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, and integration through the fundamental theorem of calculus.

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Solve integral(convolution) equation

I have been trying to find a solution to the following convolution equation: \begin{align*} e^{-ax^2/2}*\ln \left(f(x)*e^{-ax^2/2}\right)+e^{-bx^2/2}*\ln \left(f(x)*e^{-bx^2/2}\right)=cx^2 ...
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Isometric and conformal map

We defined conformal and isometric maps for surfaces $f,g: \Omega \subset \mathbb{R}^2 \rightarrow S \subset \mathbb{R}^3$. Under a reparametrization of $f$ I understand a diffeomorphism $\Phi : M ...