Starting from the very basic, the course takes to the advanced concepts on Vector calculus. I took this course as a refresher and found it very helpful. The large number of reading problems helped strengthen the understanding. For some topics, when the professor mentions something but doesn't go at length to explain, some secondary complementary resources could be useful.

This is the best and only good course I have found on the internet, that deal with vector analysis, I have learned from it awfully lot, thus I am very grateful for Prof, chasnov, and Coursera staff for the incredible effort done on this course. (and of course for their infinite patience regarding my countless missed deadlines :)). I want to give those who want to know about this course, or want to study it some notes.

1- this course in directed towards the students of physics and engineering, so it is different a lot form multi-varibale calculus.

2- Almost all the problems in this course are given with their full solution in the lecture notes of the course, but my advice to all learners is to exert all effort to solve the problems by themselves. whenever you face any step in the lecture or in the problems you did not understand well stop and contimplate about it and try all ideas you have, then if you still did not overcome it, then go to see the solutions, but try to understand each step and then try to redo the tough parts. Remember you are the easiest one to fool yourself.

3- I do not remember how many hours one shall put each week to finish this course, maybe it is 5 hours a week, I disagree with that totally, and think they have forgotten to add zero, so it should be 50 hours (at least)!!! I still remember suffering in one problem to understand why the integral boundaries was like they were.. this only took me about 7 hours!

I highly recommend this course for scientists and engineers and anyone who want to understand their mathematics.

It is challenging, but it is great helpful. there are many lectures I have watched several times.

From the lecture to the practice problem, and the solution provided, very well designed and related to practice and further reference. If I find something I can not understand, usually check the previous lectures and practice solution carefully, and then I could find the solution.

Highly recommend Jeff's other courses for engineers. Actually, I start with the numerical method for engineers and find this one (and the series) helps a lot in understanding the concepts in numerical simulation. I do appreciate this series course helps me strengthen the foundation of mathematics.

Professor Chasnov's explanations are as clear as crystal when you follow the course in structured sequence. The exercises cover a significant range of difficulty, ranging from evaluating the gradient field of a simple x,y,z function to deriving the vorticity equation from the Navier-Stokes momentum conservation equation for an incompressible fluid. Although this is not a fluid dynamics course, and does not actually derive the Navier-Stokes equation(s), it does indeed, together with his courses on matrix algebra and differential equations, provide one with the skills required to deal with such a derivation.

I took this class as a review course as I prepare to go back for a graduate degree and hadn't practiced differential equations in years. While I remember struggling while an undergraduate, Professor Chasnov did an amazing job teaching the concepts, deriving the tools we would use, and showing examples of how to solve problems. His lectures paired with his lecture notes made it a very straightforward and thorough learning experience. This was my first online course, and Professor Chasnov made the experience so interesting, in-depth, smooth, and painless that I will look forward to taking more courses.

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!

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.

This course is to learn how to calculate the summation when a fluid/ electric field / magnetic field cross through an object. First, we have to remember 3 type of coordinates. Then, we have to know what is surface integral, line integral and volume integral. Finally, we need to know 3 theroems to make our calculation of the integral convertible or easier. This course is difficult, but under the context of physics, we would understand the meaning of these integral better.

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.

I am a civil engineer since many years ago (my age is 56), and I took this course just to refresh concepts and tools I once knew and used in the past during my university years. I really enjoyed and had a lot of fan with every topic covered in this course!! I am so grateful that this type of courses exist and are available for everyone. And many thanks to Jeff, you are a great teacher! I´m already suscribed to other courses given by Jeff and can -now- begin..

The overall course is incredible, I loved it, the only comment I would leave is that in some places the narration lacks rigor and proofs of some facts, which are difficult to prove on your own, this ideed leaves me with some questions, but the majority of them is answered. Surprisingly, I did not find any topics particularly difficult, this is because the course starts with the most basic concepts to make sure you have a proper background.

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.

Ce cours est tout simplement excellent ! Les sujets abordés couvrent parfaitement le domaine et présentent des exercices adaptés au niveau . Le document de cours est bien fait et agréable à utiliser.

Le professeur est vraiment clair, pédagogue et agréable à suivre.

En résumé, ce cours est à conseiller à tous ceux qui souhaitent découvrir ou se remémorer le calcul vectoriel.

Merci à toute l'équipe qui a collaboré à cette réussite.

Thank you very much for the course Dr Chasnov!

This course gives a simple and straight and straightforward introduction to vector calculus with instructive applications from Fluid mechanics and Electromagnetism. This has helped to get an intuitive understanding of the main theories of vector calculus (Gradient, Green's, Stoke's...etc.) in different coordinate systems. I recommend this course to anyone interested in this Topic!

One of the best Coursera courses ever attended. Videos were of the right size mixed with plenty of exercises to better digest the material. The course notes were excellent and extremely helpful. I intend to attend the other 3 courses (differential equations, matrix algebra and numerical methods). I wish you also offered a tensor analysis course which is the basis for General Relativity, maybe in the future.

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.

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.

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.

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.

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.

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.

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.

It has been a pleasure to study with prof Chesnov. I had difficulties to deal with Einstein Sommation Convention (the fundamental rules of this game were not explicitly given, I found them some other place) and to get some gradient calculus in spherical coordinates.

But as I said, the total amount of joy exceeds the sum of the pains!

Thank you

It is a very good course, but those who just started studying might find it quite challenging since it is more of an overview and reminding, rather than teaching from scratch. To those who just started learning vector calculus I would recommend accompanying this course with khanacademy lessons on multivariable calculus and 3blue1brown videos.

Great fundamental course, before taking this course, I always struggled to read the equations in fluid mechanics, and this course helps me to review some of the basic vector calculus, after finishing all the course materials and all the practice problems, I've gained more confidence to read and conduct some fluid mechanics equations.