What is Calculus?

Davidson, J. (n.d.). What is calculus? Retrieved June 27, 2019, from https://www.sscc.edu/home/jdavidso/mathadvising/AboutCalculus.html

Summary:  

“What is Calculus” explores the creation (or discovery) of the branch of maths.  Calculus is not as tough as it’s reputed to be – with a good understanding of algebra then understanding calculus is the next step.  

A little history – math, arithmetic and geometry have been around since ancient times.  The idea of algebra was around, but the tools (the operations and a number system) had not yet been discovered.  It was not until the 9th century AD that these were available and used by a Persian, al-Khwarizmi, to develop algebra.  But algebra and geometry were not well linked.  

In the late 16th century, Rene Descartes used a graph with two axis (one vertical and the other horizontal) to name the position of objects on the plane.  The position was described using a pair of numbers, the horizontal position was the x’s and the vertical was y’s.  With this, Descartes was able to use algebra to represent geometric objects.

Later, in the 17th century, calculus was developed independently by two mathematicians (Newton and Leibnitz) in the 1670s as a need to understand constant change: the change in the speed of an accelerating object, or the effects of gravity on a falling object – not an average, but the speed at a specific time.  Today, calculus is the foundation for sciences, engineering, and advanced maths.

  

Things Learned:

Three things needed to be successful in calculus are: the ability to apply algebra skills, understand the concepts (not memorize), and dedication.

My Question:

This answers my question about mathematical thinking by learning about the beginning of calculus and how it was developed through the use of mathematical thinking.  These two mathematicians looked for patterns of objects in the and described how they changed using logic and patterns.