Position function and its derivatives

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SUMMARY

The discussion centers on the origins of the position function in calculus and its derivatives, specifically velocity and acceleration. Participants reflect on Isaac Newton's foundational contributions to calculus and question whether the position function was intentionally designed for differentiation or if it was a discovery. The conversation highlights the evolution of mathematical notation and abstraction since Newton's time, emphasizing the beauty and structure of mathematics as it relates to physical concepts.

PREREQUISITES
  • Understanding of basic calculus concepts, including differentiation and integration.
  • Familiarity with the position, velocity, and acceleration relationships in physics.
  • Knowledge of Isaac Newton's contributions to calculus and physics.
  • Awareness of the historical development of mathematical notation and abstraction.
NEXT STEPS
  • Explore the historical context of calculus and Newton's methodologies.
  • Study the mathematical definitions and applications of position, velocity, and acceleration.
  • Learn about the evolution of mathematical notation from Newton's time to modern practices.
  • Investigate the philosophical implications of mathematical discovery versus invention.
USEFUL FOR

Students of calculus, physics enthusiasts, educators in mathematics, and anyone interested in the historical development of mathematical concepts.

PapalPhysicist
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Okay so I'm currently in cal 3. I've also taken physics 1 and 2. When I first saw the position function differentiated into velocity and then to acceleration I was awestruck. Math is beautiful and divinely structured. That's what I thought.

But as I've gone on and worked with it more and more a question has occurred. Newton created the basics of calculus. Much of what I have learned has been additions to his foundation, all the theorems and methods that allow for more complex integration and differentiation.

Now to my question. Did Newton create the position function? Was it created with the ability to then derive velocity and acceleration from it in mind?

Or was it something "discovered"?

I may be asking the wrong question here. Please guide me in the right direction if I am. The more math I've studied the more I see its beauty. I may not be the most studious but I'm definitely a curious person.
 
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Mathematics was primitive when Newton was alive. Newton expressed his thinking more in sentences and diagrams than in functions and equations. A lot of the abstraction and symbology we use today in mathematics was developed since then.
 

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