Newton's Calculus: What He Came Up With & Notation Used

  • Thread starter Thread starter pi-r8
  • Start date Start date
  • Tags Tags
    Calculus
AI Thread Summary
Newton developed foundational concepts in calculus, focusing on limits and real-world applications, but his notation differed significantly from what is used today. Most modern calculus notation, including symbols for derivatives and integrals, was introduced by Leibniz, who favored a more abstract approach. While Newton contributed to the understanding of derivatives and integrals, he did not formalize them in the same way as Leibniz. The credit for the invention of calculus is often shared between the two due to their distinct methodologies and contexts. Ultimately, Newton's contributions laid essential groundwork, even if his notation was not adopted in contemporary calculus.
pi-r8
Messages
138
Reaction score
30
How much calculus did Newton himself actually come up with? And what did it look like? I've read that most of the notation we use today was actually invented by Leibniz- if that's true, then what did Newton's notation look like?
 
Physics news on Phys.org
Netwon went a long way and for this reason 'credit' for the 'invention' of calculus is often shared as Newton was based primarily on true reality nad the use of limits where as Leibniz was far mroe embracing of the abstract and infinite.

Perhaps this reflects the very different way they approached the problem due to their situations.
 
So did Newton come up with the equations for equations for derivatives and integrals that we use today? I'm thinking of things like (d/dx)(sinx) = cosx, and such.
 
Hello everyone, Consider the problem in which a car is told to travel at 30 km/h for L kilometers and then at 60 km/h for another L kilometers. Next, you are asked to determine the average speed. My question is: although we know that the average speed in this case is the harmonic mean of the two speeds, is it also possible to state that the average speed over this 2L-kilometer stretch can be obtained as a weighted average of the two speeds? Best regards, DaTario
Thread 'Beam on an inclined plane'
Hello! I have a question regarding a beam on an inclined plane. I was considering a beam resting on two supports attached to an inclined plane. I was almost sure that the lower support must be more loaded. My imagination about this problem is shown in the picture below. Here is how I wrote the condition of equilibrium forces: $$ \begin{cases} F_{g\parallel}=F_{t1}+F_{t2}, \\ F_{g\perp}=F_{r1}+F_{r2} \end{cases}. $$ On the other hand...
I know that mass does not affect the acceleration in a simple pendulum undergoing SHM, but how does the mass on the spring that makes up the elastic pendulum affect its acceleration? Certainly, there must be a change due to the displacement from equilibrium caused by each differing mass? I am talking about finding the acceleration at a specific time on each trial with different masses and comparing them. How would they compare and why?

Similar threads

Replies
17
Views
5K
Replies
5
Views
2K
Replies
6
Views
2K
Replies
10
Views
3K
Replies
17
Views
6K
Back
Top