Online Course
Vector Calculus for Engineers
The Hong Kong University of Science and Technology via Coursera
- Provider Coursera
- Cost Free Online Course (Audit)
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- 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
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Reviews for Coursera's Vector Calculus for Engineers Based on 25 reviews
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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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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.
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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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.
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.
This course is fluent, well organized, effective, concise, useful. All topics are treated in a very didactic way, also facilitating the understanding of simple questions often overlooked in textbooks. The proposed exercises complement the explanation and allow the student who solves them to truly understand.
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Anonymous
Anonymous
completed this course.
Another fine short course from Professor Chasnov. In addition to Lecture problems there are 3-4 practice quizzes and weekly quizzes. Excellent PDF course notes are provided with solutions to lecture problems and practice quizzes. Lightboard videos are great. Check out his other short courses!
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Anonymous
Anonymous
completed this course.
I really thank to our sir...It's really awesome..This help me to improve my knowledge in maths.Actually I am an btech students so as you know how much maths is important in our life..I learn different methods and it's highly useful for my future
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Anonymous
Anonymous
completed this course.
Excellent course, teacher with impressive personality, syllabus perfectly prepared. The exercises illustrate the concepts clearly without unnecessary calculations. Answers are worked out, as I don't think I could have done without them.
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Anonymous
Anonymous
completed this course.
Professor Chasov always does a great job. This is very dense material. I am taking the course for the second time in about 40 years, so there was much review. I highly recommend this course as a refresher for working engineers.
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Anonymous
Anonymous
completed this course.
The course was actually good with new topics
But some topics were tough and hard to understand. They were new to me . I feel this course is quite high level course which explains about higher level topics .
But some topics were tough and hard to understand. They were new to me . I feel this course is quite high level course which explains about higher level topics .
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Anonymous
Anonymous
completed this course.
It is really helped me alot.i learnt applications of vectors and how we are appling in real world.i enjoyed very well by taking this course thanks to our couresera providing such a nice opportunity
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Anonymous
Anonymous
completed this course.
Video lectures was very nice and the good part of this course was that , there are practice questions after every lecture which is very very helpful to test the understanding through the videos
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Anonymous
Anonymous
completed this course.
the professor explains real good and the topics are presented in a well structured way, I recommend this course to others who want to review or reinforce their knowledge of vector calculus
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Anonymous
Anonymous
completed this course.
Vector calculus is very hard to learn.But in this course we enjoy learning vector calculus.It is very interesting to learn.I felt very excited to learn vector calculus.Thank u sir.
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Anonymous
Anonymous
completed this course.
Vector calculus is very hard to learn.But this course is very interesting.It is very useful for the students who feel vector calculus hard.I felt excited during the course.Thank u sir.
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Anonymous
Anonymous
completed this course.
Another good although challenging course from prof. Chasnov. I wouldn't recommend you start this course unless you have some strong foundation in single variable calculus.
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Anonymous
Anonymous
completed this course.
It is a nice course.relation between divergence theorems, stokes theorems is explained nicely.applications of divergence and curl to various fields is explained excellently.
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Anonymous
Anonymous
completed this course.
Easy to follow course with great notes to help you through it, and also very useful once you've finished the course and need to go back to refresh knowledge or ideas.
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