Bob Pego
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 Jan8 awarded Good Answer Oct30 awarded Yearling Jun13 answered What was the book that opened your mind to the beauty of mathematics? Jun6 comment $p_n(x)=p_{n-1}(x)+p_{n-1}^{\prime}(x)$, then all the roots of $p_k(x)$ are real @Edwin I believe $p_0(x)$ is just some arbitrary polynomial, and is taken here to be of degree $m$. May28 comment counterexample for ill posedness of the laplace equation "Laplace's equation" would be most accurate. May24 comment Differentiable Path of Operators and their Inverses I'd suggest to consult one of the classic texts on operator theory for the relevant theory: Dunford and Schwarz vol. 1, or Kato's Perturbation Theory for Linear Operators, say. I think I recall that the calculation that ${\mathcal P}$ is a projection involves reducing a double integral to a single one. Basically, the point is that the contour $\Gamma$ encircles all the spectrum of $A(t)$ except zero. May23 answered Differentiable Path of Operators and their Inverses May13 comment Proving Taylor's Theorem by integrating n times? Perhaps this answer to a related question will help. In short: Apply the mean value argument to the n-fold integral first to pull out $f^{(n)}(\xi)$, then evaluate the n-fold integral with constant integrand. Apr23 awarded Enthusiast Apr22 answered How prove this integral inequality $6\left(\int_{0}^{1}f(x)dx\right)^2\le 1+ 8\int_{0}^{1}f^3(x)dx$ Apr17 comment Modification of Gronwall's Lemma The proof of Lemma 1.3.3 in [201] looks messed up. Perhaps it's left over from some earlier draft of the book. It's not too difficult though to derive the result by an approach similar to the proof of Lemma 1.3.1: Let $\Phi$ be the right hand side and differentiate, etc. Apr16 revised Determining why $\int_{\partial R} z\ dz = 0$ and $\int_{\partial R} z\ dz = 0$ independently of Cauchy's Theorem for a Rectangle fixed bug in endpoint evaluations Apr16 suggested approved edit on Determining why $\int_{\partial R} z\ dz = 0$ and $\int_{\partial R} z\ dz = 0$ independently of Cauchy's Theorem for a Rectangle Apr15 answered A game with $\delta$, $\epsilon$ and uniform continuity. Apr7 awarded Nice Answer Apr3 revised if $f(x)-a\int_x^{x+1}f(t)~dt$ is constant, then $f(x)$ is constant or $f(x)=Ae^{bx}+B$ fixed a sign mistake Mar31 answered if $f(x)-a\int_x^{x+1}f(t)~dt$ is constant, then $f(x)$ is constant or $f(x)=Ae^{bx}+B$ Mar3 revised Question on proof of the Bolzano-Weierstrass theorem clarified subject Mar3 suggested approved edit on Question on proof of the Bolzano-Weierstrass theorem Feb28 comment Continuity of the derivative I appreciate that I didn't answer the question you asked, and I should have mentioned it. A point I'd like to stress, though, is that proving the Cauchy integral formula without continuity of the derivative does not need to seem nearly as subtle and complicated as the roundabout approach taken in standard books suggests. In particular, it does not require a 2D integration theory, which arguably makes this approach considerably less complicated than one invoking Green's theorem.