微积分发展简史(二)(国外英文资料).docVIP

微积分发展简史(二)(国外英文资料) A large circle represents what I have learned, but there are so many blanks outside the circle that means ignorance to me. And the bigger the circle, the longer the circumference of the circle, and the greater the gap between it and the outside world. This shows that I do not understand the place is still very big. A brief history of calculus (two) The creation of calculus Because of the integrity of the operation and the universality of the application Make it a powerful tool for the study of Natural Science Hailed as the supreme victory of the human spirit Since eighteenth Century Calculus is widely used at the same time Has also been continuously developed and improved Content is more and more rich Generalized integral The Riemann integral is defined in terms of bounded integrand and finite integral intervals However, these restrictions need to be removed in application This leads to the concept of generalized integrals Generalized integrals include two kinds of integral and integral 1823 French mathematician Cauchy (A.L. Cauchy) (1789~1857) in his introduction to the infinitesimal analysis tutorial, he discusses the improper integral at which some values of the integral interval become infinite (improper integral) or when the integral interval tends to (infinite integral) He also puts forward the concept of integral principal value in combination with physical meaning The concept of generalized integral is extended to the generalized integral with parametric variables In the aspects of the properties of generalized integral and parametric integral, the convergence of generalized integral and the study of convergence Cauchy, Abel (N.H., Abel 1802~1829), de Nicolai (P.G.L, Dirichlet) 1805~1859) and Wells Dreas (K.T.W. Weierstrass) 1815~1897) mathematicians have done a lot of work Two. Multivariate calculus Calculus of multivariate functions It is an important part of calculus Multivariate calculus is naturally formed in the development and appli