十八世纪的数学发展【英文】.pptVIP

In 18th century mathematics is already a modern science Mathematics begins to develop very fast because of introducing it to schools Therefore everyone have a chance to learn the basic learnings of mathematics Thanks to that, large number of new mathematicians appear on stage There are many new ideas, solutions to old mathematical problems,researches which lead to creating new fields of mathematics. Old fields of mathematics are also expanding. FAMOUS MATHEMATICIANS LEONHARD EULER Leonhard Paul Euler(1707-1783) He was a Swiss mathematician Johann Bernoulli made the biggest influence on Leonhard 1727 he went to St Petersburg where he worked in the mathematics department and became in 1731 the head of this department 1741 went in Berlin and worked in Berlin Academy for 25 years and after that he returned in St Ptersburg where he spent the rest of his life. Euler worked in almost all areas of mathematics: geometry, calculus, trigonometry, algebra,applied mathematics, graph theory and number theory, as well as , lunar theory, optics and other areas of physics. He introduced several notational conventions in mathematics Concept of a function as we use today was introduced by him;he was the first mathematician to write f(x) to denote function He also introduced the modern notation for the trigonometric functions, the letter e for the base of the natural logarithm (now also known as Euler’s number), the Greek letter Σ for summations and the letter i to denote the imaginary unit He wrote 45 books an over 700 theses. His main book is Introduction in Analisyis of the Infinite. Analysis He discovered ways to express various logarithmic functions using power series, and he successfully defined logarithms for negative and complex numbers He also defined the exponential function for complex numbers, and discovered its relation to the trigonometric functions EULER’ S FORMULA For any real number x, Euler’s formula states that the complex exponential function satis