一般来说,“一个”微积分是以纯粹形式化的方式发展起来的抽象理论。
“微积分”,更恰当地称为分析(或实分析,或在较旧的文献中称为无穷小分析),是数学的一个分支,研究量的变化率(可以解释为曲线的斜率)以及物体的长度、面积和体积。微积分有时分为微分和积分微积分,分别关注导数
和积分
。
虽然与微积分相关的思想早已为人所知(阿基米德的穷竭法是微积分的一种形式),但直到牛顿和莱布尼茨的独立工作,才发展出现代优雅的微积分工具和思想。即便如此,也过了很多年,直到像魏尔斯特拉斯这样的数学家才将这门学科置于数学上严谨的基础之上。
另请参阅
弧长,
面积,
变分法,
变量替换定理,
导数,
微分,
椭球微积分,
外代数,
流数,
流数,
分数微积分,
泛函微积分,
微积分基本定理,
亥维赛德微积分,
积分,
积分,
雅可比行列式,
Lambda 演算,
Kirby 微积分,
Malliavin 微积分,
多元微积分,
偏导数,
谓词演算,
命题演算,
斜率,
张量微积分,
影演算,
体积 在 MathWorld 课堂中探索该主题
使用 Wolfram|Alpha 探索
参考文献
Anton, H. Calculus: A New Horizon, 6th ed. New York: Wiley, 1999.Apostol, T. M. Calculus, 2nd ed., Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra. Waltham, MA: Blaisdell, 1967.Apostol, T. M. Calculus, 2nd ed., Vol. 2: Multi-Variable Calculus and Linear Algebra, with Applications to Differential Equations and Probability. Waltham, MA: Blaisdell, 1969.Apostol, T. M.; Chrestenson, H. E.; Ogilvy, C. S.; Richmond, D. E.; and Schoonmaker, N. J. A Century of Calculus, Part I: 1894-1968. Washington, DC: Math. Assoc. Amer., 1992.Apostol, T. M.; Mugler, D. H.; Scott, D. R.; Sterrett, A. Jr.; and Watkins, A. E. A Century of Calculus, Part II: 1969-1991. Washington, DC: Math. Assoc. Amer., 1992.Ayres, F. Jr. and Mendelson, E. Schaum's Outline of Theory and Problems of Differential and Integral Calculus, 3rd ed. New York: McGraw-Hill, 1990.Borden, R. S. A Course in Advanced Calculus. New York: Dover, 1998.Boyer, C. B. A History of the Calculus and Its Conceptual Development. New York: Dover, 1989.Courant, R. and John, F. Introduction to Calculus and Analysis, Vol. 1. New York: Springer-Verlag, 1999.Courant, R. and John, F. Introduction to Calculus and Analysis, Vol. 2. New York: Springer-Verlag, 1990.Hahn, A. Basic Calculus: From Archimedes to Newton to Its Role in Science. New York: Springer-Verlag, 1998.Kaplan, W. Advanced Calculus, 4th ed. Reading, MA: Addison-Wesley, 1992.Marsden, J. E. and Tromba, A. J. Vector Calculus, 4th ed. New York: W. H. Freeman, 1996.MathPages. "Calculus and Differential Equations." http://www.mathpages.com/home/icalculu.htm.Mendelson, E. 3000 Solved Problems in Calculus. New York: McGraw-Hill, 1988. Strang, G. Calculus. Wellesley, MA: Wellesley-Cambridge Press, 1991.Weisstein, E. W. "Books about Calculus." http://www.ericweisstein.com/encyclopedias/books/Calculus.html.在 Wolfram|Alpha 中引用
微积分
引用为
韦斯坦因,埃里克·W. “微积分”。来自 MathWorld——Wolfram Web 资源。 https://mathworld.net.cn/Calculus.html
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