CS118 Programming Languages

Differential and Integral Calculus

The formulas of analysis

If you use it a lot, it should be simple to read and write

• zero
• one
• addition
• equality
• the base of natural logarithms
• the ratio of diameter to circumference
• square root of -1

The slope of a line

dy/dt	. y
Leibniz	Newton
d-ism	dot-age

Leibniz, a few years junior to Newton, traveled to Britain to show Newton his work in calculus. Newton stayed with the dots. British mathematicians proudly refused to recognize the "continental" notation. So, the calculus was developed by

Bernoulli, Euler, Fourier, Lagrange, Laplace, Legendre, Poisson...

One hundred years later a secret society was formed at Cambridge to study the notation introduced by Leibniz. Simple formal algebraic rules such as

(dx/dy).(dy/dz) = dx/dz

actually represented limit theorems, but one did not have to rethink the limits time after time.

In a final twist of fate, the Bishop Berkely, who despised the shameless modern disbelief in God, used Leibniz' notation to twit his opponents (the mathematicians among them), saying "There is more evidence of the existence of God than of being able to divide by zero." He had learned his schoolboy algebra well.