ProofWiki:Mathematicians/Jacob Bernoulli

Swiss mathematician (also known as James, Jacques or Jakob) best known for his work on probability theory and development of the calculus.

Developed the technique of Separation of Variables, and in 1696 solved what is now known as Bernoulli's (Differential) Equation.

Elder brother of Johann Bernoulli, with whom he famously quarrelled.

Nationality

Swiss

History

• Born: 27 Dec 1654 in Basel, Switzerland
• Died: 16 Aug 1705 in Basel, Switzerland

Theorems

• Bernoulli Distribution, Bernoulli Trial and Bernoulli Process
• Bernoulli Numbers
• Bernoulli Differential Equation
• Bernoulli's Theorem, or the Law of Large Numbers

Books and Papers

• 1713: Ars Conjectandi (The Art of Conjecture) (posthumous)

Also see

• John J. O'Connor and Edmund F. Robertson: "Jacob Bernoulli": MacTutor History of Mathematics archive

• George F. Simmons: Differential Equations (1972): $\S 6$
• George F. Simmons: Calculus Gems (1992), Chapter $\text {A}.20$