The Greeks
The first person to view the world as fundamentally mathematical.
Who was Pythagoras?
This person replaced Aristotle as the ruler of science after the Scientific Revolution.
Something that stands for-or represents-things that change.
What is a variable?
The value you approach but never reach.
What is a limit?
What is average velocity?
All is number.
What is the Pythagorean motto?
The mathematics of change.
What is Calculus?
A relation between variables.
What is a function?
The limit of g(x) as x approaches 0.
lim g(x) = lim (x+1)
x->0 x->0
What is 1?
When we imagine plugging in a forbidden value for the limit of a function.
What is the method of Direct Substitution?
Nonphysical objects that literally exist outside the physical world, independent of any minds. They are absolutely perfect, they exist eternally, and they never, ever change.
What are Forms?
This person fired the first shot of the Scientific Revolution?
Who was Copernicus?
A picture of a function showing how variables behave together.
What is a graph?
Daily Double!!
The three central concepts of calculus.
What is the limit of a function, the derivative of a function, and the integral of a function? (acceptable: What is limit, derivative, and integral?)
Find a formula for delta d/delta t and then take the limit of delta d/delta t as t approaches 0.
What is the Method of Increments?
The mysterious, nonphysical "realm" or "world" where the Ideas or Forms exist.
What is "Plato's Heaven?"
A period in Western history when folks saw a chance to turn from religion to reason.
What is the Enlightenment?
A mathematical system that combines algebraic formulas with pictures in Cartesian coordinates.
What is analytical geometry?
The example used over and over in the book: something that is clearly real in the physical world, but seems mathematically incoherent because it requires dividing by zero.
What is the paradox of speed?
Calculate multiple average velocities, with the interval of time getting smaller and smaller, and determine to what value the average velocity is approaching.
What is the Method of Approximation?
The combination of Aristotle with Christianity.
What is Scholasticism?
This person invented "new science" using the methods of mathematics and experiments, which was the science of motion.
Who was Galileo?
Daily Double!!!
This has to do with how much velocity changes as time changes.
What is acceleration?
The limit of the rate of change in the dependent variable with respect to the independent variable as the change in the independent variable approaches 0.
What is a Derivative?
The ability to manipulate symbols and numbers in order to arrive at knowledge of the physical world without actually doing any experiments.
What is theoretical physics?