Reading...
Play button
Play button
Use LEFT and RIGHT arrow keys to navigate between flashcards;
Use UP and DOWN arrow keys to flip the card;
H to show hint;
A reads text to speech;
12 Cards in this Set
- Front
- Back
|
Newton
|
When he lived: 1642-1727
Where he worked: England (Cambridge and London) Generalized the binomial theorem using an infinite series Used coordinate geometry to find solutions to Diophantine equations Inventor of Infinitesimal calculus (used series a lot) |
|
|
Lagrange
|
When he lived: 1736-1813
Where he worked: Prussia (Berlin) and France Lagrange multipliers and differential calculus Lagrange’s Theorem (group theory) |
|
|
Cauchy
|
First to define complex numbers as pairs of real numbers
Couchy’s integral theorem Series and the idea of convergence |
|
|
D'Alembert
|
When he lived: 1717-1783
Where he worked: France Ratio tests of convergence for a series Fundamental theorem of algebra Work on the development of partial differential equations |
|
|
History of Algebra
|
Algebra was fully geometric in 1800BC - Babylonian
Could only go up to cubics Diophantus contributed by completing the square Could not use negatives |
|
|
Theory of Equations
|
Ferro depressed cubic and Tartaglia could solve cubics
Ferrari figured out how to solve all quartics Galois proved that n-degree polynomials when n≥5 could not be solved in the general case using radicals |
|
|
Trigonometry
|
Trig was used to find the ratio of the distance between the earth and sun and the earth and moon
Used tabe of chords instead of angles Pascal and Newton: derivitive of trig functions |
|
|
Logarithms
|
Napier published a book about logarithms
Napier invents new function Nap(X) = n nap(x) defined mechanically |
|
|
Coordinate Geometry
|
used in late greek geometry
Fermat used polar and clyindrical coordinates to graph w/o negative numbers Laying foundation for calculus |
|
|
Calculus
|
Problems precipitating calculus
(1) Volume, area, length (2) Study of Motion (3) Ballistics (4) Optics Galileo solved ballistics problem Fermat invents algebraic method to find slope of tangent line |
|
|
Solving Diophantine Equations
|
50 US coins make $1. What is the number of coins of each type?
100 people, 1 each per vehicle pay $100 to cross a river ib a ferry. It costs $5/truck, $3/car, .10/bicycle. How many trucks, cars, bicycles? |
|
|
Computing LCM and GCD
|
GCD(3005,1001)
LCM(3005, 1001) GCD (1024, 986) LCM (1024, 986) |
