Online books
- Keisler, H. Jerome, Elementary Calculus: An Approach Using Infinitesimals, University of Wisconsin
- Stroyan, K.D., A Brief Introduction to Infinitesimal Calculus, University of Iowa
- Mauch, Sean, Sean's Applied Math Book, CIT, an online textbook that includes a complete introduction to calculus
- Crowell, Benjamin, Calculus, Fullerton College, an online textbook
- Garrett, Paul, Notes on First-Year Calculus
- Hussain, Faraz, Understanding Calculus, an online textbook
- Kowalk, W.P., Integration Theory, University of Oldenburg. A new concept to an old problem. Online textbook
- Sloughter, Dan, Difference Equations to Differential Equations, an introduction to calculus
- Numerical Methods of Integration at Holistic Numerical Methods Institute
- P.S. Wang, Evaluation of Definite Integrals by Symbolic Manipulation (1972) - a cookbook of definite integral techniques
| Integrals |
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| Methods |
Riemann integral In the branch of mathematics known as real analysis, the Riemann integral, created by Bernhard Riemann, was the first rigorous definition of the integral of a function on an interval. While the Riemann integral is unsuitable for many theoretical purposes, it is one of the easiest integrals to define. Some of these technical deficiencies can be · Lebesgue integral In mathematics, Lebesgue integration refers to both the general theory of integration of a function with respect to a general measure, and to the specific case of integration of a function defined on a sub-domain of the real line or a higher dimensional Euclidean space with respect to the Lebesgue measure. This article focuses on the more general · Bochner integral In mathematics, the Bochner integral, named for Salomon Bochner, extends the definition of Lebesgue integral to functions which take values in a Banach space, as the limit of integrals of simple functions · Daniell integral One of the main difficulties with the traditional formulation of the Lebesgue integral is that it requires the initial development of a workable measure theory before any useful results for the integral can be obtained. However, an alternative approach is available, developed by Percy J. Daniell in his 1918 paper "A general form of integral& · Darboux integral In real analysis, a branch of mathematics, the Darboux integral or Darboux sum is one possible definition of the integral of a function. Darboux integrals are equivalent to Riemann integrals, meaning that a function is Darboux-integrable if and only if it is Riemann-integrable, and the values of the two integrals, if they exist, are equal. Darboux · Henstock–Kurzweil integral · Haar integral In mathematical analysis, the Haar measure is a way to assign an "invariant volume" to subsets of locally compact topological groups and subsequently define an integral for functions on those groups · Lebesgue-Stieltjes integral In measure-theoretic analysis and related branches of mathematics, Lebesgue-Stieltjes integration generalizes Riemann-Stieltjes and Lebesgue integration, preserving the many advantages of the latter in a more general measure-theoretic framework · Pettis integral In mathematics, the Pettis integral or Gelfand–Pettis integral, named after I. M. Gelfand and B.J. Pettis, extends the definition of the Lebesgue integral to functions on a measure space which take values in a Banach space, by the use of duality. The integral was introduced by Gelfand for the case when the measure space is an interval with · Pfeffer integral In mathematics, the Pfeffer integral is an integration technique created by Washek Pfeffer as an attempt to extend the Henstock integral to a multidimensional domain. This was to be done in such a way that the fundamental theorem of calculus would apply analogously to the theorem in one dimension, with as few preconditions on the function under · Riemann-Stieltjes integral In mathematics, the Riemann–Stieltjes integral is a generalization of the Riemann integral, named after Bernhard Riemann and Thomas Joannes Stieltjes · Regulated integral In mathematics, the regulated integral is a definition of integration for regulated functions, which are defined to be uniform limits of step functions. The use of the regulated integral instead of the Riemann integral has been advocated by Nicolas Bourbaki and Jean Dieudonné
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| Improper Integrals |
Improper integral In calculus, an improper integral is the limit of a definite integral as an endpoint of the interval of integration approaches either a specified real number or ∞ or −∞ or, in some cases, as both endpoints approach limits · Gaussian integral The Gaussian integral, or probability integral, is the integral of the Gaussian function e−x2 over the entire real line. It is named after the German mathematician and physicist Carl Friedrich Gauss. The integral is:
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| Stochastic integrals |
Itō integral Itō calculus, named after Kiyoshi Itō, extends the methods of calculus to stochastic processes such as Brownian motion . It has important applications in mathematical finance and stochastic differential equations. The central concept is the Itō stochastic integral · Stratonovich integral In stochastic processes, the Stratonovich integral is a stochastic integral, the most common alternative to the Itō integral. While the Ito integral is the usual choice in applied math, the Stratonovich integral is frequently used in physics · Skorokhod integral In mathematics, the Skorokhod integral, often denoted δ, is an operator of great importance in the theory of stochastic processes. It is named after the Ukrainian mathematician Anatoliy Skorokhod. Part of its importance is that it unifies several concepts:
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Categories: Integral calculus | Integrals | Functions and mappings | Linear operators in calculus
<<Table of Contents Integration is an important concept in mathematics which, together with differentiation, forms one of the main operations in calculus. Given a function ƒ of a real variable x and an interval [a, b] of the real line, the definite integral | Show All>>
