Calculus is the “Mathematics of Change”. Originally calculus was about change that occurred in tiny incremental steps, but 200 years ago, mathematics became obsessed with the concept of “infinity” and calculus became about change that occurred in incremental steps that are so infinitely small they effectively don’t exist.
And so by making the step-size of change so infinitesimally small, we can mathematically say that “in the limit to infinity” the size of each step effectively goes to zero; and thus coarse incremental change effectively becomes smooth continuous change.
In this section we will briefly look at the history of smooth compressible mathematical change…
Here we examine
- How “Linearization” and “Linear Dynamics” have, to-date, been the cornerstone of all of mathematical science: Linearization
- How the mathematics defines smooth “Continuous Change”using an infinitesimally small “Unit of Change”: Calculus
- How to define a mathematical “Step-Size of Growth and Decay” using an infinitesimally small “Unit of Linear Change”: What is “e” ?
- How to define a mathematical “Step-Size of Oscillation” using an infinitesimally small “Unit of Angular Change”: Euler’s Identity