|Data Reduction and Error Analysis for the Physical Sciences
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Author: Philip R. Bevington
Brand: McGraw Hill
The purpose of this book is to provide an introduction to the concepts of statistical analysis of data for students at the undergraduate and graduate level, and to provide tools for data reduction and error analysis commonly required in the physical sciences. The presentation is developed from a practical point of view, including enough derivation to justify the results, but emphasizing methods of handling data more than theory. The text provides a variety of numerical and graphical techniques. Computer programs that support these techniques will be available on an accompanying website in both Fortran and C++.
|Elements of the Random Walk: An introduction for Advanced Students and Researchers
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Author: Joseph Rudnick
Brand: Brand: Cambridge University Press
Random walks have proven to be a useful model in understanding processes across a wide spectrum of scientific disciplines. This book is an introduction to some of the most powerful and general techniques used in the application of these ideas. Its self-contained text will appeal to graduate students across science, engineering and mathematics who need to understand the applications of random walk techniques, as well as to established researchers.
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|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 space-time 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 steady-state 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.
|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, one-sided Fourier transforms, and Laplace transforms.
|Operator Algebras, Mathematical Physics, and Low Dimensional Topology (Research Notes in Mathematics)
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Brand: Brand: A K Peters/CRC Press
This volume records the proceedings of an international conference that explored recent developments and the interaction between mathematical theory and physical phenomena.
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|Kalman Filtering: With Real-Time Applications
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Author: C.K. Chui
"Kalman Filtering with Real-Time Applications" presents a thorough discussion of the mathematical theory and computational schemes of Kalman filtering. The filtering algorithms are derived via different approaches, including a direct method consisting of a series of elementary steps, and an indirect method based on innovation projection. Other topics include Kalman filtering for systems with correlated noise or colored noise, limiting Kalman filtering for time-invariant systems, extended Kalman filtering for nonlinear systems, interval Kalman filtering for uncertain systems, and wavelet Kalman filtering for multiresolution analysis of random signals. The last two topics are new additions to this third edition. Most filtering algorithms are illustrated by using simplified radar tracking examples. The style of the book is informal, and the mathematics is elementary but rigorous. The text is self-contained, suitable for self-study, and accessible to all readers with a minimum knowledge.
|Generalized Coherent States and Their Applications (Texts & Monographs in Physics)
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Author: A. Perelomov
Brand: Brand: Springer-Verlag
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 Physico-Technical 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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|Applied Integral Transforms (Crm Monograph Series)
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Author: M. Ya. Antimirov
Brand: Brand: Amer Mathematical Society
This book does what few books on integral transforms do: it constructs the kernels of the integral transforms by solving the generalized Sturm--Liouville problems associated with the partial differential equations at hand. In the first part of the book, the authors construct the kernels and then use them to solve elementary problems of mathematical physics. This section, which proceeds mainly by examples and includes exercises, requires little mathematical background and provides an introduction to the subject of integral transforms. In the second part of the book, the method of integral transforms is used to solve modern applied problems in convective stability, temperature fields in oil strata, and eddy current testing. The choice of topics reflects the authors' research experience and involvement in industrial applications. The first part of the book is accessible to undergraduates, while the second part is aimed more at graduate students and researchers. Because of the applications it discusses, the book will interest engineers (especially petroleum engineers) and physicists.
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|Inverse Problems in Mathematical Physics: Proceedings of the Lapland Conference on Inverse Problems Held at Saariselka, Finland, 14-20 June 1992 (Lecture Notes in Physics)
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Author: L. Paivarinta
The book contains presentations of recent and ongoing research on inverse problems and its application to engineering and physical sciences. The articles are structured around three closely related topics: Inverse scattering problems, inverse boundary value problems, and inverse spectral problems. The applications range from quantum and electromagnetic scattering to medical imaging, geophysical sounding of the Earth, and non-destructive material evaluation. The book gives an up-to-date presentation of the most recent developments in these rapidly changing and evolving fields of applied research. The contributors of the volume give extra emphysis to the pedagogical aspects of their presentation to make this collection eysily accessible to graduate students as well as to people working on nearby fields of research.
|Theoretical Physics: A Classical Approach
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Author: Josef Honerkamp
Theoretical Physics is a thorough introduction to classical theoretical physics. While concise in its use of terminology, the book is intended to provide the means to understand the fundamentals of this field. Worked examples throughout the text and 39 problems help the student to become familiar with the physics presented here. With a view to achieving completeness, statistical mechanics, thermodynamics, and fluid dynamics are also discussed. After careful study of the book the student will be familiar with a wide variety of fields from advanced theoretical physics or applied physics.