What did Gottfried Leibniz discover?
Gottfried Wilhelm Leibniz (b. 1646, d. 1716) was a German philosopher, mathematician, and logician who is probably most well known for having invented the differential and integral calculus (independently of Sir Isaac Newton).
Did Archimedes discover calculus?
With these techniques, scholars determined Archimedes was well on his way to developing calculus, nearly 1,000 years before Isaac Newton. Archimedes also explored a branch of mathematics, now known as combinatorics, which deals with multiple ways of solving a problem.
What did Leibniz discover about calculus?
In the same manuscript the product rule for differentiation is given. By autumn 1676 Leibniz discovered the familiar d(xn)=nxn−1dx for both integral and fractional n. Leibniz began publishing his calculus results during the 1680s.
Why Gottfried Leibniz is the Father of calculus?
He was perhaps the first to explicitly employ the mathematical notion of a function to denote geometric concepts derived from a curve, and he developed a system of infinitesimal calculus, independently of his contemporary Sir Isaac Newton.
What did Archimedes do for calculus?
Considered to be the greatest mathematician of ancient history, and one of the greatest of all time, Archimedes anticipated modern calculus and analysis by applying the concept of the infinitely small and the method of exhaustion to derive and rigorously prove a range of geometrical theorems, including: the area of a …
Who invented calculus first Newton or Leibniz?
While Newton began development of his fluxional calculus in 1665–1666 his findings did not become widely circulated until later. In the intervening years Leibniz also strove to create his calculus. In comparison to Newton who came to math at an early age, Leibniz began his rigorous math studies with a mature intellect.
Who invented calculus Leibniz?
Gottfried Wilhelm Leibniz
But Gottfried Wilhelm Leibniz independently invented calculus. He invented calculus somewhere in the middle of the 1670s. He said that he conceived of the ideas in about 1674, and then published the ideas in 1684, 10 years later.
Who invented calculus bhaskaracharya?
Bhāskara and his works represent a significant contribution to mathematical and astronomical knowledge in the 12th century….
| Bhāskara II | |
|---|---|
| Discipline | Mathematician, astronomer |
| Main interests | Algebra, Arithmetic, Trigonometry |
Who invented calculus derivatives?
Calculus is commonly accepted to have been created twice, independently, by two of the seventeenth century’s brightest minds: Sir Isaac Newton of gravitational fame, and the philosopher and mathematician Gottfried Leibniz.
What is the rate constant of a first order reaction?
Differential Rate Law for a First-Order Reaction 1 ‘k’ is the rate constant of the first-order reaction, whose units are s -1. 2 ‘ [A]’ denotes the concentration of the first-order reactant ‘A’. 3 d [A]/dt denotes the change in the concentration of the first-order reactant ‘A’ in the time interval ‘dt’.
How do you find the Order of a first order reaction?
Units of k = M (1-n).s -1 (where ‘n’ is the order of the reaction) Since the reaction order of a first-order reaction is equal to 1, the equation is transformed as follows: Units of k = M (1-1).s -1 = s -1 For a first-order reaction, if a graph is plotted with ln [A] on the Y-axis and time on the X-axis, what will it look like?
What is the integrated rate equation for a first-order reaction?
The integrated rate equation for a first-order reaction is: [A] = [A] 0 e -kt. Where, [A] is the current concentration of the first-order reactant. [A] 0 is the initial concentration of the first-order reactant. t is the time elapsed since the reaction began. k is the rate constant of the first-order reaction.
What is the differential equation for first order kinetics?
The differential equation describing first-order kinetics is given below: (2.3.1) R a t e = − d [ A] d t = k [ A] 1 = k [ A] The “rate” is the reaction rate (in units of molar/time) and k is the reaction rate coefficient (in units of 1/time). However, the units of k vary for non-first-order reactions.