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====== Vector Calculus ====== | ====== Vector Calculus ====== | ||
- | ===== Why is it interesting? ===== | ||
- | ===== Layman ===== | ||
- | ===== Student===== | ||
- | ==== Recommended Readings ==== | + | <tabbox Intuitive> |
+ | <note tip> | ||
+ | Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party. | ||
+ | </note> | ||
+ | | ||
+ | <tabbox Concrete> | ||
+ | * [[http://www2.eng.cam.ac.uk/~alj3/vc.pdf|A Survival Guide to Vector Calculus]] by Aylmer Johnson | ||
+ | |||
+ | **Recommended Textbooks:** | ||
+ | |||
+ | |||
+ | * http://mathinsight.org/thread/vector_algebra | ||
+ | * A nice introduction can be found in Section 3 of Vol. 2 of Feynman's Lectures on Physics, which are available [[http://www.feynmanlectures.caltech.edu/II_03.html|here]] | ||
+ | * A Student's Guide to Vectors and Tensors by Daniel A. Fleisch | ||
* DIV, Grad, Curl, and All That: An Informal Text on Vector Calculus by H. M Schey | * DIV, Grad, Curl, and All That: An Informal Text on Vector Calculus by H. M Schey | ||
+ | * [[http://www.physics.miami.edu/~nearing/mathmethods/|Mathematical Tools for Physics]] by James Nearing | ||
+ | <tabbox Abstract> | ||
- | ===== Researcher===== | + | <note tip> |
+ | The motto in this section is: //the higher the level of abstraction, the better//. | ||
+ | </note> | ||
- | ===== Examples ===== | + | |
+ | <tabbox Why is it interesting?> | ||
- | ===== History ===== | + | Vector calculus is an important tool, whenever we want to understand systems where directions play a role. A vector is an arrow that points in some direction. Thus, a vector is a tool to denote a direction. |
+ | |||
+ | This is needed, for example, to describe in which spatial direction a ball moves or how a fluid flows. | ||
+ | |||
+ | <blockquote>A vector is the mathematical representation of a physical entity that may be | ||
+ | characterized by size (or “magnitude”) and direction. In keeping with this definition, speed (how fast an object is going) is not represented by a vector, but velocity (how fast and in which direction an object is | ||
+ | going) does qualify as a vector quantity. Another example of a vector quantity | ||
+ | is force, which describes how strongly and in what direction something is being | ||
+ | pushed or pulled. But temperature, which has magnitude but no direction, is not | ||
+ | a vector quantity<cite>A Student's Guide to Vectors and Tensors by Daniel A. Fleisch | ||
+ | </cite></blockquote> | ||
+ | |||
+ | |||
+ | <tabbox History> | ||
https://en.m.wikipedia.org/wiki/A_History_of_Vector_Analysis | https://en.m.wikipedia.org/wiki/A_History_of_Vector_Analysis | ||
+ | |||
+ | </tabbox> | ||
+ | |||
+ |