BASIC CALCULUS

• Egyptian Moscow Papyrus


  Calculating volumes and areas can be traced to the
• Calculus


  Known in its early history as infinitesimal calculus
• Infinitesimal calculus focused on

  Limits

  Functions

  Derivatives

  Integrals

  Infinite series
• Isaac Newton & Gottfried Leibniz 


  Invented calculus in the mid 17th century
• Calculus

  A small stone used for counting
• Branch of mathematics

  Limits

  Derivatives

  Integrals

  Infinite sum
• 2 major branches

  Differential calculus

  Integral calculus
• Integral calculus 


  Was being used as an idea
• Eudoxus (408-355BC)


  Used the method of exhaustion
• Archimedes (287-212BC)


  Continued eudoxus idea and invented HEURISTICS
• Ibn al-Haytham (Athens) 


  Derived a formula for the sum of the fourth powers of an arithmetic
• In the 12th century

  Indian mathematician Bhaskara describe "Rolles Theorem"
• Sharaf al-din al-tusi


  Discovered the derivative of a cubic polynomial
• Bonaventura Cavalieri


  Argued that volumes be computed by the sums of the volumes of cross sections
• Bonaventura Cavalieri 


  Work's was not well respected
• Infinitesimal quantities with finite difference in Europe was done by

  John Wallis

  Isaac Barrow

  James Gregory
• Proved the 2nd fundamental theorem of calculus in 1675


  Isaac barrow

  James Gregory
• Isaac Newton 


  Credited with many of the beginnings of calculus
• Isaac Newton 


  Introduced product rule
• Chain rule & higher deratives


  Solves physic problems
• Isaac Newton 


  Used calculus to explain many physics problems. He also manipulate infinitesimal
• Gottfried Wilhelm Leibniz (German)


  Systemized the ideas of calculus of infinitesimal

  Spent time determining appropriate symbols

  Paid more attention to formality
• Gottfried Wilhelm Leibniz


  Began with integrals
• Isaac Newton 


  Derived result first

  But Leibniz published first

  Claimed Leibniz stole ideas from unpublished notes
• Isaac Newton & Gottfried Wilhelm Leibniz 


  The name of study called "The science of fluxions"
• He was the one who validated the second fundamental theorem of calculus

  Barrow
• What year calculating volumes and ares traced to the Egyptian Moscow Papyrus?

  1820 BC
• In the mid-17th century, he was the one wh ocreated calculus

  Gottfried Leibniz
• Calculus known in its early history as _ calculus

  infinitesimal
• Newton claimed leibniz stole ideas from unpublished notes writtin to the

  Royal Society
• In what year Archimedes continued Eudoxus idea and invented heuristics, similar to integration to calculate area.

  287-212 BC
• He derived a formula for the sum of the fourth powers of an arithmetic progression.

  Ibn al-haytham
• He discovered the derivative of a cubic polynomial

  Saraf al-din al-tusi