学术报告

#Math101 Session 38

Time：Apr. 9, 2026, 14:00-16:00

Location：C-208 East Teaching Building, Chang'an Campus

Speaker：Mr. Fei, Xiaoyue (Class of 2025)

Title：Exponential and trigonometric functions

Abstract：In this session, we focus on the rigorous construction and analysis of fundamental transcendental functions. We begin by developing the exponential function from a foundational perspective, emphasizing its definition via limits and power series. We then introduce double-indexed series and examine the conditions under which such series can be summed, with particular attention to convergence, rearrangement, and the interchange of summation order. Building on these results, we establish the key algebraic properties of the exponential function. Finally, we define the trigonometric functions in terms of the exponential function and recover their classical properties.

（文：申爽/审核：郭千桥）