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Everything about Integral
Operation in calculus
In mathematics, an integral is the continuous analog of a sum, and is used to calculate areas, volumes, and their generalizations. The process of computing an integral, called integration, is one of the two fundamental operations of calculus, along with differentiation. Integration was initially used to solve problems in mathematics and physics, such as finding the area under a curve, or determining displacement from velocity. Usage of integration expanded to a wide variety of scientific fields thereafter. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: IntegralA 5-minute orientation
- Skim a recent paper: Hyperglycemia and Oxidative Stress: An Integral, Updated and Critical Overview of Their Metabolic InterconnectionsInfluential work since 2022
- Pick up a classic book: Calculus Made EasyThe most-reprinted book on the subject
- Read the landmark paper: A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and CracksCited 7,371 times
- Go sideways: Fundamental theorem of calculusA closely related topic
- Go sideways: Riemann integralA closely related topic
📖 Definitions
Adjective Constituting a whole together with other parts or factors; not omittable or removable.
Adjective Of, pertaining to, or being an integer.
Adjective Relating to integration (“the process of finding the integral [noun] of a function”).
Adjective Being the root of some monic polynomial in A.
🏆 Landmark papers (most cited)
A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks
A new integral equation formalism for the polarizable continuum model: Theoretical background and applications to isotropic and anisotropic dielectrics
An iteration method for the solution of the eigenvalue problem of linear differential and integral operators
Phase separation of integral membrane proteins in Triton X-114 solution.
Crystal structure of an integral membrane light-harvesting complex from photosynthetic bacteria
Path integral approach to quantum Brownian motion
CONTIN: A general purpose constrained regularization program for inverting noisy linear algebraic and integral equations
A constrained regularization method for inverting data represented by linear algebraic or integral equations
🆕 Influential since 2022
Hyperglycemia and Oxidative Stress: An Integral, Updated and Critical Overview of Their Metabolic Interconnections
The SHARK integral generation and digestion system
Integral multi-valorization of agro-industrial wastes: A review
An Adaptive Sliding-Mode Controller With a Modified Reduced-Order Proportional Integral Observer for Speed Regulation of a Permanent Magnet Synchronous Motor
The Athena X-ray Integral Field Unit: a consolidated design for the system requirement review of the preliminary definition phase
📚 Books worth reading
Calculus Made EasySilvanus Phillips Thompson · 1914
Complex integration and Cauchy's theoremG. N. Watson · 1914
HomelandR. A. Salvatore · 1990
Digital designM. Morris Mano, Michael Ciletti · 1984
ProphetFrank E. Peretti · 1992
Vorlesungen über Differential- und IntegralrechnungRichard Courant · 1927
Design with operational amplifiers and analog integrated circuitsSergio Franco · 1988
The BoxMarc Levinson · 2006
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Fundamental theorem of calculus The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating its slopes, or rate of change at every…
- Riemann integral In real analysis, the Riemann integral is a rigorous definition of the integral of a function on an interval. It defines the integral by approximating…
- Antiderivative In calculus, an antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral of a function f is a differentiable function…
- Improper integral In mathematical analysis, an improper integral is an extension of the notion of a definite integral to cases that violate the usual assumptions for that…
- Riemann–Stieltjes integral In mathematics, the Riemann–Stieltjes integral is a generalization of the Riemann integral, named after Bernhard Riemann and Thomas Joannes Stieltjes.…
- Numerical integration In analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral. The term numerical…
- Line integral In mathematics, a line integral is an integral where the function to be integrated is evaluated along a curve. The terms path integral, curve integral…
- Lebesgue integral In mathematics, the integral of a non-negative function of a single variable can be regarded, in the simplest case, as the area between the graph of that…