The point of this chapter is to gather together all of the standard ``transcendental'' functions, dealing with their definitions, their properties, their derivatives and integrals, and why they come up in calculus.
Many new functions, such as the square root or the logarithm, are first described as the inverse of other functions. This section deals with the general way of dealing with inverses, and a method, called implicit differentiation, to find the derivative of the inverse from the original function.
Trigonometric functions really come into their own in calculus. As a subject of its own, trigonometry is often an overwhelming list of identities and definitions, but in calculus, these functions model behavior that is essential for understanding many natural phenomena, and quantify geometric relationships.
Logarithms used to be primarily a calculational tool for dealing with complex arithmetic computations. They formed the basis for the construction of slide rules. But even though they are only of historical interest as a calculational tool, they are still vital in calculus. These functions provide another great source of models of natural processes, including many biological systems.
Hyperbolic functions are often viewed as merely an arcane exercise in constructing functions that look somewhat like trigonometric functions, but they do legitimately model some physical and geometric phenomena, and are widely used in the sciences and engineering. Since they are defined entirely in terms of exponential functions, in a sense they are nothing new, but they do provide some new twists.
Copyright (c) by David L. Johnson, last modified
On 25 Apr 2000, 16:37..