The History of Calculus
Pendidikan Matematika Universitas Negeri Jakarta
The concept of infinity
• Time seems without end
• Space and time can be unendingly subdivided
• Space is without bound
https://www.youtube.com/watch?v=rBVi_9qAKTU
Katz, 2009
https://www.youtube.com/watch?v=hS8spfLuLl0
Newton: calculus as mathematics of change and motion (the method of fluxions)
• Newton was a physicist, mathematician and cosmologist who was prominent in the 17th century.
• One of his many achievements was the invention of calculus. His own work in physics undoubtedly brought him to this issue.
• Newton started by trying to describe the speed of a falling object. When he did this, he found that the speed of a falling object increases every second, but that there was no existing mathematical explanation for this.
• For Newton, the basic ideas of calculus had to do with motion.
Leibniz: differential and integral notations
• Leibniz’s idea, out of which his calculus grew, was the inverse relationship of sums and differences in the case of sequences of numbers. He investigated relationships between the summing and differencing of finite and infinite sequences of numbers.
• He demonstrated integral calculus for the first time to find the area under the graph of y =
ƒ(x). Integral calculus is part of infinitesimal calculus, which in addition also comprises differential calculus.
• In general, infinitesimal calculus is the part of mathematics concerned with finding
tangent lines to curves, areas under curves, minima and maxima, and other geometric and analytic problems.
• Leibniz’s calculus differed from Newton’s mainly in notation. Interestingly, many students of calculus today have come to prefer Leibniz’s notation.
• Leibniz introduced the two notations: d and to represent his generalization of the idea of difference and sum.
https://www.youtube.com/watch?v=6wb60tcilMQ
‘Calculus Priority Dispute’
Katz, 2009
The Great Calculus Controversy
Who did it first?
LEIBNIZ
Leibniz developed calculus mainly for general problems
NEWTON
Newton developed calculus
mainly as a tool to solve dynamic
problems such as motion,
velocity, acceleration and gravity
LEIBNIZ
• The differential dx satisfying the rules
d(x + y) = dx + dy and d(xy) = xdy + ydx
• The symbol ∫ for integration NEWTON
A variable was regarded as a
“fluent,” a magnitude that flows with time;
Its derivative or rate of change with respect to time was called a
“fluxion,”
