题目：三角函数的定义

报告人：李良攀

报告类型：山东大学本科生分析数学选讲

报告时间：2020.09.25 Friday 17:00-18:00

腾讯会议 ID: 601 050 237

摘要：Using the least upper bound property of the real number system and the concept of length of monotone curves, we propose a definition of trigonometric functions for the teaching of Calculus.

本科生分析数学选讲的内容安排：

Definition of trigonometric functions, real numbers as infinite decimals, inverse function theorems, open mapping theorems, implicit function theorems, definition of Riemann's zeta function, Lebesgue measure on Euclidean spaces, Littlewood's fourth principle, oscillatory integrals, compactness in Functional Analysis, generalised functions, Brownian motion, heat and wave kernels.