We apply the arguments from elementary calculus that are used to differentiate cosine and sine to hyperbolic cosine and hyperbolic sine, and by so doing produce the natural exponential function by ...

Mathematics Magazine presents articles and notes on undergraduate mathematical topics in a lively expository style that appeals to students and faculty throughout the undergraduate years. The journal ...

A PHASE relation familiar to students of applied mathematics exists between a simple harmonic oscillation and its derivative. Similar relations exist between exponential functions and their ...