Infinitesimal Calculus 2025 pdf epub mobi 用户评价 评分☆☆☆ 其实是 Elementary nonstandard analysis (on the real line) 。用了hyperreal之后几乎所有原本需要极限的证明都变成了借助hyperreal代数性质而得到形式化的直观。证明连续的非标准定义和极限定义的等价性的时候才发现自己并没有完全掌握epsilon-delta。实轴...
Baron - The origin of infinitesimal calculus (无穷小微积分的起源,1969) 英文回复此楼» 本帖附件资源列表欢迎监督和反馈:小木虫仅提供交流平台,不对该内容负责。 本内容由用户自主发布,如果其内容涉及到知识产权问题,其责任在于用户本人,如对版权有异议,请联系邮箱:xiaomuchong@tal.com 附件1 : Baron_-_...
(1989). Infinitesimal calculus interpreted in infinitary logic. In: Shinoda, J., Tugué, T., Slaman, T.A. (eds) Mathematical Logic and Applications. Lecture Notes in Mathematics, vol 1388. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083672 Download citation .RIS .ENW .BIB ...
, or have ricci curvature bounded from below . in these contexts, sobolev spaces constitute a key ingredient for the development of a non-smooth calculus (see [ 5 , 9 , 13 , 28 , 29 ] and the references therein). all these conditions are in strong contrast to the upper sectional curva...
In 1734, Bishop Berkeley called the infinitesimals of Newton's calculus foundations “ghosts of departed quantities.” He was questioning the intellectual consistency of atheists who believed in infinitesimals. It was not until 1960, that the “fiction” of infinitesimals became a reality with the ...
They present it as being "just calculus" and expanding [itex] f(x_1,y_1) = f( x + \alpha \ u_x(x,y), y + \alpha \ u_y(x,y) ) [/itex] is indeed just calculus. This is exactly equivalent to what I wrote above, only instead of [itex]\alpha u_x(x,y) [/itex...
Vector Calculus James R. Kirkwood, in Mathematical Physics with Partial Differential Equations, 2013 Surface Integrals of Vector Functions A major reason why we study vector functions over a surface is to measure flux—an idea that we now describe. Flux is an important concept in electricity and ...
Could O’Hagan have been using the word as an attributive noun? After all, infinitesimal calculus (a.k.a. calculus) is not meant to be infinitely small; it the calculus of infinitesimals (a.k.a. infinitesimal quantities). (Just kidding.) ...
很好的一本书
In a general geodesic space little can be said about the structure of tangent cones, but if Y is locally a CAT(κ) space then tangent cones have interesting geometric properties and can be used as basic tools to build a robust first-order calculus. In order to understand the geometry of ...