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N.-Y.: Wiley-VCH, 2014. - 634p.The intensely fruitful symbiosis between physics and mathematics is nothing short of

miraculous. It is not a symmetric interaction; however, physical laws, which involve

relations between variables, are always in need of rules and techniques for manipulating

these relations: hence, the role of mathematics in providing tools for physics, and hence,

the need for books such as this one. Physics, in its turn, supplies motivation for the

development of mathematically sound techniques and concepts; it is enough to mention

the importance of celestial mechanics in the evolution of perturbation methods and the

impetus Dirac’s delta function gave to the work on generalized functions. So perhaps a

sister volume to the present compendium would be Physical Insights forMathematicians.

(From the above, one might get the impression that physics and mathematics are two

separate, even opposing, domains. This is of course not true; there is a well-established

field of mathematical physics and many mathematicians working in fluid and continuum

mechanics would be hard-pressed to separate the mathematics and the physics elements

of their seamless activity.)

The present book is intended for the use of advanced undergraduates, graduate students,

and researchers in physics, who are aware of the usefulness of a particular mathematical

approach and need a quick point of entry into its vocabulary, main results,

and the literature. However, one cannot cleanly single out parts of mathematics that are

useful for physics and ones that are not; for example, while the theory of operators in

Hilbert spaces is undoubtedly indispensable in quantum mechanics, an area as abstruse

as category theory is becoming increasingly popular in cosmology and has found applications

in developmental biology.1) Hence, the concept of mathematics useful in physics

arguably covers the same area as mathematics tout court, and anyone embarking on the

publication of a book such as the present one does so in the certainty that no single

book can do justice to the intricate interpenetration of mathematics and physics. It is

quite possible to write a second, and perhaps a third volume of an encyclopedia such as

ours.

Let us quickly mention significant areas that are not being covered here. These

include combinatorics, deterministic chaos, fractals, nonlinear partial differential

equations, and symplectic geometry. It was also felt that a separate chapter on contextfree

modeling was not necessary as there is an ample literature on modeling case

studies.

What this book offers is an attractive mix of classical areas of applications of mathematics

to physics and of areas that have only come to prominence recently.Thus, we have

substantive chapters on asymptotic methods, calculus of variations, differential geometry

and topology of manifolds, dynamical systems theory, functional analysis, group theory,

numerical methods, partial differential equations of mathematical physics, special functions,

and transform methods. All these are up-to-date surveys; for example, the chapter

on asymptotic methods discusses recent renormalized group-based approaches, while the

chapter on variational methods considers examples where no smooth minimizers exist.

These chapters appear side by side with a decidedly modern computational take on algebraic

topology and in-depth reviews of such increasingly important areas as graph and network

theory, Monte Carlo simulations, stochastic differential equations, and algorithms

in symbolic computation, an important complement to analytic and numerical problemsolving

approaches.

It is hoped that the layout of the text allows for easy cross-referencing between chapters,

and that by the end of a chapter, the reader will have a clear view of the area under

discussion and will be know where to go to learn more. Bon voyage!

miraculous. It is not a symmetric interaction; however, physical laws, which involve

relations between variables, are always in need of rules and techniques for manipulating

these relations: hence, the role of mathematics in providing tools for physics, and hence,

the need for books such as this one. Physics, in its turn, supplies motivation for the

development of mathematically sound techniques and concepts; it is enough to mention

the importance of celestial mechanics in the evolution of perturbation methods and the

impetus Dirac’s delta function gave to the work on generalized functions. So perhaps a

sister volume to the present compendium would be Physical Insights forMathematicians.

(From the above, one might get the impression that physics and mathematics are two

separate, even opposing, domains. This is of course not true; there is a well-established

field of mathematical physics and many mathematicians working in fluid and continuum

mechanics would be hard-pressed to separate the mathematics and the physics elements

of their seamless activity.)

The present book is intended for the use of advanced undergraduates, graduate students,

and researchers in physics, who are aware of the usefulness of a particular mathematical

approach and need a quick point of entry into its vocabulary, main results,

and the literature. However, one cannot cleanly single out parts of mathematics that are

useful for physics and ones that are not; for example, while the theory of operators in

Hilbert spaces is undoubtedly indispensable in quantum mechanics, an area as abstruse

as category theory is becoming increasingly popular in cosmology and has found applications

in developmental biology.1) Hence, the concept of mathematics useful in physics

arguably covers the same area as mathematics tout court, and anyone embarking on the

publication of a book such as the present one does so in the certainty that no single

book can do justice to the intricate interpenetration of mathematics and physics. It is

quite possible to write a second, and perhaps a third volume of an encyclopedia such as

ours.

Let us quickly mention significant areas that are not being covered here. These

include combinatorics, deterministic chaos, fractals, nonlinear partial differential

equations, and symplectic geometry. It was also felt that a separate chapter on contextfree

modeling was not necessary as there is an ample literature on modeling case

studies.

What this book offers is an attractive mix of classical areas of applications of mathematics

to physics and of areas that have only come to prominence recently.Thus, we have

substantive chapters on asymptotic methods, calculus of variations, differential geometry

and topology of manifolds, dynamical systems theory, functional analysis, group theory,

numerical methods, partial differential equations of mathematical physics, special functions,

and transform methods. All these are up-to-date surveys; for example, the chapter

on asymptotic methods discusses recent renormalized group-based approaches, while the

chapter on variational methods considers examples where no smooth minimizers exist.

These chapters appear side by side with a decidedly modern computational take on algebraic

topology and in-depth reviews of such increasingly important areas as graph and network

theory, Monte Carlo simulations, stochastic differential equations, and algorithms

in symbolic computation, an important complement to analytic and numerical problemsolving

approaches.

It is hoped that the layout of the text allows for easy cross-referencing between chapters,

and that by the end of a chapter, the reader will have a clear view of the area under

discussion and will be know where to go to learn more. Bon voyage!

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- Раздел: Физика → Матметоды и моделирование в физике

Princeton University Press, 2007. - 672 pages.
What can a physicist gain by studing mathematics? By gathering together everything a physicist needs to know about mathematics in one comprehensive and accessible guide, this is the question Mathematics for Physics and Physicists successfully takes on.
The author, Walter Appel, is a renowned mathematics educator hailing from one...

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- Раздел: Физика → Матметоды и моделирование в физике

Springer, 2014. - 329 pp.
This book is intended for undergraduates and young researchers who wish to understand the role that different branches of physics and mathematics play in the execution of actual experiments. The unique feature of the book is that all the subjects addressed are strictly interconnected within the context of the execution of a single experiment with very...

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- Раздел: Физика → Матметоды и моделирование в физике

N.-Y.: Springer, 2015. - 440p.
Supports learning and teaching with extended exercises at the end of every chapter including solutions
Contains numerous examples for efficient description of anisotropies in physical phenomena
Describes how to use tensors to calculate anisotropical properties of orientational phenomena in the theoretical description, in addition to vector...

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- Раздел: Физика → Матметоды и моделирование в физике

2nd edition. — Wiley-VCH, 2009. — 538 p.
All there is to know about functional analysis, integral equations and calculus of variations in one handy volume, written for the specific needs of physicists and applied mathematicians.
The new edition of this handbook starts with a short introduction to functional analysis, including a review of complex analysis, before continuing...

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Cambridge University Press, 2007. — 1262 p.
Authors:
William H. Press - Raymer Chair in Computer Sciences and Integrative Biology The University of Texas at Austin
Saul A. Teukolsky - Hans A. Bethe Professor of Physics and Astrophysics Cornell University
William T. Vetterling - Research Fellow and Director of Image Science ZINK Imaging, LLC
Brian P. Flannery - Science,...

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