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Results tagged with ca.classical-analysis-and-odes
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user 35416
Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
9
votes
Freshman's definition of sin(x)?
I agree with Mark that your reservation against using "advanced" notions such as limits and derivative seem to be more applicable to high school mathematics, than to the undergraduate syllabus, since …
- 13k
2
votes
Functions which form continuous curve with its own iterations
A necessary and sufficient condition for continuity is that you have two end points $a < b$ such that $f(f(a)) = f(a)$ and similarly for $b$, in other words both $f(a)$ and $f(b)$ should be fixed poin …
- 13k
1
vote
Function with range equal to whole reals on every open set
Here is an explicit construction that uses only elementary functions and limits: define $f(x)=\lim_{n\rightarrow \infty}(n!\pi x)$ when that limit exists, and e.g. 0 otherwise. Notice that this $f$ is …
- 13k