| LC control no. | sh 85082129 |
|---|---|
| LC classification | QC19.2 QC20.85 |
| Topical heading | Mathematical physics |
| Variant(s) | Physical mathematics Physics--Mathematics |
| See also | Mathematics Physics |
| Scope note | Here are entered works on the use of mathematical tools and methods in physics. Works on the use of computers and computational tools and methods in physics are entered under Computational physics. |
| Subject example tracing | Note under Computational physics |
| Found in | Proof wiki, Oct. 24, 2022 (Mathematical physics is the branch of mathematics concerned with the development of mathematical methods for application to problems in physics.) Mathematical physics, via Duke University Department of Mathematics website, Oct. 24, 2022 (Mathematical physics applies rigorous mathematical ideas to problems inspired by physics; Traditionally mathematical physics has been quite closely associated to ideas in calculus, particularly those of differential equations. In recent years however, in part due to the rise of superstring theory, many more branches of mathematics have become major contributors to physics) Britannica online, Oct. 24, 2022 (mathematical physics, branch of mathematical analysis that emphasizes tools and techniques of particular use to physicists and engineers. It focuses on vector spaces, matrix algebra, differential equations (especially for boundary value problems), integral equations, integral transforms, infinite series, and complex variables. Its approach can be tailored to applications in electromagnetism, classical mechanics, and quantum mechanics) McGraw-Hill concise encyclopedia of physics, ©2002, via TheFreeDictionary website, Oct. 24, 2022 (Mathematical physics: An area of science concerned with the application of mathematical concepts to the physical sciences and the development of mathematical ideas in response to the needs of physics. Historically, the concept of mathematical physics was synonymous with that of theoretical physics. In present-day terminology, however, a distinction is made between the two. Whereas most of theoretical physics uses a large amount of mathematics as a tool and as a language, mathematical physics places greater emphasis on mathematical rigor, and devotes attention to the development of areas of mathematics that are, or show promise to be, useful to physics. The results obtained by pure mathematicians, with no thought to applications, are almost always found to be both useful and effective in formulating physical theories. Mathematical physics forms the bridge between physics as the description of nature and its structure on the one hand, and mathematics as a construction of pure logical thought on the other. This bridge between the two disciplines benefits and strengthens both fields enormously. The methods employed in mathematical physics range over most of mathematics, the areas of analysis and algebra being the most commonly used. Partial differential equations and differential geometry, with heavy use of vector and tensor methods, are of particular importance in the formulation of field theories, and functional analysis as well as operator theory in quantum mechanics. Group theory has become an especially valuable tool in the construction of quantum field theories and in elementary-particle physics. There has also been an increase in the use of general geometrical approaches and of topology. For solution methods and the calculation of quantities that are amenable to experimental tests, of particular prominence are Fourier analysis, complex analysis, variational methods, the theory of integral equations, and perturbation theory.) Wikipedia, Oct. 24, 2022: Mathematical physics (Mathematical physics refers to the development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines the field as "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories". An alternative definition would also include those mathematics that are inspired by physics (also known as physical mathematics)) Computational physics (Computational physics is the study and implementation of numerical analysis to solve problems in physics for which a quantitative theory already exists. Historically, computational physics was the first application of modern computers in science, and is now a subset of computational science. It is sometimes regarded as a subdiscipline (or offshoot) of theoretical physics, but others consider it an intermediate branch between theoretical and experimental physics - an area of study which supplements both theory and experiment) |
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