Trigonometric integration without trigonometric functions

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2016-12-01 DOI:10.1093/teamat/hrv020

James Quinlan;Joseph Kolibal

引用次数: 0

Abstract

Teaching techniques of integration can be tedious and often uninspired. We present an obvious but underutilized approach for finding antiderivatives of various trigonometric functions using the complex exponential representation of the sine and cosine. The purpose goes beyond providing students an alternative approach to trigonometric integrals. It introduces a framework in which students can better understand more advanced mathematical ideas such as the inverse Laplace transform and also affords an opportunity to work with detailed algebraic manipulations involving the binomial expansion.

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没有三角函数的三角积分

整合的教学技巧可能很乏味，而且往往缺乏灵感。我们提出了一种明显但未充分利用的方法，使用正弦和余弦的复指数表示来寻找各种三角函数的反导数。其目的不仅仅是为学生提供一种三角积分的替代方法。它介绍了一个框架，在这个框架中，学生可以更好地理解更先进的数学思想，如拉普拉斯逆变换，并提供了一个机会来处理涉及二项式展开的详细代数运算。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.