28 - Euler's Method in Euler's Words

Summary

Introduction

Euler's method is a technique for finding approximate solutions to differential equations addressed in a number of undergraduate mathematics courses. Various current texts include Euler's method for calculus [4], differential equations [1], mathematical modeling [9], and numerical methods [2] students. Each of those courses are opportunities to give students an opportunity to read Euler's own brief description of the algorithm, and in the process come to understand the technique and its limitations from Euler himself. This capsule includes historical information about Euler and his development of the approximation method. Additionally, I describe Student Assignments (Appendix A) I use to connect that history to the mathematics the students are learning. The activities are designed to deepen student understanding of Euler's method specifically and reinforce learning of calculus skills in general. I also include a translation of Euler's writing on the topic (Appendix B).

Historical preliminaries

Leonhard Euler (1707–1783) was one of the most gifted of all mathematicians. Excellent biographies of Euler, some identifying the voluminous quantity of his mathematical writing, are available [6], which interested readers are encouraged to explore. One of Euler's many gifts was his ability to write mathematics clearly and understandably.