Vector Calculus for Engineers
The Hong Kong University of Science and Technology
We can’t emphasize enough the importance of Vector Calculus. A solid understanding lays the foundations for further learning of electromagnetism, fluid mechanics and many disciplines. This course is one of the best I have met. I can’t help but recommend to those who are interested in vector calculus.
The course covers tons of things, but still starts from the very basics: what vector is, how to calculate dot and cross products, what Cartesian coordinates are, what fields are, etc. You probably have learned them in high school, but they are not “no biggie”, they are the most fundamental building blocks.
From here on, the course is getting faster: partial derivative, gradient, divergence, curl, Laplacian, and electromagnetic wave… what the heck! Oh trust me, don’t hasten, slow down, spend some time on these concepts and operators here. You will encounter them again and again.
Cartesian coordinates are never the best way to deal with all kinds of problems. The week 3 covers polar, cylindrical and spherical coordinates. They are not that difficult to imagine and comprehend, but you will meet divergence, curl, Laplacian again. Transforming from one type of coordinates to another type is critical, since certain problem will be trivial to solve in certain type of coordinates.
Now we are ready to move on to linear and surface integral. The infinitesimal element area and element volume probably will make you pause and think. I also found some online reference like Wolfram are very useful when doing the homework.
It has been a long journey, finally it is time to tackle the fundamental theorems: the gradient theorem, the divergent theorem, the curl Green’s theorem and its generalization Stokes’ theorem. The derivation of them are marveling. The grand finale is transforming Maxwell’s equations from their integral form to the differential form, using all we have learned in this course.
Professor Jeffrey R. Chasnov is a top instructor on Coursera. I have finished 3 of his courses, all of them are top-notch. Enjoy!
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