함수

개요

• 함수와 관련된 기본적인 개념과 수학에서 가장 기본적인 함수 몇가지를 배움.

배우기 전에 알고 있어야 하는 것들

• 기초적인 집합의 개념

중요한 개념 및 정리

• 일대일대응

초등함수의 예

• 다항함수 - 상수함수, 일차함수, 이차함수, ...
• 유리함수
• 지수함수
• 로그함수
• 삼각함수
• 쌍곡함수

메모

Early attempts to define a function were made by James Gregory (1687), Euler (1748), and, later in the 18th century, by La Croix, Lagrange, and d'Alembert.

All these attempts were intuitive, rough-and-ready affairs and none gained acceptance. Fourier and Cauchy, both around 1820, offered improved versions;

finally Dirichlet in 1837 identified the essential property of uniqueness": y is a function of x when to each value of x in a given interval there correspond as unique value of y". This is not quite the end of the story, of course;in time it became apparentt.

• [Atkinson2002]

관련논문

• [Atkinson2002]Where Do Functions Come from? Leigh Atkinson, The College Mathematics Journal, Vol. 33, No. 2 (Mar., 2002), pp. 107-112

• Evolution of the Function Concept: A Brief Survey Israel Kleiner, The College Mathematics Journal, Vol. 20, No. 4 (Sep., 1989), pp. 282-300

• An Introduction to Logarithms F. G. Brown, The Mathematical Gazette, Vol. 11, No. 160 (Oct., 1922), pp. 164-166

• A Brief History of Logarithms R. C. Pierce, Jr., The Two-Year College Mathematics Journal, Vol. 8, No. 1 (Jan., 1977), pp. 22-26
• History of the Exponential and Logarithmic Concepts Florian Cajori, The American Mathematical Monthly, Vol. 20, No. 1 (Jan., 1913), pp. 5-14