Back to Vector Calculus for Engineers

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1,037 ratings

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282 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 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 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 subhasree b

•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 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 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 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 Arthur Z

•Feb 25, 2020

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

By ka

•Feb 16, 2020

Excellent course on the subject.

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 KHÔI Đ M

•Jul 8, 2021

This course covers all essential concept of partial, line and surface integral, gradient, divergence, curl, laplacian which are the useful mathematical tools for convert the abstraction of physics theory to nice, able to evaluated equations. Overall, the content of this course is more difficult than the general conception of matrix algebra and differential equation course , the formulas is complicated and its application is abstract and theoretical. It takes more time to digest these new knowledge! More challenging more attractive of the world of mathematics. Worth your time to enroll this course!

By Melani

•Nov 1, 2020

In this course I will remind myself of calculus 2 concepts according to the program of my university, however I realized that I did not know topics like Levi Cita and I will take knowledge that will serve not only in the field of calculus but in other areas such as mechanics of materials in said course I was even able to apply my knowledge of numerical methods to the subject of least squares, returning to the subject of calculus. I think I still need to improve my knowledge of Stokes and divergence since I consider they were heavy subjects.

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 Nafis F

•Aug 8, 2020

I cannot thank Professor Chasnov enough for teaching in such a nice way, providing the right amount of intuition and rigour that an engineering student requires. I really liked the course. It would've been nice if the solution to the homework problems were given in text format as many wouldn't like to go through the course text searching for it. Nevertheless, I found the course very very helpful when studied with a text and I will always be grateful to Professor Chasnov.

By Eduardo P

•Jul 12, 2021

I had previously taken an opencourseware course from MIT in Vector Calculus. I recently has taken this one as a refresh while taken a course in electromagnetism. As a refresher, it is VERY, VERY GOOD. Not only it refreshed my previous knowledge, but it has given me a deeper understanding of it. I do not know how useful it can be as a first course in Vector Calculus, since, as I have told, I had previous knowledge on the matter.

By CARLOS R A H

•Jan 10, 2021

Absolutely great course. It is very challenging and requires commitment and a lot of dedication, but it's perfectly organized and will definetely make you learn a lot. I took this before taking Calculus 3 at uni this semester because I was feeling a bit intimidated, but know I have a great overview of what's coming. Definetely looking forward for the 5 week version and the other courses by Dr. Chaznov.

By Frank O

•Dec 22, 2020

This is an excellent course in vector calculus and Jeff is an excellent instructor. I like the fact that it is condensed into 4 weeks (I believe it is usually taught as a full semester course at most colleges) such that it is not a big time commitment. The online textbook is also excellent and has the solutions to the problems worked out in case you get stuck. Overall I highly recommend this course.

By Bellam J B

•Aug 8, 2020

This course is well designed for engineers and very useful to students taking electromagnetic courses, to that matter any engineering course based on vector calculus. I took this course to gain some more knowledge on vector calculus to teach engineering students electromagnetic theory. As a physicist I was expecting more physical significance and explanation but however the objectives are fulfilled.

By Brendon L

•Jun 3, 2020

Professor Chasnov is a gifted lecturer with a gift for delivering intuitive and accessible explanations of some very abstract mathematical concepts. The course notes he provides are likewise quite excellent. One of my favorite features of this course is that it focuses on teaching you how to actually *do* problems in vector calculus. You'll learn a lot if you take and finish this course.

By Jorge L

•Jul 16, 2021

It is an outstanding course based on five weeks. It includes all basics you need to know to be involved in Vector Calculus. From Vectors, Operators, Differentiation, Integration (Line and Surface integrals), Curvilinear Coordinates, and Fundamental Theorems. Also, it provides a book with detailed information on each topic. So then, Jeffrey Chasnov thanks for this amazing journey.

By 173 N T 1

•Jun 24, 2020

This is a magnificent and top-notch course! The professor is very student-friendly and explains all the concepts in very good detail. Even difficult topics are made to look easy. The structure, organization, content and the flow of the course are very well-maintained and excellently planned. Overall, it is a course I would recommend to everyone trying to learn Vector Calculus.

By Arowosegbe D O

•Jun 25, 2020

The course topics were arranged accordingly to help students understand each of them completely using knowledge from previous topics and also serving as a sort of revision for previous topics. The lecture also had examples that made it easier to understand the topics and layout for the course. The questions were okay and reliable feedback after submission.

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