Thanks for that link, the animations look really cool! Visualizing these concepts makes them so much clearer.

Again, appreciate the comment!

I wish to tell you a story.

As a young kid and in the high school I had few to no problems with math; it was easy to understand and the examples in the maths books were quite intuitive and visual.

What a shock it was to attend the first math courses in the university. I don’t know about the ones for math majors, but at least the math course materials for us engineering students were conjured from some fiery bowels of hell.

With no clarifying pictures and even less explanations (”divergence measures the change of vector function in its direction and the spreading of the direction. Now do the exam.” is pretty much all we get), the typical brute-force technique among tech students here is to memorize the ten or so calculations that the exam questions are picked from each year and vomit them on the test paper. Formula after formula. Equation, equation, equation.

Somebody just forgot to tell what the hell these formulas do and what they are used for anyway.

All this bitter rambling is here for a reason… I really wish to thank you for your explanations! This is the first time that instead of memorizing some stupid upside down triangles and strange-looking d’s with no comprehension of them whatsoever I really do understand, what the hell a “curl” actually is.

I am going to recommend your site to every tech and math student I know. Something like this is really missing from the teaching of mathematics and I don’t know whether the professors are too jaded, indifferent or too alienized from the real world to notice this.

In case you haven’t noticed, there are some neat animations of divergence and curl in
www.math.umn.edu/~nykamp/m2374/readings/divcurl
also.

Once again… A big great thanks to you, Kalid! Keep up the good work!