Alice and the Wonderland of the exponential saga.
Thuy Nguyen
eBook
(, March 3, 2019)
After writing the short book “Help me with the exponential function!” (HEXP), it became apparent that there should be an exposition on the elementary transcendental functions built from the first principle. So this book is in a way a sequel to the other one. Computer is extensively used to illustrate the theoretical proposal, some codes in “small basic” and “Scilab” are given with enough details to jump starting the novice on writing short codes with these tools.Exponential is so familiar that we do not give much thoughts on the subject; however, the hyperbolic functions present such a wealth of curiosity that a humoristic style is used is this book, following Lewis Carroll’s steps as hinted in the title. Complex numbers were built from the rotation operation, trigonometric functions defined through triangles were reviewed and redefined to lead to the construction of Euler’s formula, using the properties of the exponential derived in the HEXP mentioned above. Applications in astronomy, engineering, physics and geometry were presented.Despite humor, the mathematics are serious. Like HEXP, the book is intended to be used by high-school students, parents who want to help their children in mathematics, students taking calculus and people who just need to brush up in mathematics.