# integral calculus

## Definitions

• WordNet 3.6
• n integral calculus the part of calculus that deals with integration and its application in the solution of differential equations and in determining areas or volumes etc.
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Webster's Revised Unabridged Dictionary
• Integral calculus a method which in the reverse of the differential, the primary object of which is to learn from the known ratio of the indefinitely small changes of two or more magnitudes, the relation of the magnitudes themselves, or, in other words, from having the differential of an algebraic expression to find the expression itself.
• Integral calculus See under Calculus.
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Chambers's Twentieth Century Dictionary
• Integral calculus the summation of an infinite series of differentials
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## Etymology

Chambers's Twentieth Century Dictionary
L.—calx.

## Usage

### In literature:

CALCULUS, DIFFERENTIAL AND INTEGRAL, in mathematics, is the method by which we discuss the properties of continuously varying quantities.
"The Nuttall Encyclopaedia" by Edited by Rev. James Wood
It was on differential and integral calculus.
"The World's Greatest Books, Vol X" by Various
W. S. B. WOOLHOUSE 1/6 Integral Calculus.
"French Polishing and Enamelling" by Richard Bitmead
A Treatise on the Integral Calculus and its Applications.
"The Works of William Shakespeare [Cambridge Edition] [9 vols.]" by William Shakespeare
In his work he gave the first sketch of an infinitesimal calculus and in his own way performed an integration.
"Progress and History" by Various
If we had lectured each other alternately on the Integral Calculus, Blanquette would have given us her rapt and happy attention.
"The Belovéd Vagabond" by William J. Locke
Their music is the integral calculus of the spheres.
"Shadows of Flames" by Amelie Rives
He may be regarded as the originator of the integral calculus.
"The New Gresham Encyclopedia. Vol. 1 Part 3" by Various
In the last century Maria Agnesi gave us a treatise on the differential and integral calculus.
"Woman in Science" by John Augustine Zahm
Elements of the Integral Calculus.
"Rob of the Bowl, Vol. I (of 2)" by John P. Kennedy
ELEMENTARY ILLUSTRATIONS OF THE DIFFERENTIAL AND INTEGRAL CALCULUS.
"Darwin, and After Darwin (Vol 3 of 3)" by George John Romanes
The differential calculus and the integral calculus were rapidly developed in the writings of Leibnitz and the Bernoullis.
"Encyclopaedia Britannica, 11th Edition, Volume 14, Slice 5" by Various
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### In news:

What do you know — integral calculus is actually good for something.
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### In science:

We refer to Dunford and Schwartz [18, Chapter VII.3] or to Gohberg et al. [19, 20] for an introduction to functional calculus for operators related with Riesz integrals.
Minimax adaptive tests for the Functional Linear model
However, due to their intuitive formulation and beauty, we begin by stating without proof Maxwell’s equations in integral form, and then the differential equations can be derived from well-known theorems of vector calculus.
Technical Notes on Classical Electromagnetism, with exercises
In order to obtain Maxwell’s equations in differential form in vacuum, one applies two theorems of calculus on the corresponding integral equations.
Technical Notes on Classical Electromagnetism, with exercises
Loop calculus deals with the Hilbert space of square-integrable functions which describe closed loops C (up to reparametrizations), and functionals thereof, F (C ).
SU(N) gauge theories at large N
In this appendix a differentiation and integration calculus for Grassmann variables will be established.
A Review of Minimal Supersymmetric Electro-Weak Theory
Using the calculus of variations, one minimizes the action integral, based upon eq. (1), A = Z Ldτ = Z m0 cdτ = Z m0 c√uαuα dτ , which is clearly invariant under the Lorentz group.
Polydimensional Relativity, a Classical Generalization of the Automorphism Invariance Principle
The integral in eq.(12) can be easily evaluated by closing the l0 -contour e.g. in the lower half-plane and using residue calculus.
Peripheral Nucleon-Nucleon Phase Shifts and Chiral Symmetry
Among the directions that were represented were dynamical triangulations, random surface theory, Regge calculus, causal sets, decoherent histories, topological quantum ﬁeld theory and lattice and path integral approaches to nonperturbative quantum gravity.
Matters of Gravity, the newsletter of the APS TG on gravitation
However, it is clear there has been progress on the issue of the measure of the path integral in Regge calculus.
Matters of Gravity, the newsletter of the APS TG on gravitation
Rewriting this by aj and integrating it over the period, one can ﬁnd the 1-instanton contribution to the prepotential and the result coincides with the instanton calculus.
Non-perturbative Solutions to N=2 Supersymmetric Yang-Mills Theories -Progress and Perspective-
Abstract This paper gives a summary of our approach to invariants of three manifolds via right integrals on ﬁnite dimensional Hopf algebras and their relation to the Kirby calculus.
Right integrals and invariants of three-manifolds
The deﬁning property of a right integral is a categorical algebra translation of the handle-sliding move in the Kirby calculus.
Right integrals and invariants of three-manifolds
A basic result in one-variable calculus is “integration by substitution”.
Some calculus with extensive quantities: wave equation
Recall that a vector space in the present context just means an R-module. A vector space E is called Euclidean if differential and integral calculus for functions R → E is available.
Some calculus with extensive quantities: wave equation
In fact, the basis of transform calculus is the integration of functions of a complex variable.
Complex functions as lumps of energy
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