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The Evolution of Calculus
Transcript of The Evolution of Calculus
•method behind fundamental theorem
Kerala school of astronomy and mathematics
•Independently created mathematical concepts
•located in India
Yuktibhāā: first text on calculus.
Madhava of Sangamagrama
•Findings: taylor series, infinite series, early forms of differentiation, area under curve = integral by Sarah Fall and Olivia Zerphy The Evolution of Calculus The Greeks Creation of Numbers Calculus in Medieval Times Gottfried Wilhelm Leibniz Sir Isaac Newton Calculus Continues to Evolve Hilbert's 23 Unsolved Problems of Mathematics Eoxodus (408-355 BC)- Method of Exhaustion
First use of the ideas behind limits
Archimedes (287-212 BC)
Precurser to ideas of integral calculus
Posed four famous paradoxes. http://mathforum.org/isaac/problems/zeno1.html
Years later, when Aristotle tried to solve them, he stumbled upon some of the ideas behind calculus. •500 AD- The number zero is invented in India Went to Cambridge in 1661
Taught himself mathematics
Published the Pricipia Mathematica (1687): explains motion of the universe with geometric approach.
differentiable calculus "Method of Fluxions"
Invented fundamental theorem of calculus Discovered Calculus between 1673 and 1676
1684- Published first accounts of differential calculus
Analytical approach (approach used today)
Modern calculus notation is from Leibniz, focused on infinite and abstract fewer contradictions
independently developed fundamental theorem of calculus
invented dy/dx notation
Invented matrixes to solve linear problems
Did work with integrals and infinitesimals Bolzano- first analytical proof of intermediate value theorem
Cauchy- Defined continuity in terms of infinitesimals
Differential calculus evolves with help from Gauss and Riemann.
Maclaurin, Rolle, and Euler developed different ways of using calculus. 1900
Solutions meant to further the discipline of math
Seven remain, called Millennium problems
Riemann Hypothesis most important unsolved conjecture.
New mathematics it always being discovered
Calculus has and will help to discover and prove knew disciplines in math. Zeno, Archimedes, and Eudoxus This allowed them to make numbers infinitely large or small
Ancient Greeks struggled with the concept of zero First known counting system was tallying tally marks found on bones from pre-historic time 3400 BC- Mesopotamian Base-60 system
3100 BC- Base 10 counting system is used in Egypt •Calculus is the study of change.
•Name comes from the Latin word for a rock used for counting.
•Before Leibniz and Newton, the term referred to any form of mathematics
•Differential Calculus and Integral Calculus
•Fundamental Theorem ZERO •First appeared in Babylon 3rd century BC
•Mayans independently invented zero in the 4th century
•First appeared 1st-5th centuries
•Initially used only as a placeholder
Brought to the West by Fibonacci in 1200 Greeks saw numbers as ratios of integers
•This caused wholes in the number line
•Developed methods to solve for these "holes" "In order to celebrate mathematics in the new millennium, The Clay Mathematics Institute of Cambridge, Massachusetts (CMI) established seven Prize Problems. The Prizes were conceived to record some of the most difficult problems with which mathematicians were grappling at the turn of the second millennium; to elevate in the consciousness of the general public the fact that in mathematics, the frontier is still open and abounds in important unsolved problems; to emphasize the importance of working towards a solution of the deepest, most difficult problems; and to recognize achievement in mathematics of historical magnitude."
http://www.claymath.org/millennium New mathematics it always being discovered
Calculus has and will help to discover and prove knew disciplines in math. New mathematics it always being discovered
Calculus has helped and will help to discover and prove new disciplines in math.
Calculus is only the beginning of what math with accomplish. What now? Caunchy's residue formula Sources lhttp://www.uiowa.edu/~c22m025c/history.html