exploring vector calculus and/or people interested in refreshing their math skills.

By Rich G

•Sep 28, 2021

Excellent!. This is a really heavy course that covers a broad range of material in a very short time. If you are already proficient with calculus an vectors, it's a good review. If you are knew to calculus and vectors, it's a lot of time and work, but definitely worth it.

By Gilberto U

•Sep 15, 2021

I am a retired engineering professor reviewing my knowledge of mathematics, and I found this course excellent for that purpose. The instructor was direct and to the point, yet he covered all interesting subject matters on vector calculus. I really enjoyed this course.

By Ian B

•Jan 24, 2020

Jeffrey Chasnov has a good command of the subject and is a good communicator. The course is well laid out and his PDF textbook is a great resource for the course and will be useful to the student for future work in mathematics and the sciences.

By Gregg R

•Jan 5, 2021

Great course, with challenging but motivating problems and explanations. I had to rework the problems by myself, and by the end of the course, I could see everything come together

By Sree K

•Jun 26, 2020

I understood many useful concepts in this course, along with the applications was great piece !

Feels like filled with super power of calculus after completing this course ...

By V V V S S P S S

•Apr 15, 2020

This material is very useful for our career, I liked gauss divergence and stokes theorems and applications.

By Dave M

•Aug 17, 2020

Had to watch youtube videos to brush up on some of the stuff, but in general excellent review

By Jose I S

•Sep 29, 2021

Great review of Vector Calculus!!! Professor Jeff Chasnov explantions a extremely clear!!!

By Arthur Z

•Feb 25, 2020

Very high-quality instruction and documentation from a very talented instructor.

By Deleted A

•Jun 26, 2020

this is the fundemental for engineering students

By Sharmila A K

•Jul 10, 2020

A very good course for engineering stidents.

By G C

•Sep 13, 2020

A well delivered course with applications !

By BECOA140_Sumedh J

•Apr 15, 2020

Nice, starter course on vector calculus.

By ka

•Feb 16, 2020

Excellent course on the subject.

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