Online Course
Vector Calculus for Engineers
The Hong Kong University of Science and Technology via Coursera
- Provider Coursera
- Cost Free Online Course (Audit)
- Session Upcoming
- Language English
- Certificate Paid Certificate Available
- Effort 4 hours a week
- Duration 4 weeks long
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Overview
Class Central Tips
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
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.
-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
Class Central Charts
- #2 in Subjects / Mathematics / Calculus
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Reviews for Coursera's Vector Calculus for Engineers Based on 82 reviews
- 5 stars 83%
- 4 stars 15%
- 3 stars 2%
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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 student simply to "look up". Therefore, I recommend...
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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.
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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.
An extremely valuable course for anyone in physics or engineering. Take it as soon as you can.
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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.
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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 following side by side with the .pdf file available...
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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 - or references to them - would have consolidated the concepts and methods. There are more theoretical diversions where Jeff's love of vector identity proofs is obvious; for me this was very welcome but the dive into the associated problems was a bit abrupt.
My concern with the course is that a lot of the more complicated cylindrical and spherical coordinate versions of VDOs were treated very briefly and the web articles dealing with these in detail were posted in the discussions could have been mentioned in the lectures.
However I learnt a lot in a short time and can highly recommend the course.
The content is for the most part very practical and straightforward but some more optional practice problems - or references to them - would have consolidated the concepts and methods. There are more theoretical diversions where Jeff's love of vector identity proofs is obvious; for me this was very welcome but the dive into the associated problems was a bit abrupt.
My concern with the course is that a lot of the more complicated cylindrical and spherical coordinate versions of VDOs were treated very briefly and the web articles dealing with these in detail were posted in the discussions could have been mentioned in the lectures.
However I learnt a lot in a short time and can highly recommend the course.
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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 electromagnetics were almost all of the topics can be applied. For beginners, the pace of the lectures is just fine. For the readings, most of the assigned reading were manageable except in the last part particularly in the readings of navier-stokes equation. For non-mechanical engineers like me, it was a little bit difficult on comprehending its derivation. But the lecture notes is very essential since it helped in the understanding of the process. Thank you very much for this great ooportunity learning something through Coursera. And Thank you Prof. Jeff Chasnov for the job well done.
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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 added bonus, solutions are provided for each and everyone of them. The companion text for this course is also quite simple to understand and sticks to the point. Additional appendices ensure you don't have to take external help for anything, and makes the course a stand-alone product. A few parts like 'Einstein-Summation Convention' are bit difficult to understand, with quite a vague explanation, but a simple internet search will clear most of your doubts. I would recommend this course for a beginner (like myself) who has had trouble understanding this topic.
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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 problems should have been talked about in the lectures.
As other users have pointed out, vector calculus is a course that deserves more than 4 weeks of learning, however this has to do much more with coursera than the professor. So overall, the course is good but you will need other resources to fully understand some problems and derivations. For someone like me who was never introduced to Kronecker Delta, Levi Cevita and many many derivations, this was a rewarding but challenging course.
As other users have pointed out, vector calculus is a course that deserves more than 4 weeks of learning, however this has to do much more with coursera than the professor. So overall, the course is good but you will need other resources to fully understand some problems and derivations. For someone like me who was never introduced to Kronecker Delta, Levi Cevita and many many derivations, this was a rewarding but challenging course.
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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.
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.
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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.
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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
Thank You prof. for taking the wonderful session. looking forward to join you back.
Cheers
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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.
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.
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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.
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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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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.
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Anonymous
Anonymous
completed this course.
Really tough course but the professor made this easy enough for us to catch on to the basics. Also appreciated the application of theoretical concepts to some other courses such as fluid mechanics. I still feel lacking in how I learn through all the course but it is already sufficient enough to learn more from other courses that requires proper comprehension of vector calculus.
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Anonymous
Anonymous
completed this course.
It´s an excellent course, It helped me a lot with my studies, I´m studying aeronautical engeenering and the next semester I´ll see vector calculus on my program, I decided to find a course to help me to make me a better student and a better engeener, I found this course and I didn´t think to take it. Jeff is a excellent professor and I want and hope to take another course with him.
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Anonymous
Anonymous
completed this course.
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.
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Anonymous
Anonymous
completed this course.
The course seemed very challenging up until the end but the lecturer has a very good insight and understanding so he always sought of pushed me to finish. I might not really need it anymore but have a background understanding of how these things work is very good for me and has helped me more ways than I can imagine. Thank you very much
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