Theoretical foundations of calculus: limits, convergence of sequences, construction of the real numbers, least upper bound property, and related analysis topics such as continuity, differentiation, integration through the fundamental theorem of calculus.

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15
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1answer
555 views
+50

n'th derivative does not vanish, but $\lim_{n\to \infty} f^{(n)}=0$.

Let $f\,$$\in$$\,C^\infty[\mathbb{R},\mathbb{R}]$ . Apparently the only functions $f$ for which there exists $n\in\mathbb{N}$ such that $f^{(n)}=0$ are polynomials in $\mathbb{R}[x]$. Is it ...
31
votes
8answers
1k views
+100

Is $dx\,dy$ really a multiplication of $dx$ and $dy$?

On the answers of the question Is $\frac{dy}{dx}$ not a ratio? it was told that $\frac{dy}{dx}$ cannot be seen as a quotient, even though it looks like a fraction. My question is: does $dxdy$ in the ...
3
votes
0answers
49 views
+50

Question about proof of Browder, Minty Theorem

Could someone please assist with the following question: In the following set of notes, I am interested to know how the author obtains "By Lemma 1.11, the Galerkin equations (2.5 has a solution ...