Mathematical physics refers to development of mathematical methods for application to problems in physics.
The Journal of Mathematical Physics defines this area 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.". There are several distinct branches of mathematical physics, and these roughly correspond to particular historical periods. The theory of partial differential equations (and the related areas of variational calculus, Fourier analysis, potential theory, and vector analysis) are perhaps most closely associated with mathematical physics.
Scope of the subject
These were developed intensively from the second half of the eighteenth century (by, for example, D'Alembert, Euler, and Lagrange) until the 1930s. Physical applications of these developments include hydrodynamics, celestial mechanics, elasticity theory, acoustics,thermodynamics, electricity, magnetism, and aerodynamics.
The theory of atomic spectra (and, later, quantum mechanics) developed almost concurrently with the mathematical fields of linear algebra, thespectral theory of operators, and more broadly, functional analysis. These constitute the mathematical basis of another branch of mathematical physics.
The special and general theories of relativity require a rather different type of mathematics. This was group theory: and it played an important role in both quantum field theory and differential geometry. This was, however, gradually supplemented by topology in the mathematical description of cosmological as well as quantum field theory phenomena.
Statistical mechanics forms a separate field, which is closely related with the more mathematical ergodic theory and some parts of probability theory.
There are increasing interactions between combinatorics and physics, in particular statistical physics.
The usage of the term 'Mathematical physics' is sometimes idiosyncratic. Certain parts of mathematics that initially arose from the development of physics are not considered parts of mathematical physics, while other closely related fields are. For example, ordinary differential equationsand symplectic geometry are generally viewed as purely mathematical disciplines, whereas dynamical systems and Hamiltonian mechanics belong to mathematical physics.
The theory of atomic spectra (and, later, quantum mechanics) developed almost concurrently with the mathematical fields of linear algebra, thespectral theory of operators, and more broadly, functional analysis. These constitute the mathematical basis of another branch of mathematical physics.
The special and general theories of relativity require a rather different type of mathematics. This was group theory: and it played an important role in both quantum field theory and differential geometry. This was, however, gradually supplemented by topology in the mathematical description of cosmological as well as quantum field theory phenomena.
Statistical mechanics forms a separate field, which is closely related with the more mathematical ergodic theory and some parts of probability theory.
There are increasing interactions between combinatorics and physics, in particular statistical physics.
The usage of the term 'Mathematical physics' is sometimes idiosyncratic. Certain parts of mathematics that initially arose from the development of physics are not considered parts of mathematical physics, while other closely related fields are. For example, ordinary differential equationsand symplectic geometry are generally viewed as purely mathematical disciplines, whereas dynamical systems and Hamiltonian mechanics belong to mathematical physics.
Mathematical Methods for Physicists: A concise introduction
Author: TAI L. CHOW
was born and raised in China. He received a BS degree in physics from the National Taiwan University, a Masters degree in physics from Case Western Reserve University, and a PhD in physics from the University of Rochester. Since 1969, Dr Chow has been in the Department of Physics at California State University, Stanislaus, and served as department chairman for 17 years, until 1992. He served as Visiting Professor of Physics at University of California (at Davis and Berkeley) during his sabbatical years. He also worked as Summer Faculty Research Fellow at Stanford University and at NASA. Dr Chow has published more than 35 articles in physics journals and is the author of two textbooks and a solutions manual.
Sumber:
1. Wikipedia
2. Google book
Ucapan Terima Kasih
Kepada Ibunda Roswati Mudjiarto
Sumber:
1. Wikipedia
2. Google book
Ucapan Terima Kasih
Kepada Ibunda Roswati Mudjiarto
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