Exam 2 Flashcards
among newton and leibniz who discovered calculus first and who was the first to publish
newton discovered first leibniz published first
which mathematicians were considered the greatest of the 18th century
Lagrange and euler
which mathematician was the first to recognize the fundamental theorem of calculus (differentiation and integration are inverse)
issac barrow
which greek philosopher is widely known for his paradoxes of motion
Zeno of Elea
which mathematician wrote a 5 volume treatise on celestial mechanics
Pierre Simon Laplace
who was the first mathematician to propose that a rigorious definition of the limit was necessary
Jean le Rond d’Alembert
which 3 feats were achieved prior to the development of calculus by newton/leibniz
determination of the volume of a sphere
determination of the volume of a pyramid/cone
area of a parabolic arch
whose work did L’opital publish in his calculus textbook
Johann Benoulli
who used his clout with the prussian academy of sciences to cut off scientific communication and collaboration with england
compare and contrast laplace and lagrange
Laplace focused on having solid basis for his work and made sure to clearly explain his discoveries. Lagrange’s work was harder to understand. He often wrote things such as “it is clear that []” which actually required hours of work to prove.
describe lagrange’s contributions to the foundations of calculus, why they were significant, and the reason his approach failed
wanted to make calculus more rigorous
important because there were many advancements in the field, but they did not have a strong foundation and were mainly based on intuition and trial and error. Lagrange based calculus on taylor series but failed to properly account for convergence so he was unsuccessful
five aspects of leonhard euler’s life and work
extremely prolific, but had a less rigorious basis for his work
developed the constant e
developed the equation e^ix = cos(x)+isin(x) or e^ipi = 1
described as most prominent mathematician of 18th century
also took an interest in other fields that were not mathematics
