History of Calculus 
History of Calculus
by UNSW / N.J. Wildberger
Video Lecture 15 of 32
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Date Added: January 19, 2015

Lecture Description

Calculus has its origins in the work of the ancient Greeks, particularly of Eudoxus and Archimedes, who were interested in volume problems, and to a lesser extent in tangents. In the 17th century the subject was widely expanded and developed in an algebraic way using also the coordinate geometry of Descartes. This is one of the most important developments in the history of mathematics. Calculus has two branches: the differential and integral calculus. The former arose from the study by Fermat of maxima and minima of functions via horizontal tangents. The integral calculus computes areas and volumes beyond the techniques of Archimedes. It was developed independently by Newton and Leibnitz, but others contributed too. Newton's focus was on power series, for which differentiation and integration can be done term by term using a formula of Cavalieri, and which gave remarkable new formulas for pi and the circular functions. He had a dynamic view of the subject, motivated in large part by physics. Leibnitz was more interested in closed forms, and introduced the notation which we use today. Both used infinitesimals, in the form of differentials.

Course Index

Course Description

In this course, Prof. N.J. Wildberger from UNSW provides a great overview of the history of the development of mathematics. The course roughly follows John Stillwell's book 'Mathematics and its History' (Springer, 3rd ed)Starting with the ancient Greeks, we discuss Arab, Chinese and Hindu developments, polynomial equations and algebra, analytic and projective geometry, calculus and infinite series, number theory, mechanics and curves, complex numbers and algebra, differential geometry, topology and hyperbolic geometry.  This course is meant for a broad audience, not necessarily mathematics majors. All backgrounds are welcome to take the course and enjoy learning about the origins of mathematical ideas. Generally the emphasis will be on mathematical ideas and results, but largely without proofs, with a main eye on the historical flow of ideas. At UNSW, this is MATH3560 and GENS2005. NJ Wildberger is also the developer of Rational Trigonometry: a new and better way of learning and using trigonometry.

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