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basic_tools:vector_calculus
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Vector Calculus
Intuitive
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.
Concrete
- A Survival Guide to Vector Calculus by Aylmer Johnson
Recommended Textbooks:
- A nice introduction can be found in Section 3 of Vol. 2 of Feynman's Lectures on Physics, which are available 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
- Mathematical Tools for Physics by James Nearing
Abstract
The motto in this section is: the higher the level of abstraction, the better.
Why is it interesting?
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.
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 quantityA Student's Guide to Vectors and Tensors by Daniel A. Fleisch
basic_tools/vector_calculus.1522232554.txt.gz · Last modified: 2018/03/28 10:22 (external edit)
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