双曲函数在力学、非欧几何学、复变函数论等学科中都有重要的应用,但在中学的初等微积分或大学的数学分析的教学中,却常常不予介绍,或者语焉不详。其实,即使对于微积分的计算来讲,双曲函数也常可起到简化计算的作用。并且,只要将其与三角函数相联系并相类比,学生便能够利用熟知 Hyperbolic functions have important applications in mechanics, non-Euclidean geometry, complex function theory and other disciplines, but they are often not introduced in the teaching of elementary calculus in elementary schools or mathematics analysis in universities, or are unknown. In fact, even for calculus calculations, hyperbolic functions often serve to simplify calculations. And, as long as it is linked and analogous to the trigonometric function, students can use the familiar