This preview shows page 1. Sign up to view the full content.
Calculus, Part 1
Predecessors of Newton/Leibniz
•
Area by Method of Exhaustion in antiquity
◦
Eudoxus
◦
Archimedes
•
India
•
Pedersen: “Many methods were developed to solve calculus problems; common to most of
them was their
ad hoc
character. It is possible to Fnd examples from the time before Newton
and Leibniz which, when translated into modern mathematical language, show that di±er
entiation and integration are inverse procedures; however, these examples are all related to
speciFc problems and not to general theories.”
•
Descartes’ Method for Fnding tangents
•
²ermat’s Method of Maxima and Minima
•
Cavalieri’s Principle: If crosssections are in a constant ratio, areas are in that same ratio.
•
Roberval’s quadrature of the cycloid
•
Wallis’s “arithmetic” integration
•
²ermat’s “logarithmic” integration
Newton and Leibniz
•
Pedersen: “The special merit of Newton and Leibniz was that they both worked out a general
theory of the inFnitesimal calculus. However, it cannot be said that either Newton or Leibniz
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 12/29/2011 for the course MATH 378 taught by Professor Wen during the Fall '10 term at SUNY Stony Brook.
 Fall '10
 wen
 Calculus

Click to edit the document details