John Gaston Leathern devotes his attention to "Volume and Surface Integrals Used in Physics," and more especially, perhaps, to a skilled inquiry into the difficulties which underlie their application in dealing with certain branches of applied mathematics.
The writer discusses in order the following subjects:—
the validity of the use of volume integrals to express the potential
the component attractions of bodies of discontinuous structure
the potentials and attractions of accurately continuous bodies
volume integrals:
their connection with surface integrals
their differentiation
their application to the theories of potential and of magnetism
their evaluation over regions extending to infinity
The reader is confronted with the problem of adapting to the generally admitted discrete properties of matter the principles of integration, involving as they do the endless subdivision of quantity and magnitude. Each point of serious difficulty is clearly presented, and the author shows, nevertheless, that there is justification for the use of the methods of the calculus, and that it is to be found in the appreciation of a principle not unknown in other branches of applied mathematics, and which, in the case considered, consists in the introduction of a subsidiary system of continuous structure capable of being integrated over, and of a density such that the potential or attraction when evaluated for the ideal substance is equivalent to the corresponding quantity which is the actual desideratum, or sensibly so, at least.
1103352667
The writer discusses in order the following subjects:—
the validity of the use of volume integrals to express the potential
the component attractions of bodies of discontinuous structure
the potentials and attractions of accurately continuous bodies
volume integrals:
their connection with surface integrals
their differentiation
their application to the theories of potential and of magnetism
their evaluation over regions extending to infinity
The reader is confronted with the problem of adapting to the generally admitted discrete properties of matter the principles of integration, involving as they do the endless subdivision of quantity and magnitude. Each point of serious difficulty is clearly presented, and the author shows, nevertheless, that there is justification for the use of the methods of the calculus, and that it is to be found in the appreciation of a principle not unknown in other branches of applied mathematics, and which, in the case considered, consists in the introduction of a subsidiary system of continuous structure capable of being integrated over, and of a density such that the potential or attraction when evaluated for the ideal substance is equivalent to the corresponding quantity which is the actual desideratum, or sensibly so, at least.
VOLUME AND SURFACE INTEGRALS USED IN PHYSICS
John Gaston Leathern devotes his attention to "Volume and Surface Integrals Used in Physics," and more especially, perhaps, to a skilled inquiry into the difficulties which underlie their application in dealing with certain branches of applied mathematics.
The writer discusses in order the following subjects:—
the validity of the use of volume integrals to express the potential
the component attractions of bodies of discontinuous structure
the potentials and attractions of accurately continuous bodies
volume integrals:
their connection with surface integrals
their differentiation
their application to the theories of potential and of magnetism
their evaluation over regions extending to infinity
The reader is confronted with the problem of adapting to the generally admitted discrete properties of matter the principles of integration, involving as they do the endless subdivision of quantity and magnitude. Each point of serious difficulty is clearly presented, and the author shows, nevertheless, that there is justification for the use of the methods of the calculus, and that it is to be found in the appreciation of a principle not unknown in other branches of applied mathematics, and which, in the case considered, consists in the introduction of a subsidiary system of continuous structure capable of being integrated over, and of a density such that the potential or attraction when evaluated for the ideal substance is equivalent to the corresponding quantity which is the actual desideratum, or sensibly so, at least.
The writer discusses in order the following subjects:—
the validity of the use of volume integrals to express the potential
the component attractions of bodies of discontinuous structure
the potentials and attractions of accurately continuous bodies
volume integrals:
their connection with surface integrals
their differentiation
their application to the theories of potential and of magnetism
their evaluation over regions extending to infinity
The reader is confronted with the problem of adapting to the generally admitted discrete properties of matter the principles of integration, involving as they do the endless subdivision of quantity and magnitude. Each point of serious difficulty is clearly presented, and the author shows, nevertheless, that there is justification for the use of the methods of the calculus, and that it is to be found in the appreciation of a principle not unknown in other branches of applied mathematics, and which, in the case considered, consists in the introduction of a subsidiary system of continuous structure capable of being integrated over, and of a density such that the potential or attraction when evaluated for the ideal substance is equivalent to the corresponding quantity which is the actual desideratum, or sensibly so, at least.
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VOLUME AND SURFACE INTEGRALS USED IN PHYSICS
VOLUME AND SURFACE INTEGRALS USED IN PHYSICS
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Product Details
| BN ID: | 2940016224732 |
|---|---|
| Publisher: | OGB |
| Publication date: | 02/12/2013 |
| Series: | Cambridge Tracts in Mathematics and Mathematical Physics , #1 |
| Sold by: | Barnes & Noble |
| Format: | eBook |
| File size: | 5 MB |
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