Topic
Physical mathematics
About: Physical mathematics is a research topic. Over the lifetime, 41 publications have been published within this topic receiving 3219 citations.
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TL;DR: These six volumes as mentioned in this paper compile the mathematical knowledge required by researchers in mechanics, physics, engineering, chemistry and other branches of application of mathematics for the theoretical and numerical resolution of physical models on computers.
Abstract: These six volumes - the result of a ten year collaboration between the authors, two of France's leading scientists and both distinguished international figures - compile the mathematical knowledge required by researchers in mechanics, physics, engineering, chemistry and other branches of application of mathematics for the theoretical and numerical resolution of physical models on computers. Since the publication in 1924 of the Methoden der mathematischen Physik by Courant and Hilbert, there has been no other comprehensive and up-to-date publication presenting the mathematical tools needed in applications of mathematics in directly implementable form. The advent of large computers has in the meantime revolutionised methods of computation and made this gap in the literature intolerable: the objective of the present work is to fill just this gap. Many phenomena in physical mathematics may be modeled by a system of partial differential equations in distributed systems: a model here means a set of equations, which together with given boundary data and, if the phenomenon is evolving in time, initial data, defines the system. The advent of high-speed computers has made it possible for the first time to caluclate values from models accurately and rapidly. Researchers and engineers thus have a crucial means of using numerical results to modify and adapt arguments and experiments along the way. Every fact of technical and industrial activity has been affected by these developments. Modeling by distributed systems now also supports work in many areas of physics (plasmas, new materials, astrophysics, geophysics), chemistry and mechanics and is finding increasing use in the life sciences. Volumes 5 and 6 cover problems of Transport and Evolution.
2,137 citations
01 Jan 1970
TL;DR: Contemporary physical mathematics has much to offer the physicist as it provides well-defined concepts and tehcniques for the study of physical systems, helps in the very formulation of the laws of physical system and brings a better understanding to physiscs.
Abstract: Contemporary physical mathematics has much to offer the physicist as it provides well-defined concepts and tehcniques for the study of physical systems, helps in the very formulation of the laws of physical systems and brings a better understanding to physiscs.
358 citations
Book•
01 May 1983
TL;DR: Contemporary physical mathematics has much to offer the physicist as it provides well-defined concepts and tehcniques for the study of physical systems, helps in the very formulation of the laws of physical system and brings a better understanding to physiscs as mentioned in this paper.
Abstract: Contemporary physical mathematics has much to offer the physicist as it provides well-defined concepts and tehcniques for the study of physical systems, helps in the very formulation of the laws of physical systems and brings a better understanding to physiscs.
271 citations
TL;DR: A solution to the Navier-Stokes Turbulence problem has been unknown for years and the fact that it still leaves a lot of unanswered questions regarding Engineering and Pure Mathematics.
Abstract: A solution to this problem has been unknown for years and the fact that it hasn’t been solved yet leaves a lot of unanswered questions regarding Engineering and Pure Mathematics. Turbulence is a specific topic in fluid mechanics which is a vital part of the course when it comes to real life situations. In two and three dimensional systems of equations and some initial conditions, if the smooth solutions exist, they have bounded kinetic energy. In three space dimensions and time, given an initial velocity vector, there exists a velocity field and scalar pressure field which are both smooth and globally defined that solve the Navier-Stokes equations. There are difficulties in two-dimensions and three dimensions in a possible solution and which have been unsolved for a long time and our goal is to propose a solution in three-dimensions. Lets see if we can relate a couple of courses of pure mathematics to come up with an implication.
156 citations
TL;DR: Physical Mathematics By Chester H. Page. as mentioned in this paper Pp. x + 329 + 4.6d. net. (Princeton, N.J., D. Van Nostrand Company, Inc., London: Macmillan and Co., Ltd., 1955).
Abstract: Physical Mathematics By Chester H. Page. Pp. x + 329. (Princeton, N.J.: D. Van Nostrand Company, Inc.; London: Macmillan and Co., Ltd., 1955.) 42s. net. Special Functions of Mathematical Physics and Chemistry By Prof. Ian N. Sneddon. (University Mathematical Texts.) Pp. viii + 164. (Edinburgh and London: Oliver and Boyd, Ltd., 1956.) 10s. 6d. net.
116 citations