Tagged Questions

99 views

Is there a book only about epsilon delta proofs?

I want to know if there is such book, with beautiful epsilon delta proofs of all kind.
29 views

117 views

A bounded subset in $\mathbb R^2$ which is “nowhere convex”?

Let $F : \mathbb S^1 \to \mathbb R^2$ represents a simple closed curve $C$ in $\mathbb R^2$. The Jordan curve theorem says that the curves bounds a interior domain $\Omega$ and $\partial \Omega= C$. ...
140 views

Is it possible to extend a $C^1$-function smoothly from any Lipschitz domain?

If $\Omega$ is a cube in $\mathbb{R}^n$ and $f\in C^1(\overline\Omega)$. By reflection one can extend such a function to all of $\mathbb{R}^n$ and the extenstion is in $C^1(\mathbb{R}^n)$. If ...
34 views

Reference for power series

I would need some references for power series, Taylors series of elementary functions, derivation and integration of power series, convergence of sequences of functions and series of functions. The ...
102 views

Reference request: Partition of unity…

I was looking for some material that could help me understand a real analysis course (1st year undergraduate). My teacher treated the following topics: Partition of unity Existence of regular ...
47 views

Riemann Sphere/Surfaces Pre-Requisites

I have recently developed a large interest in everything to do with Riemann Sphere/Surfaces. I wish to understand the topic quite well but I know that I will need to read a good number of books on ...
9 views

analytic property of periodic properties

Can any one suggest me some books in which I can see the analysis of periodic functions? I dont have any constrain in the domain or codomain. For example this book ...
40 views

Generalization of the Riemann integral to functions on the sphere

I want to do something a bit strange: define the Riemann/Darboux integral for bounded real functions defined on the n-dimensional sphere. The catch: I cannot use Lebesgue integration theory to do ...
Is there another Analysis book that is based on the Cartesian space $\Bbb R^p$
I need some reference for the proof of the following theorem attributed to Liouville: Theorem: Let $f(x):\Omega\longrightarrow \mathbb R^n$ a $C^2$ function where $\Omega$ is an open subset of ...