**Calculus + TOK=Better Than Actual Math**

design by Dóri Sirály for Prezi

The study of how things change

Divided into:

Differential Calulus- rate of change

Integral Calculus (accumulation)

The concepts learned in algebra and geometry are extended, usually using limits (applied mathematics)- math scoop

What is Calculus?

THE CALCULUS CONTROVERSY

How Does It Connect to Ways of Knowing?

Used in more that just scientific and mathematical fields. We use it in every day life.

Algorithms used for finding people and locations on google maps, twitter, facebook, instagram, snapchat, etc. (ABC Science)

The World?

The earliest developers of math called the "Ancients" led the forefront the modern day mathemathics.

History?

Music + Calculus

Research has shown that certain pieces of music end up being more popular and mainstream because of their "mathematical structure"

Music theorists and composers often used mathematics to understand music (The Small Venue Survivalist)

Mathematics is the "basis of sound" and "sound itself" in its musical aspects

Every piece of music is really just a function

Reason

Language

Imagination

Faith

In order according to time period

Pythagoras (c. 580 - 500 B.C.)

Euclid (c. 300 B.C.)

Archimedes (c.287-212 B.C.)

Him and his followers discovered irrrational # but it went agaisnt their faith

No one belived Euclid was one man, many belived he was the leader of a group who wrote the "Elements".

Archimedes found the sum of a geometric series in such a way as to indicate that he understood the concept of limits. He also, among other things, calculated pi; used the sum of infinte rectangles to find the area under a curve

Sir Isaac Newton (1642-1727)

Newton actually discovered calculus between 1665 and 1667 after his university closed due to an outbreak of the Plague. Newton was only 22 at the time, and he preferred not to publish his discoveries. Meanwhile, in Germany, Leibniz discovered Calculus independently and he was very open with his findings. This led to a bitter dispute between the two mathematicians later known as the "Great Sulk". Today it is well known that both men discovered calculus independantly of the other, Leibniz about 8 years after Newton. Newton is best known for his work in physics, and especially his three laws of motion.

Gottfried Wilhelm Leibniz (1646-1716)

Though Leibniz is credited with discovering calculus after Newton he is thought to be the true founder of modern European mathematics. Not only was he a great mathematician, he was also a philosopher, scientist, logician, diplomat and a lawyer. Leibniz is well known for introducing notations that are still used in Calculus today, such as 'dy/dx' and the integral symbol. It is even attributed to him that the '=' symbol is used throughout the world.