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 http://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 https://www.researchgate.net/profile/...

My blog is at http://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 https://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 the Insights into Mathematics Playlists:

   • MathHistory: A course in the History ...  
   • WildTrig: Intro to Rational Trigonometry  
   • Math Foundations  
   • Wild Linear Algebra  
   • Famous Math Problems  
   • Box Arithmetic  
   • Elementary Mathematics (K-6) Explained  
   • Year9Maths  
   • Ancient Mathematics  
   • Wild West Banking  
   • Sociology and Pure Mathematics  
   • Sociology and Pure Physics  
   • Old Babylonian Mathematics  
   • Probability and Statistics: an introd...  
   • Boole's Logic and Circuit Analysis  
   • Universal Hyperbolic Geometry  
   • Differential Geometry  
   • Algebraic Topology  
   • MathSeminars  
   • Playing Go  
   • Diffusion Symmetry: A bridge between ...  

Here are the Wild Egg Maths Playlists (some available only to Members!)

   • Algebraic Calculus One  
   • Classical to Quantum (Members only)  
   • Algebraic Calculus Two  
   • Advice for mathematics exploration (M...  
   • Solving Polynomial Equations (Members...  
   • The Hexagrammum Mysticum (Members only)  
   • Algebraic Calculus and dCB curves (Me...  
   • Dynamics on Graphs (Members only)  
   • Playlist  
   • Triangle Geometry  
   • Explorations with q-series (Members o...  
   • Six: An elementary course in Pure Mat...  
   • Maxel Inverses and Orthogonal Polynom...  
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