The Greeks
The first person to view the world as fundamentally mathematical.
Who was Pathagoras?
The mathematics of change.
What is calculus?
The name for something that stands for or represents things that change.
What is a variable?
The value you approach but never reach.
What is a limit?
show: distance as a function of time
What is d(t)?
The ancient Greek thinker who argued that motion is impossible because a runner must first reach the halfway point, then half of what remains, and so on forever.
Who is Zeno?
These two brilliant rivals both invented calculus — one giving us limits and fluxions, the other giving us the integral sign and modern notation.
Who are Newton and Leibniz?
When two variables are in relation to each other.
What is a function?
lim g(x) = lim (x+1) as x approaches zero.
What is 1?
The physical property represented by delta d / delta t.
What is average velocity?
Non-physical objects that literally exist outside of the physical world, independent of minds - - absolutely perfect, eternal, and unchanging.
What are forms?
This person fired the first shot of the Scientific Revolution.
Who is Copernicus?
A visual representation for how variables behave.
What is a graph?
The three central concepts of calculus.
What are the limit, derivative, and integral of a function?
The first step in the Method of Increments.
What is find the formula for delta d / delta t.
The mysterious, non-physical realm where Ideas and Forms exist.
What is Plato's Heaven?
Who was Galileo?
How much velocity/speed changes as time changes.
What is acceleration?
The specific paradox of something real but seems incoherent because it requires we divide by zero.
What is the paradox of instantaneous speed?
What is take the limit of delta d / delta t as delta t approaches zero?
The combination of Christianity and the teachings/beliefs of Aristotle.
What is scholasticism?
A period in western history when people saw a chance to turn away from religion and toward reason.
What was the Enlightenment?
A mathematical system that combines algebraic formulas and Cartesian coordinates.
What is analytical geometry?
The name of the process for when we pretend a forbidden value is a valid value for the limit of a function.
What is the method of direct substitution?
The ability to manipulate symbols and numbers [ut] arrive at knowledge of the physical world *without* doing any experiments.
What is theoretical physics?