Fundamentals of Calculus
Calculus is defined as this
The mathematics of change
The most important philosopher & the most famous Pythagorean
Plato
Triangle represents this
Change in
He essentially developed the discipline of logic
Aristotle
The Scientific Revolution
The overthrow of Aristotle's natural philosophy, reintroduction of Platonic-Pythagorian project, the mathematization of motion, not science overthrowing religion, start and end as stated in book
A mathematical description of stationary objects, objects whose forces are in equilibrium, a principle of hydrostatics
Archimedes Principle
He dropped objects off of the Leaning Tower of Pisa
Galileo
Formula for velocity
distance/time
The West's main mathematics book for 2,500 years
Euclid's Elements
Physics comes from the Greek word physis, which means this
nature
Galileo's Law of Free Fall did not account for this
Weight or mass
He wrote "On the Rvolution of the Heavenly Spheres"
Nicholas Copernicus
Formula for a balanced lever
w1 x d1 = w2 x d2 or w1/w2 = d2/d1
According to the Greeks this was the purest form of mathematics
Geometry
Calculus is Latin for this
pebble, stone
What we now call science used to be called this
Natural Philosophy
He wrote "Principia"
Isaac Newton
Aristotle's Law of Free Fall
w1/w2 = d1/t1 x t2/d2 = v1/v2
If we don't understand the history of calculus we won't understand this
Western Culture
Your speed at a given instant
Instantaneous speed
A problem calculus was invented to solve
describe continually changing velocity & acceleration, find the slope of a curve, the tangent line to a curve & area under a curve
Their motto was "All is number"
The Pythagoreans
Galileo's Law of Free Fall
d=1/2at^2 or d1/t1^2=d2/t2^2
Asserted that motion is impossible
Zeno's paradox
This type of speed doesn't actually exist
Average Speed