Experimental Blog #108

Quotes and notes from "A Tour of the Calculus" by David Berlinski

"The calculus is the story this ... scientific culture of the West ... first told itself as it became the modern world." "In its largest aspect ... the calculus is a great ... spectacular theory of space and time ..." "The calculus is a mathematical theory ... to represent or recreate the real world in terms of the real numbers."

"The system composed of the natural numbers, the integers, the fractions, and the irrational numbers acquires a new identity as the real number system ..."

The author, David Berlinski, writes that the polynomial functions include: the constant functions, the power functions, and the root functions. He also describes the exponential functions, the logarithmic functions, and the trigonometric functions. The continuities created by these functions, or mathematical equations, have derivatives, which are real numbers at a local point on a Cartesian map of the function; and integrals, which are real numbers representing bounded areas below a Cartesian map of these functions.