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.
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Screenshot PDFs for my videos are available at the website wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary.
My research papers can be found at my Research Gate page, at www.researchgate.net/profile/
My blog is at njwildberger.com/, where I will discuss lots of foundational issues, along with other things.
Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at www.openlearning.com/courses/... Please join us for an exciting new approach to one of mathematics' most important subjects!
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Here are all the Insights into Mathematics Playlists:
Elementary Mathematics (K-6) Explained: / playlist
list=PL8403C2F0C89B1333
Year 9 Maths: • Year9Maths
Ancient Mathematics: • Ancient Mathematics
Wild West Banking: • Wild West Banking
Sociology and Pure Mathematics: • Sociology and Pure Mat...
Old Babylonian Mathematics (with Daniel Mansfield): / playlist
list=PLIljB45xT85CdeBmQZ2QiCEnPQn5KQ6ov
Math History: • MathHistory: A course ...
Wild Trig: Intro to Rational Trigonometry: • WildTrig: Intro to Rat...
MathFoundations: • Math Foundations
Wild Linear Algebra: • Wild Linear Algebra
Famous Math Problems: • Famous Math Problems
Probability and Statistics: An Introduction: • Probability and Statis...
Boole's Logic and Circuit Analysis: • Boole's Logic and Circ...
Universal Hyperbolic Geometry: • Universal Hyperbolic G...
Differential Geometry: • Differential Geometry
Algebraic Topology: • Algebraic Topology
Math Seminars: • MathSeminars
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And here are the Wild Egg Maths Playlists:
Triangle Centres: • ENCYCLOPEDIA OF TRIANG...
Six: An elementary course in pure mathematics: • Six: An elementary cou...
Algebraic Calculus One: • Algebraic Calculus One
Algebraic Calculus Two: • Algebraic Calculus Two
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