没有三角函数的三角积分

IF 1.1 Q3 EDUCATION & EDUCATIONAL RESEARCH

Teaching Mathematics and Its Applications Pub Date : 2016-12-01 DOI:10.1093/TEAMAT/HRV020

J. Quinlan, J. Kolibal

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引用次数: 0

摘要

整合的教学技巧可能是乏味的，而且往往缺乏灵感。我们提出了一种明显但未被充分利用的方法，利用正弦和余弦的复指数表示来求各种三角函数的不定积分。其目的不仅仅是为学生提供另一种处理三角积分的方法。它引入了一个框架，学生可以更好地理解更高级的数学思想，如拉普拉斯逆变换，也提供了一个机会，与详细的代数操作涉及二项展开。

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Trigonometric integration without trigonometric functions

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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来源期刊

Teaching Mathematics and Its Applications EDUCATION & EDUCATIONAL RESEARCH-

CiteScore

2.40

自引率

25.00%

发文量

期刊介绍： The journal provides a forum for the exchange of ideas and experiences which contribute to the improvement of mathematics teaching and learning for students from upper secondary/high school level through to university first degree level. A distinctive feature of the journal is its emphasis on the applications of mathematics and mathematical modelling within the context of mathematics education world-wide. The journal"s readership consists of mathematics teachers, students, researchers and those concerned with curriculum development and assessment, indeed anyone concerned about the education of users of mathematics.