Stephen Wolfram

JUNE 28, 2023

Line, Surface and Contour Integration “Find the integral of the function ” is a typical core thing one wants to do in calculus. But particularly in applications of calculus, it’s common to want to ask slightly more elaborate questions, like “What’s the integral of over the region ?”, or “What’s the integral of along the line ?”

Computer 118

Computer Calculus Construction Mathematics 118

Stephen Wolfram

MARCH 7, 2022

One can view a symbolic expression such as f[g[x][y, h[z]], w] as a hierarchical or tree structure , in which at every level some particular “head” (like f ) is “applied to” one or more arguments. and at t steps gives a total number of rules equal to: &#10005. which we can read as “there exists something a for which equals a ”.

Mathematics 120

Mathematics Physics Computer Algebra 120

Stephen Wolfram

NOVEMBER 10, 2021

For integers, the obvious notion of equivalence is numerical equality. The most elementary example of something like this is the statement ( already present in Euclid ) that if and , then. Then (by the assumed properties of equality) it follows that. elementary updating events) in physical space.

Physics 122

Physics Mathematics Computer Construction 122

Stephen Wolfram

FEBRUARY 3, 2023

Sometimes textbooks will gloss over everything; sometimes they’ll give some kind of “common-sense-but-outside-of-physics argument”. But one never quite gets there ; it always seems to need something extra. But the mystery of the Second Law has never gone away. Why does the Second Law work? What does it really depend on?

Computer 92

Computer Energy Physics Construction 92