New answers tagged applications
4
Logarithmic differentiation is used in mathematics when dealing with infinite products in complex analysis. Note the construction of $f’/f$ from $f$ does not require logarithms of $f$ as a middle step (except intuitively), so it is perfectly fine to use even when $f$ takes non-positive values. The prime number theorem and the link between prime numbers and ...
6
For the expression $x^x$ we could focus on finding occurrences of $x\ln(x)$.
One direction is Stirling's approximation $\ln(N!)\sim N\ln(N)$ so $N!$ is like $N^N$.
Another direction is that the prime number theorem gives an estimate for the $n$-th prime $p_n$ as $p_n=n\ln(n)$.
Yet another direction involves entropy. Entropy might be given by an expression ...
1
$n^n$ shows up in combinatorics (number of lists of numbers from 1-n of length n), but I doubt it will have applications for the physical world: $x$ cannot have units, since it doesn't make sense to raise something to a power with units.
Top 50 recent answers are included
Related Tags
applications × 27undergraduate-education × 7
applied-mathematics × 6
secondary-education × 5
calculus × 4
complex-numbers × 4
geometry × 3
curriculum × 3
mathematical-pedagogy × 2
textbooks × 2
examples × 2
teaching × 2
linear-algebra × 2
abstract-algebra × 2
reference-request × 1
algebra × 1
primary-education × 1
student-motivation × 1
education-research × 1
graduate-education × 1
homework × 1
general-pedagogy × 1
statistics × 1
probability × 1
interactive-teaching × 1