0
votes
1answer
23 views

Differential Maping in Elementary Analysis

The problem I stuck was : Let $ f = R^{n} \rightarrow R^{m} $ and suppose there is a constant $M$ such that for $ x \in R^{n} $, $ || f(x) || \leq M || x ||^{2} $. Prove that $ f $ is differentable ...
2
votes
1answer
195 views

Justification behind changing coordinates of a differential operator

On many websites focused on physics, (say http://skisickness.com/2009/11/20/ ) they like to represent differential operators in different coordinates. I.e. going from the standard basis to polar ...
18
votes
2answers
547 views

Applications of Pseudodifferential Operators

I am very interested in just about anything that has to do with PDE's, and inevitably pseudodifferential operators comes up. Its obvious that such a novel way of looking at PDE's would be important, ...
8
votes
4answers
320 views

Determining the action of the operator $D\left(z, \frac d{dz}\right)$

This question was motivated by a question by Tobias Kienzler and its wonderful answers. I begin as in the linked question... Using the Taylor expansion $$f(z+a) = \sum_{k=0}^\infty ...