Calculus III
Multivariable calculus: vectors, partial derivatives, multiple integrals, and vector calculus.
Notation, in plain English
A little bit of.
dx just means a tiny sliver of x — nothing more mysterious than that.
Add up all those little bits.
The stretched S stands for "sum" — integrating means adding infinitely many infinitesimal pieces.
A little bit of, changing only one thing at a time.
Same idea as d, but used when several variables are involved and the rest are held frozen.
Add up everything in the list.
Sigma is the plain sum symbol: go through each term and total them.
Plain-language readings in the spirit of Silvanus Thompson, Calculus Made Easy (1910, public domain).
Differentiation
Rates of change for functions of more than one variable.
1 topic
Multiple Integrals
Integrating over regions, volumes, and solids in two and three dimensions.
9 topics
Vector Calculus
Vector fields, gradients, and integrating along curves.
3 topics