Principles of Advanced Mathematical Physics II
Author | : R. D. Richtmyer |
Publisher | : |
Total Pages | : 336 |
Release | : 1981-11-01 |
Genre | : |
ISBN | : 9783642510779 |
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Author | : R. D. Richtmyer |
Publisher | : |
Total Pages | : 336 |
Release | : 1981-11-01 |
Genre | : |
ISBN | : 9783642510779 |
Author | : R.D. Richtmyer |
Publisher | : Springer Science & Business Media |
Total Pages | : 332 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 3642510760 |
Author | : Robert D. Richtmyer |
Publisher | : Springer |
Total Pages | : 424 |
Release | : 1985-10-01 |
Genre | : Science |
ISBN | : 9783540088738 |
A first consequence of this difference in texture concerns the attitude we must take toward some (or perhaps most) investigations in "applied mathe matics," at least when the mathematics is applied to physics. Namely, those investigations have to be regarded as pure mathematics and evaluated as such. For example, some of my mathematical colleagues have worked in recent years on the Hartree-Fock approximate method for determining the structures of many-electron atoms and ions. When the method was intro duced, nearly fifty years ago, physicists did the best they could to justify it, using variational principles, intuition, and other techniques within the texture of physical reasoning. By now the method has long since become part of the established structure of physics. The mathematical theorems that can be proved now (mostly for two- and three-electron systems, hence of limited interest for physics), have to be regarded as mathematics. If they are good mathematics (and I believe they are), that is justification enough. If they are not, there is no basis for saying that the work is being done to help the physicists. In that sense, applied mathematics plays no role in today's physics. In today's division of labor, the task of the mathematician is to create mathematics, in whatever area, without being much concerned about how the mathematics is used; that should be decided in the future and by physics.
Author | : Robert D. Richtmyer |
Publisher | : |
Total Pages | : |
Release | : 1981 |
Genre | : |
ISBN | : |
Author | : Enrico De Micheli |
Publisher | : MDPI |
Total Pages | : 182 |
Release | : 2020-12-15 |
Genre | : Mathematics |
ISBN | : 3039434950 |
The charm of Mathematical Physics resides in the conceptual difficulty of understanding why the language of Mathematics is so appropriate to formulate the laws of Physics and to make precise predictions. Citing Eugene Wigner, this “unreasonable appropriateness of Mathematics in the Natural Sciences” emerged soon at the beginning of the scientific thought and was splendidly depicted by the words of Galileo: “The grand book, the Universe, is written in the language of Mathematics.” In this marriage, what Bertrand Russell called the supreme beauty, cold and austere, of Mathematics complements the supreme beauty, warm and engaging, of Physics. This book, which consists of nine articles, gives a flavor of these beauties and covers an ample range of mathematical subjects that play a relevant role in the study of physics and engineering. This range includes the study of free probability measures associated with p-adic number fields, non-commutative measures of quantum discord, non-linear Schrödinger equation analysis, spectral operators related to holomorphic extensions of series expansions, Gibbs phenomenon, deformed wave equation analysis, and optimization methods in the numerical study of material properties.
Author | : Robert D. Richtmyer |
Publisher | : Springer Science & Business Media |
Total Pages | : 439 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 3642463789 |
A first consequence of this difference in texture concerns the attitude we must take toward some (or perhaps most) investigations in "applied mathe matics," at least when the mathematics is applied to physics. Namely, those investigations have to be regarded as pure mathematics and evaluated as such. For example, some of my mathematical colleagues have worked in recent years on the Hartree-Fock approximate method for determining the structures of many-electron atoms and ions. When the method was intro duced, nearly fifty years ago, physicists did the best they could to justify it, using variational principles, intuition, and other techniques within the texture of physical reasoning. By now the method has long since become part of the established structure of physics. The mathematical theorems that can be proved now (mostly for two- and three-electron systems, hence of limited interest for physics), have to be regarded as mathematics. If they are good mathematics (and I believe they are), that is justification enough. If they are not, there is no basis for saying that the work is being done to help the physicists. In that sense, applied mathematics plays no role in today's physics. In today's division of labor, the task of the mathematician is to create mathematics, in whatever area, without being much concerned about how the mathematics is used; that should be decided in the future and by physics.
Author | : Robert D. Richtmyer |
Publisher | : |
Total Pages | : 0 |
Release | : 1981 |
Genre | : |
ISBN | : |
Author | : Robert Davis Richtmyer |
Publisher | : |
Total Pages | : |
Release | : 1978 |
Genre | : |
ISBN | : |
Author | : R.D. Richtmyer |
Publisher | : |
Total Pages | : 0 |
Release | : |
Genre | : |
ISBN | : |
Author | : Alexandru Kristály |
Publisher | : Cambridge University Press |
Total Pages | : 385 |
Release | : 2010-08-19 |
Genre | : Mathematics |
ISBN | : 0521117828 |
A comprehensive introduction to modern applied functional analysis. Assumes only basic notions of calculus, real analysis, geometry, and differential equations.