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Online Course

Vector Calculus for Engineers

The Hong Kong University of Science and Technology via Coursera

Overview

We cover 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 integrating fields. The fourth 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 42 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 four weeks to the course, and at the end of each week there is an assessed quiz.

Lecture notes can be downloaded from
http://www.math.ust.hk/~machas/vector-calculus-for-engineers.pdf

Syllabus

Vectors
-A vector is a mathematical construct that has both length and direction. We will define vectors and learn how to add and subtract them, and how to multiply them using the scalar and vector products (dot and cross products). We will use vectors to learn some analytical geometry of lines and planes, and learn about the Kronecker delta and the Levi-Civita symbol to prove vector identities. The important concepts of scalar and vector fields will be introduced.

Differentiation
-Scalar and vector fields can be differentiated. We define the partial derivative and derive the method of least squares as a minimization problem. We learn how to use the chain rule for a function of several variables, and derive the triple product rule used in chemical engineering. From the del differential operator, we define the gradient, divergence, curl and Laplacian. We learn some useful vector calculus identities and how to derive them using the Kronecker delta and Levi-Civita symbol. Vector identities are then used to derive the electromagnetic wave equation from Maxwell's equation in free space. Electromagnetic waves form the basis for all modern communication technologies.

Integration and Curvilinear Coordinates
-Scalar and vector fields can be integrated. We learn about double and triple integrals, and line integrals and surface integrals. Curvilinear coordinates, namely polar coordinates in two dimensions, and cylindrical and spherical coordinates in three dimensions, are used to simplify problems with cylindrical or spherical symmetry. We learn how to change variables in multidimensional integrals using the Jacobian of the transformation.

Fundamental Theorems
-The fundamental theorem of calculus links integration with differentiation. Here, we learn the related fundamental theorems of vector calculus. These include the gradient theorem, the divergence theorem, and Stokes' theorem. We show how these theorems are used to derive continuity equations, define the divergence and curl in coordinate-free form, and convert the integral version of Maxwell's equations into their more famous differential form.

Taught by

Jeffrey R. Chasnov

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Reviews

4.8 rating, based on 99 reviews

Start your review of Vector Calculus for Engineers

  • Anonymous

    Anonymous completed this course.

    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...
  • Syed J.

    Syed completed this course.

    This indeed is one of the BEST courses in Vector Calculus with the BEST instructor teaching it. Professor Chasnov is highly organized and presents the contents in a clear manner. I have become fond of his excellent teaching style. Over and above, all engineers must take this course. I hope he teaches courses in PDEs, Integral Transforms, Complex Variables, ... in times to come to benefit the motivated mathematics learners all around the globe! This is terrific effort from him. I wish the best comes his way as a reward for his dedication. God bless.
  • Anonymous

    Anonymous completed this course.

    Week three is the pivotal week for learning that I struggled with. Line and Surface integrals just did not come easy to me. A tutorial on the line and surface integrals in greater depth would have helped me since it is difficult to visualize what these always mean. The instruction was excellent, but I feel I needed extra help. Would love to take a course in just line and surface integrals.

    An extremely valuable course for anyone in physics or engineering. Take it as soon as you can.
  • Anonymous
    our professors explanation and command on the subject is very high. sir, has helped me in understanding physics concepts in a much simpler way.this course is very useful for both mathematics and physics students.In short duration it could cover all areas of vector calculus I request sir to include more no. of problems and solve them so that students can be confident applying the concepts of vector calculus in solving problems related to electromagnetic waves and transmission lines
  • Anonymous

    Anonymous completed this course.

    Finished all the course in about 2 weeks. It is very good if you want to refresh your memory on vector calculus(in my case). If you want a solid foundation, then you should supplement it with lots of more examples from some textbook(s). Otherwise, things are explained very well, and the examples are not too difficult to scare you away! Great course.
  • Anonymous
    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...
  • Anonymous
    This Course is helpful for more knowledge about Vector.

    This course easy to understand and always helps us☺️
  • Anonymous

    Anonymous completed this course.

    Prof. Jeff has one of the best MOOCs out there for Vector Calculus, although it might not seem like it at first. A gem hidden in the rough, all in all, although I'd say that the latter two weeks were far from being as easy as the first two. I'd recommend...
  • Anonymous

    Anonymous completed this course.

    The content is fairly comprehensive and along the way you get to revise things you may have learnt elsewhere and you will also be challenged. The content is for the most part very practical and straightforward but some more optional practice problems...
  • Anonymous

    Anonymous completed this course.

    Professor Jeff explained well the topics covered. I learned a lot from him especially on the application of the Kronecker delta and levi-civita identities. All of the topics discussed on this course are very important when handling subjects like engineering...
  • Anonymous

    Anonymous completed this course.

    This course is really helpful for someone who wants an easy approach for vector calculus. The included exercises have few questions each, but really test your concept application. Thus, they are not stressful, while remaining worthy of solving. As an...
  • Anonymous

    Anonymous completed this course.

    I took the course as complementary material to my vector calculus class, since I felt many things were skipped and not talked about in my class. I enjoyed that the course encourages you to do derivations and practice by yourself, however, I felt certain...
  • Anonymous

    Anonymous completed this course.

    My experience during the progress of this course has been enlightening and refreshing. The words used were very relatable, and the mode of teaching was also commendable. It has been a highly exciting journey, and I am proud of what I have learnt.
    Vector Calculus for Engineers on Coursera superseded my expectations because I have had some lessons on vectors and I have not been so enlightened as I am. My work here has been a very fantastic journey and I sincerely just want to say that Coursera should keep up the excellent work. It has been a tremendous journey with you, and I hope to experience more like this as I progress.
  • Profile image for Eftekhar Sadik
    Eftekhar S.
    Well, before joining this course , my knowledge in vector calculus was not mentionable. But I have learnt pretty much good stuffs in this course and obviously it is going to help me a lot , in my engineering career. Specifically, to say I have enjoyed the use of divergence theorem and the stokes theorem in Maxwell's equation . I kind of knew about the Maxwell's equation but I was totally unware of the fact that it can be converted to the differential form from the integral form . And , above all , truly to speak ,all the learnings boosted up my interest in vector calculus .Thank you , Sir , for your valuable knowledge.
  • Anonymous

    Anonymous completed this course.

    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. If you find vector calculus hard, you can take this course, but do remember it still requires work.
  • Dr. P.

    Dr. completed this course, spending 4 hours a week on it and found the course difficulty to be hard.

    The course is proved very beneficial for intermediate students. The concepts on vector dot and cross products are good. The concepts on kronecker delta and Levi cevita symbol with its applications in proving the identities are amazing. The concepts of line integral, surface integral and volume integral found bit tough and the applications of divergence and Stokes theorem in proving Navier-Stokes and continuity equation also Maxwells equation are treat to understand.
    Thank You prof. for taking the wonderful session. looking forward to join you back.
    Cheers
  • Profile image for Amrita Chakrabarty
    Amrita C.

    Amrita completed this course, spending 9 hours a week on it and found the course difficulty to be medium.

    It was good. I have learned the topic . I felt interesting. The learning process was good . It is really helpful for the students.
    It was good. I have learned the topic . I felt interesting. The learning process was good . It is really helpful for the students.
    In future i will try to take part in such courses again if I got the opportunity to join . Thanks to Coursera . It was good. I have learned the topic . I felt interesting. The learning process was good . It is really helpful for the students.



  • Anonymous

    Anonymous completed this course.

    Well structured and self explainatory videos with interesting assignments. All the major topics even those which are not taught in university courses. I personally found the description of different coordinate systems quite fascinating. Plus at the end of the course there were videos on the physical significance of divergence and curl. The application of vector calculus in solving Maxwell's equations was also quite interesting. Thoroughly enjoyed the course.
  • Anonymous

    Anonymous completed this course.

    The best course in vector calculus! The course page states that it only requires basic algebra knowledge, although any experience you have with linear algebra and calculus will be helpful with gaining a deeper understanding of the material. You can access all the quizzes and assignments without paying for the full course, but if you want to get credit as having completed the course, you have to pay for the certificate.
  • Anonymous

    Anonymous completed this course.

    I really enjoyed taking Vector Calculus. I always thought that it was a complicated course especially the vector identity part. Professor Chasnov really made it easier to understand and the learning was fun. I'm so glad that i completed this course in three weeks. As an aspiring engineer this will really help and besides this semester I'm taking Vector Calculus in My University so everything will just be a revision for me.

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