a repository of mathematical know-how

Revision of I have a problem to solve in real analysis from Thu, 16/04/2009 - 13:07

Quick description

This is an experimental page that is designed to provide automatic assistance to anybody who wants to solve a problem in real analysis. The idea is that by choosing appropriate answers to questions that will be put to you, you will be led to a Tricki page that will help you with your particular analysis problem (if a helpful page exists). The article is not by any means complete, but the hope is that it will eventually be able to provide assistance with a wide range of problems that might be set as not too difficult exercises on a first course in real analysis.

How to solve your problem

Let's begin by narrowing down the subject matter of the problem a little. Most first courses in real analysis begin with a discussion of the real numbers and limits of sequences and sums, then they move to continuous functions, then they discuss differentiability, and then Riemann integration. Further topics may include pointwise and uniform convergence of sequences of functions, and differentiability of functions from \mathbb{R}^n to \mathbb{R}^m. While there are some techniques that work for more than one of these subareas, it will be convenient to discuss them on separate pages. So the first question is this: which of the following descriptions best fits the area that your problem is about?

I need to find a real number with a certain property

I have a problem about the convergence of a sequence

I have a problem about an infinite sum

I have a problem about a continuous function

I have a problem about differentiation

I have a problem about integration

I have a problem about uniform convergence

I have a problem about differentiation in higher dimensions