 |
|
| |
|
|
|
at Global Oneness Community.
Share your dreams and let others help you with the interpretation!
Dream Sharing Forum
|
|
Multiple integral - Multiple integrals are not the same as iterated integrals | | Multiple integral - Multiple integrals are not the same as iterated integrals: Encyclopedia II - Multiple integral - Multiple integrals are not the same as iterated integrals | | It is easy to confuse the concepts of mutliple integral and iterated integral, especially since the same notation is often used for either concept. The notation
in some cases means an iterated integral rather than a true double integral. In an iterated integral, the outer integral
is the integral with respect to x of the following function of x:
A double integral, on the other hand is defined with respect to area in the xy-plane. I ...
See also:Multiple integral, Multiple integral - Multiple integrals are not the same as iterated integrals, Multiple integral - Multiple integrals, Multiple integral - Some practical applications, Multiple integral - Mathematical definition, Multiple integral - Theorems, Multiple integral - Double integral, Multiple integral - Triple integral, Multiple integral - Methods of integration, Multiple integral - Direct examination, Multiple integral - Formulas of reduction, Multiple integral - Change of variables, Multiple integral - Example of mathematical applications - Calculations of volume, Multiple integral - Multiple improper integral, Multiple integral - Bibliography | | | Multiple integral, Multiple integral - Bibliography, Multiple integral - Change of variables, Multiple integral - Direct examination, Multiple integral - Double integral, Multiple integral - Example of mathematical applications - Calculations of volume, Multiple integral - Formulas of reduction, Multiple integral - Mathematical definition, Multiple integral - Methods of integration, Multiple integral - Multiple improper integral, Multiple integral - Multiple integrals, Multiple integral - Multiple integrals are not the same as iterated integrals, Multiple integral - Some practical applications, Multiple integral - Theorems, Multiple integral - Triple integral, Integral, Divergence theorem, Stokes theorem, Green's theorem | | |
| | | Multiple integral: Encyclopedia II - Multiple integral - Multiple integrals are not the same as iterated integrals
Multiple integral - Multiple integrals are not the same as iterated integrals
It is easy to confuse the concepts of mutliple integral and iterated integral, especially since the same notation is often used for either concept. The notation
in some cases means an iterated integral rather than a true double integral. In an iterated integral, the outer integral
is the integral with respect to x of the following function of x:
A double integral, on the other hand is defined with respect to area in the xy-plane. If the double integral exists, then it is equal to either of the two iterated integrals (either "dy dx" or "dx dy"; see Fubini's theorem) and one often computes it by computing either of the iterated integrals. But sometimes the two iterated integrals exist when the double integral does not, and in some such cases the the two iterated integrals are different numbers, i.e., one has
For an elementary example (doable by the methods of first-year calculus), see examples of Fubini's theorem. This is an instance of rearrangement of a conditionally convergent integral.
The notation
may be used if one wishes to be emphatic about intending a double integral rather than an iterated integral.
Other related archivesCalculus, Cylinder, Divergence theorem, Fubini's theorem, Green's theorem, Integral, Jacobian determinant, Maxwell's equations, Pythagorean trigonometric identity, Sphere, Stokes theorem, Tetrahedron, antiderivative, area, boundary, calculus, conditionally convergent, constant functions, continuous function, coordinates (mathematics), cylinder, density, determining of the Jacobian matrix, distribution of charges, domain, double integral, electric field, electromagnetism, engineering, examples of Fubini's theorem, functions, hypervolumes, improper integral, inequality, infinitesimal, integral, iterated integral, measure, mechanics, moment of inertia, nabla in cylindrical and spherical coordinates, parallelepiped, parity, partial derivatives, physics, pyramid, radius, rectangle, simplex, sphere, variable, volume
 Adapted from the Wikipedia article "Multiple integrals are not the same as iterated integrals", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki |
|
|
|
More material related to Multiple Integral can be found here:
|
|
|
« Back
|
Search the Global Oneness web site |
|
|
|
|
|
Sneak-Peek of Global Oneness Community
Hi friend! The Global Oneness Community, the place for information and sharing about Oneness is not really launched yet (you will see there is still some clean up to do) ...but it is now open for a sneak-peek! And if you wish - please register and become one of the very first members to do so! Jonas
Forum Home,
Articles,
Photo Gallery,
Videos,
News,
Sitemap
...and much more!
|
