History of Calculus
Since Pre-Calculus is a course that is meant to prepare you for Calculus, I thought that I would give you a timeline of the history of Calculus. The history can be broken into three different eras: ancient, medieval, and modern.
Ancient
1820 B.C -- Calculations of volumes and areas (one goal of integral calculus). Found in the Eqyptian Moscow papyrus but the formulas were just instructions without any indication on how they were performed and some of them were later found out to be wrong.
408-355 B.C -- Exodus used the method of exhaustion, which uses the concept of the limit to calculate areas and volume.
287-212 B.C-- Archimedes developed the idea of the method of exhaustion further and invented heuristics which resembles the methods of integral calculus.
3rd Century AD -- From China Liu Hui reinvented the method of exhaustion in order to find the area of a circle.
5th Century AD -- Zu Chongzhi developed a method called Cavalieri's Principle in order to find the volume of a sphere
Medieval
14th Century -- Indian mathematician Madhava of Sangamagrama and the Kerala School of Astronomy and Mathematics stated
components of calculus such as the taylor series, approximations of the infinite series, an integral test of convergence, early forms of
differentiation, term by term integration, iterative methods for solutions of non-linear equations, and the theory that the area under a curve is its
integral.
Modern
1658 -- Blaise Pascal works on the sine function and almost discovers calculus
1665- Issac Newton discovers the first form of calculus
1669 -- Newton writes the book On the Analysis of Equations Unlimited in their Number of Terms and includes his mthod for finding areas under curves
1670 -- Isaac Barrow uses methods similar to calculus to draw tangents to curves, find the lengths of curves, and the areas bounded by curves
1675 -- Gottfried Leibniz introduces the modern notation for integration and the notation dx/dy for differentiation; he also determines the product rule for
differentiation.
1677 -- Leibniz finds the quotient rule for differentiation.
1686 -- Leibniz publishes his method of integral calculus in an issue of Acta Eruditorum.
1694 -- Jean Bernoulli discovers the method known as l'Hospital's Rule; it is known by that name because Marquis Antoine de l'Hospital bought it from Bernoulli and introduced it in his influential 1696 textbook Analysis of Infinitesimals.
1797 -- Joseph-Louis Lagrange introduces the notations f'(x) and y' for the derivatives of f(x) and y,respectively.
1854 -- Bernhard Riemann defines the integral in a way that does not require continuity.
Ancient
1820 B.C -- Calculations of volumes and areas (one goal of integral calculus). Found in the Eqyptian Moscow papyrus but the formulas were just instructions without any indication on how they were performed and some of them were later found out to be wrong.
408-355 B.C -- Exodus used the method of exhaustion, which uses the concept of the limit to calculate areas and volume.
287-212 B.C-- Archimedes developed the idea of the method of exhaustion further and invented heuristics which resembles the methods of integral calculus.
3rd Century AD -- From China Liu Hui reinvented the method of exhaustion in order to find the area of a circle.
5th Century AD -- Zu Chongzhi developed a method called Cavalieri's Principle in order to find the volume of a sphere
Medieval
14th Century -- Indian mathematician Madhava of Sangamagrama and the Kerala School of Astronomy and Mathematics stated
components of calculus such as the taylor series, approximations of the infinite series, an integral test of convergence, early forms of
differentiation, term by term integration, iterative methods for solutions of non-linear equations, and the theory that the area under a curve is its
integral.
Modern
1658 -- Blaise Pascal works on the sine function and almost discovers calculus
1665- Issac Newton discovers the first form of calculus
1669 -- Newton writes the book On the Analysis of Equations Unlimited in their Number of Terms and includes his mthod for finding areas under curves
1670 -- Isaac Barrow uses methods similar to calculus to draw tangents to curves, find the lengths of curves, and the areas bounded by curves
1675 -- Gottfried Leibniz introduces the modern notation for integration and the notation dx/dy for differentiation; he also determines the product rule for
differentiation.
1677 -- Leibniz finds the quotient rule for differentiation.
1686 -- Leibniz publishes his method of integral calculus in an issue of Acta Eruditorum.
1694 -- Jean Bernoulli discovers the method known as l'Hospital's Rule; it is known by that name because Marquis Antoine de l'Hospital bought it from Bernoulli and introduced it in his influential 1696 textbook Analysis of Infinitesimals.
1797 -- Joseph-Louis Lagrange introduces the notations f'(x) and y' for the derivatives of f(x) and y,respectively.
1854 -- Bernhard Riemann defines the integral in a way that does not require continuity.