Chapter 4: Differentiable and Continuous Functions on the Real Line

Differentiation involves taking the limit of a function of a continuously varying quantity, so it involves a different kind of limit from sequences. We start by studying limits of this kind, and introduce limits of functions and continuity. Nevertheless, Proposition 4.2 shows how to relate a lot of this to the results of the last chapter on seuences. In this chapter we'll also prove the basic rules of calculus for computing derivatives: the Chain rule, the product rule, and the quotient rule.

Chapter Contents

Class 14
- Limits of Functions
Class 15
- Continuous Functions
- Special Functions
Class 16
Class 17
- Definition and Arithmetic Properties
Class 18
- Composition of Functions
- Where Are We Now?
Class 19

Analysis WebNotes by John Lindsay Orr.
Comments to the author: jorr@math.unl.edu

All contents copyright (C) 1996 John L. Orr
University of Nebraska--Lincoln
All rights reserved

Last modified: May 1996