Physics: Algebra/Trig
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Author: Eugene Hecht
Brand: Brand: Brooks/Cole Pub Co

In Hecht's groundbreaking book, you'll find reallife applications, an unparalleled art and photography program, a presentation that anticipates students' questions, and an approach that emphasizes contemporary physics while interweaving historical perspectives. Hecht's coverage of classical physics is clear and insightful. He shows students how 21stcentury physics illuminates the classical topics of each chapter, adding excitement to the subject matter. Over 1,300 illustrations make it possible for students to visualize a diversity of physical phenomena. Many of these are multiframe, sequential drawings allowing students to comprehend the temporal unfolding of complex events. A selection of sketch art teaches students how to create problemsolving diagrams. This new edition of the text was designed to aggressively address the issue of problem solving for students (guided by contemporary physics education research). To this end Hecht has provided not only his approach to the fivestep problemsolving framework but also a wide range of new problems and solutions specifically designed to build student capability and confidence.
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Group Theoretical Methods in Physics: Proceedings of the XVI International Colloquium (INTERNATIONAL COLLOQUIUM ON GROUP THEORETICAL METHODS IN ... THEORETICAL METHODS IN PHYSICS: PROCEEDINGS)
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Author: H. D. Doebner



The Complex Wkb Method for Nonlinear Equations I: Linear Theory (Progress in Mathematical Physics)
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Author: V. P. Maslov

When first published (in Russian), this book proved to become the fountainhead of a major stream of important papers in mathematics, physics and even chemistry. Indeed, it formed the basis of new methodology and opened new directions for research. The present English edition includes new examples of applications to physics, hitherto unpublished or available only in Russian. It uses topological methods to analyze isotropic invariant manifolds in order to obtain symptotic series of eigenvalues and eigenvectors for the multidimensional Schrödinger equation also taking into account the socalled tunnel effects.


Generalized Coherent States and Their Applications (Texts & Monographs in Physics)
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Author: A. Perelomov
Brand: Brand: SpringerVerlag

This monograph treats an extensively developed field in modern mathematical physics  the theory of generalized coherent states and their applications to various physical problems. Coherent states, introduced originally by Schrodinger and von Neumann, were later employed by Glauber for a quantal description of laser light beams. The concept was generalized by the author for an arbitrary Lie group. In the last decade the formalism has been widely applied to various domains of theoretical physics and mathematics. The area of applications of generalized coherent states is very wide, and a comprehensive exposition of the results in the field would be helpful. This monograph is the first attempt toward this aim. My purpose was to compile and expound systematically the vast amount of material dealing with the coherent states and available through numerous journal articles. The book is based on a number of undergraduate and postgraduate courses I delivered at the Moscow PhysicoTechnical Institute. In its present form it is intended for professional mathematicians and theoretical physicists; it may also be useful for university students of mathematics and physics. In Part I the formalism is elaborated and explained for some of the simplest typical groups. Part II contains more sophisticated material; arbitrary Lie groups and symmetrical spaces are considered. A number of examples from various areas of theoretical and mathematical physics illustrate advantages of this approach, in Part III. It is a pleasure for me to thank Dr. Yu. Danilov for many useful remarks.
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Classical Orthogonal Polynomials of a Discrete Variable (SPRINGER SERIES IN COMPUTATIONAL PHYSICS)
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Author: A. F. Nikiforov

While classical orthogonal polynomials appear as solutions to hypergeometric differential equations, those of a discrete variable emerge as solutions of difference equations of hypergeometric type on lattices. The authors present a concise introduction to this theory, presenting at the same time methods of solving a large class of difference equations. They apply the theory to various problems in scientific computing, probability, queuing theory, coding and information compression. The book is an expanded and revised version of the first edition, published in Russian (Nauka 1985). Students and scientists will find a useful textbook in numerical analysis.


The Mathematical Analysis of Physical Systems
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Author: Ronald Mickens

Contents: 11. The Unreasonable Effectiveness of Mathematics in the Natural Sciences / Eugene P. Wigner; 12. The Unreasonable Effectiveness of Mathematics / R.W. Hamming; 2. Gauge Invariance in Nature: A Simple View / Sylvester J. Gates, Jr.; 3. The Radon Transform / Stanley R. Deans; 4. The Geometry of Quantum Flow / James V. Lindesay and Harry L. Morrison; 5. Classical Chaos, the Geometry of Phase Space, and Semiclassical Quantization / William P. Reinhardt; 6. The Adiabatic Method in the Theory of ManyBody Systems / Vladimir Z. Kresin and William A. Lester, Jr.; 7. Catastrophe Theory: What It Is, Why It Exists, How It Works / Robert Gilmore


Inverse Schrodinger Scattering in Three Dimensions (Texts & Monographs in Physics)
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Author: Roger G. Newton

Most of the laws of physics are expressed in the form of differential equations; that is our legacy from Isaac Newton. The customary separation of the laws of nature from contingent boundary or initial conditions, which has become part of our physical intuition, is both based on and expressed in the properties of solutions of differential equations. Within these equations we make a further distinction: that between what in mechanics are called the equations of motion on the one hand and the specific forces and shapes on the other. The latter enter as given functions into the former. In most observations and experiments the "equations of motion," i. e. , the structure of the differential equations, are taken for granted and it is the form and the details of the forces that are under investigation. The method by which we learn what the shapes of objects and the forces between them are when they are too small, too large, too remote, or too inaccessi ble for direct experimentation, is to observe their detectable effects. The question then is how to infer these properties from observational data. For the theoreti cal physicist, the calculation of observable consequences from given differential equations with known or assumed forces and shapes or boundary conditions is the standard task of solving a "direct problem. " Comparison of the results with experiments confronts the theoretical predictions with nature.


Computational Methods in Bifurcation Theory and Dissipative Structures: Springer Series in Computational Physics
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Author: M. Kubicek

"Dissipative structures" is a concept which has recently been used in physics to discuss the formation of structures organized in space and/or time at the expense of the energy flowing into the system from the outside. The spacetime structural organization of biological systems starting from the subcellular level up to the level of ecological systems, coherent structures in laser and of elastic stability in mechanics, instability in hydro plasma physics, problems dynamics leading to the development of turbulence, behavior of electrical networks and chemical reactors form just a short list of problems treated in this framework. Mathematical models constructed to describe these systems are usually nonlinear, often formed by complicated systems of algebraic, ordinary differ ential, or partial differential equations and include a number of character istic parameters. In problems of theoretical interest as well as engineering practice, we are concerned with the dependence of solutions on parameters and particularly with the values of parameters where qualitatively new types of solutions, e.g., oscillatory solutions, new stationary states, and chaotic attractors, appear (bifurcate). Numerical techniques to determine both bifurcation points and the depen dence of steadystate and oscillatory solutions on parameters are developed and discussed in detail in this text. The text is intended to serve as a working manual not only for students and research workers who are interested in dissipative structures, but also for practicing engineers who deal with the problems of constructing models and solving complicated nonlinear systems.


Fundamentals of the Finite Element Method
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Author: Hartley, Jr. Grandin

The basic concepts of the finite element method are presented in a clear and logical manner. The first chapter offers a brief discussion of matrix analysis of structures and is designed to establish a working knowledge of the matrix operations common to finite element solution procedures. The finite element method is then introduced as a discretized application of the RayleighRitz method using the energy functional of the uniaxial elasticity problem. The method's applicability to other physical problems is set forth with an introduction to variational calculus and the derivation of the functionals corresponding to the differential equations of these problems. Finally, the Galerkin weighted residual method is developed as an alternative technique.


Mathematical Methods For Physics
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Author: H. W. Wyld

This classic book helps students learn the basics in physics by bridging the gap between mathematics and the basic fundamental laws of physics. With supplemental material such as graphs and equations, Mathematical Methods for Physics creates a strong, solid anchor of learning. The text has three parts: Part I focuses on the use of special functions in solving the homogeneous partial differential equations of physics, and emphasizes applications to topics such as electrostatics, wave guides, and resonant cavities, vibrations of membranes, heat flow, potential flow in fluids, plane and spherical waves. Part II deals with the solution of inhomogeneous differential equations with particular emphasis on problems in electromagnetism, Green's functions for Poisson's equation, the wave equation and the diffusion equation, and the solution of integral equations by iteration, eigenfunction expansion and the Fredholm series. Finally, Part II explores complex variable techniques, including evalution of itegrals, dispersion relations, special functions in the complex plane, onesided Fourier transforms, and Laplace transforms.
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