Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Reformulating $ε$-$δ$ Limits in a Pedagogically Cleaner Way

Joel Q. L. Chang

Abstract

We provide a simple reformulation of the $ε$-$δ$ limit definition introduced in undergraduate calculus courses that enhances its pedagogical value for conceptual understanding and computational skill.

Reformulating $ε$-$δ$ Limits in a Pedagogically Cleaner Way

Abstract

We provide a simple reformulation of the - limit definition introduced in undergraduate calculus courses that enhances its pedagogical value for conceptual understanding and computational skill.
Paper Structure (9 sections, 19 theorems, 106 equations)

This paper contains 9 sections, 19 theorems, 106 equations.

Table of Contents

  1. Introduction
  2. The Reformulation
  3. Common Pedogogical Examples
  4. Implementing the Limit Theorems
  5. Generalising the Limit Theorems
  6. Reformulating Infinity-Related Limits
  7. Further Applications
  8. Conclusion
  9. Appendix

Key Result

Theorem 1

Let $c \in \mathbb{R}$, $A \subseteq \mathbb{R}$, and $f : A \to \mathbb{R}$ be a real-valued function. Then Alternately phrased using the fizzle function vocabulary,

Theorems & Definitions (53)

  • Definition 1
  • Definition 2
  • Theorem 1
  • proof : Proof of Theorem \ref{['thm: novel_epsilon_delta']}
  • Theorem 2
  • Remark 1
  • Example 1
  • proof : Solution to Example \ref{['eg: polynomial']}
  • Theorem 3
  • Remark 2
  • ...and 43 more