Mathematical Analysis of Physical Problems

Author: Philip Russell Wallace

Publisher: Courier Corporation

ISBN: 0486646769

Category: Science

Page: 616

View: 2816

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This mathematical reference for theoretical physics employs common techniques and concepts to link classical and modern physics. It provides the necessary mathematics to solve most of the problems. Topics include the vibrating string, linear vector spaces, the potential equation, problems of diffusion and attenuation, probability and stochastic processes, and much more. 1972 edition.

Mathematical Analysis of Problems in the Natural Sciences

Author: Vladimir Zorich

Publisher: Springer Science & Business Media

ISBN: 9783642148132

Category: Mathematics

Page: 133

View: 1813

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Based on a two-semester course aimed at illustrating various interactions of "pure mathematics" with other sciences, such as hydrodynamics, thermodynamics, statistical physics and information theory, this text unifies three general topics of analysis and physics, which are as follows: the dimensional analysis of physical quantities, which contains various applications including Kolmogorov's model for turbulence; functions of very large number of variables and the principle of concentration along with the non-linear law of large numbers, the geometric meaning of the Gauss and Maxwell distributions, and the Kotelnikov-Shannon theorem; and, finally, classical thermodynamics and contact geometry, which covers two main principles of thermodynamics in the language of differential forms, contact distributions, the Frobenius theorem and the Carnot-Caratheodory metric. It includes problems, historical remarks, and Zorich's popular article, "Mathematics as language and method."

Mathematical Analysis in Engineering

How to Use the Basic Tools

Author: Chiang C. Mei

Publisher: Cambridge University Press

ISBN: 9780521587983

Category: Mathematics

Page: 461

View: 1995

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A paperback edition of successful and well reviewed 1995 graduate text on applied mathematics for engineers.

Group Theory and Its Application to Physical Problems

Author: Morton Hamermesh

Publisher: Courier Corporation

ISBN: 9780486661810

Category: Science

Page: 509

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"A remarkably intelligible survey . . . well organized, well written and very clear throughout." — Mathematical Reviews This excellent text, long considered one of the best-written, most skillful expositions of group theory and its physical applications, is directed primarily to advanced undergraduate and graduate students in physics, especially quantum physics. No knowledge of group theory is assumed, but the reader is expected to be familiar with quantum mechanics. And while much of the book concerns theory, readers will nevertheless find a large number of physical applications in the fields of crystallography, molecular theory, and atomic and nuclear physics. The first seven chapters of the book are concerned with finite groups, focusing on the central role of the symmetric group. This section concludes with a chapter dealing with the problem of determining group characters, as it discusses Young tableaux, Yamanouchi symbols, and the method of Hund. The remaining five chapters discuss continuous groups, particularly Lie groups, with the final chapter devoted to the ray representation of Lie groups. The author, Professor Emeritus of Physics at the University of Minnesota, has included a generous selection of problems. They are inserted throughout the text at the place where they naturally arise, making the book ideal for self-study as well as for classroom assignment. 77 illustrations. "A very welcome addition to [the] literature. . . . I would warmly recommend the book to all serious students of Group Theory as applied to Physics." — Contemporary Physics. Index. Bibliography. Problems. Tables.

Mathematical Tools for Changing Scale in the Analysis of Physical Systems

Author: William G. Gray,Anton Leijnse,Randall L. Kolar,Cheryl A. Blain

Publisher: CRC Press

ISBN: 9780849389344

Category: Mathematics

Page: 256

View: 7282

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Mathematical Tools for Changing Scale in the Analysis of Physical Systems presents a new systematic approach to changing the spatial scale of the differential equations describing science and engineering problems. It defines vectors, tensors, and differential operators in arbitrary orthogonal coordinate systems without resorting to conceptually difficult Riemmann-Christoffel tensor and contravariant and covariant base vectors. It reveals the usefulness of generalized functions for indicating curvilineal, surficial, or spatial regions of integration and for transforming among these integration regions. These powerful mathematical tools are harnessed to provide 128 theorems in tabular format (most not previously available in the literature) that transform time-derivative and del operators of a function at one scale to the corresponding operators acting on the function at a larger scale. Mathematical Tools for Changing Scale in the Analysis of Physical Systems also provides sample applications of the theorems to obtain continuum balance relations for arbitrary surfaces, multiphase systems, and problems of reduced dimensionality. The mathematical techniques and tabulated theorems ensure the book will be an invaluable analysis tool for practitioners and researchers studying balance equations for systems encountered in the fields of hydraulics, hydrology, porous media physics, structural analysis, chemical transport, heat transfer, and continuum mechanics.

Mathematical Analysis of Evolution, Information, and Complexity

Author: Wolfgang Arendt,Wolfgang P. Schleich

Publisher: John Wiley & Sons

ISBN: 3527628037

Category: Science

Page: 502

View: 1382

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Mathematical Analysis of Evolution, Information, and Complexity deals with the analysis of evolution, information and complexity. The time evolution of systems or processes is a central question in science, this text covers a broad range of problems including diffusion processes, neuronal networks, quantum theory and cosmology. Bringing together a wide collection of research in mathematics, information theory, physics and other scientific and technical areas, this new title offers elementary and thus easily accessible introductions to the various fields of research addressed in the book.

Ill-posed Problems of Mathematical Physics and Analysis

Author: Mikhail Mikha_lovich Lavrent_ev,Vladimir Gavrilovich Romanov,Serge_ Petrovich Shishatski_

Publisher: American Mathematical Soc.

ISBN: 9780821898147

Category: Mathematics

Page: 290

View: 2669

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Physical formulations leading to ill-posed problems Basic concepts of the theory of ill-posed problems Analytic continuation Boundary value problems for differential equations Volterra equations Integral geometry Multidimensional inverse problems for linear differential equations

Acoustics, Mechanics, and the Related Topics of Mathematical Analysis

CAES Du CNRS, Frejus, France, 18-22 June 2002

Author: Armand Wirgin

Publisher: World Scientific

ISBN: 9789812704405

Category: Mathematics

Page: 301

View: 5048

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This book concerns the mathematical analysis OCo modeling physical concepts, existence, uniqueness, stability, asymptotics, computational schemes, etc. OCo involved in predicting complex mechanical/acoustical behavior/response and identifying or optimizing mechanical/acoustical systems giving rise to phenomena that are either observed or aimed at. The forward problems consist in solving generally coupled, nonlinear systems of integral or partial (integer or fractional) differential equations with nonconstant coefficients. The identification/optimization of the latter, of the driving terms and/or of the boundary conditions, all of which are often affected by random perturbations, forms the class of related inverse or control problems."

A Collection of Problems on a Course of Mathematical Analysis

International Series of Monographs in Pure and Applied Mathematics

Author: G. N. Berman

Publisher: Elsevier

ISBN: 1483137341

Category: Mathematics

Page: 602

View: 9752

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A Collection of Problems on a Course of Mathematical Analysis is a collection of systematically selected problems and exercises (with corresponding solutions) in mathematical analysis. A common instruction precedes a group of problems of the same type. Problems with a physics content are preceded by the necessary physical laws. In the case of more or less difficult problems, hints are given in the answers. This book is comprised of 15 chapters and begins with an overview of functions and methods of specifying them; notation for and classification of functions; elementary investigation of functions; and trigonometric and inverse trigonometric functions. The following chapters deal with limits and tests for their existence; differential calculus, with emphasis on derivatives and differentials; functions and curves; definite and indefinite integrals; and methods of evaluating definite integrals. Some applications of the integral in geometry, statics, and physics are also considered; along with functions of several variables; multiple integrals and iterated integration; line and surface integrals; and differential equations. The final chapter is devoted to trigonometric series. This monograph is intended for students studying mathematical analysis within the framework of a technical college course.

Applied Analysis

Author: Cornelius Lanczos

Publisher: Courier Corporation

ISBN: 0486319261

Category: Mathematics

Page: 576

View: 1410

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Classic work on analysis and design of finite processes for approximating solutions of analytical problems. Features algebraic equations, matrices, harmonic analysis, quadrature methods, and much more.

A Primer of Infinitesimal Analysis

Author: John L. Bell

Publisher: Cambridge University Press

ISBN: 0521887186

Category: Mathematics

Page: 124

View: 3740

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A rigorous, axiomatically formulated presentation of the 'zero-square', or 'nilpotent' infinitesimal.

Mathematical Methods of Analysis of Biopolymer Sequences

Author: Semen Grigorʹevich Gindikin

Publisher: American Mathematical Soc.

ISBN: 9780821871157

Category: Science

Page: 150

View: 4530

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This collection contains papers by participants in the seminar on mathematical methods in molecular biology who worked for several years at the Laboratory of Molecular Biology and Bioorganic Chemistry (now the Institute of Physical and Chemical Problems in Biology) at Moscow State University. The seminar united mathematicians and biologists around the problems of biological sequences. The collection includes original results as well as expository material and spans a range of perspectives, from purely mathematical problems to algorithms and their computer realizations. For this reason, the book is of interest to mathematicians, statisticians, biologists, and computational scientists who work with biopolymer sequences.

Mathematical Analysis of Groundwater Resources

Author: Bruce Hunt

Publisher: Elsevier

ISBN: 1483103072

Category: Science

Page: 280

View: 3170

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Mathematical Analysis of Groundwater Resources focuses on groundwater flow. The book first discusses the scope of the study, definition of terms, and mathematical preliminaries. The text examines the equations of groundwater flow. Continuum concepts; flux and pore velocities; Darcy's Law for Anisotropic Aquifers; Conservation of Mass equations; and boundary conditions are discussed. The book also underscores the formulation of boundary-value problems. Regional problems, confined flow problems, sea water intrusion problems, and free surface flows are discussed. The text also looks at the approximate solution of boundary-value problems, inverse problems, and groundwater pollution. The book then presents the exact solutions of steady-flow problems. Problem formulations; analytic coordinate transformations; analytic functions of a complex variable; applications of the Schwarz-Christoffel transformation; and superposition of solutions are described. The text also discusses the exact solution of unsteady problems. The Laplace transform, groundwater recharge problems, well storage effect, and two well recovery problems are discussed. The book is a good source of data for researchers who are interested in groundwater flow.

Partial Differential Equations of Mathematical Physics

Author: S. L. Sobolev

Publisher: Courier Corporation

ISBN: 9780486659640

Category: Science

Page: 427

View: 8628

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This volume presents an unusually accessible introduction to equations fundamental to the investigation of waves, heat conduction, hydrodynamics, and other physical problems. Topics include derivation of fundamental equations, Riemann method, equation of heat conduction, theory of integral equations, Green's function, and much more. The only prerequisite is a familiarity with elementary analysis. 1964 edition.

Mathematical Analysis, Approximation Theory and Their Applications

Author: Themistocles M. Rassias,Vijay Gupta

Publisher: Springer

ISBN: 3319312812

Category: Mathematics

Page: 741

View: 1945

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Designed for graduate students, researchers, and engineers in mathematics, optimization, and economics, this self-contained volume presents theory, methods, and applications in mathematical analysis and approximation theory. Specific topics include: approximation of functions by linear positive operators with applications to computer aided geometric design, numerical analysis, optimization theory, and solutions of differential equations. Recent and significant developments in approximation theory, special functions and q-calculus along with their applications to mathematics, engineering, and social sciences are discussed and analyzed. Each chapter enriches the understanding of current research problems and theories in pure and applied research.

Mathematical and Experimental Modeling of Physical and Biological Processes

Author: H.T. Banks,H.T. Tran

Publisher: CRC Press

ISBN: 9781420073386

Category: Mathematics

Page: 298

View: 5788

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Through several case study problems from industrial and scientific research laboratory applications, Mathematical and Experimental Modeling of Physical and Biological Processes provides students with a fundamental understanding of how mathematics is applied to problems in science and engineering. For each case study problem, the authors discuss why a model is needed and what goals can be achieved with the model. Exploring what mathematics can reveal about applications, the book focuses on the design of appropriate experiments to validate the development of mathematical models. It guides students through the modeling process, from empirical observations and formalization of properties to model analysis and interpretation of results. The authors also describe the hardware and software tools used to design the experiments so faculty/students can duplicate them. Integrating real-world applications into the traditional mathematics curriculum, this textbook deals with the formulation and analysis of mathematical models in science and engineering. It gives students an appreciation of the use of mathematics and encourages them to further study the applied topics. Real experimental data for projects can be downloaded from CRC Press Online.

Modern Mathematics for the Engineer: Second Series

Author: Edwin F. Beckenbach

Publisher: Courier Corporation

ISBN: 0486316122

Category: Technology & Engineering

Page: 480

View: 5703

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The second in this two-volume series also contains original papers commissioned from prominent 20th-century mathematicians. A three-part treatment covers mathematical methods, statistical and scheduling studies, and physical phenomena. 1961 edition.

Elementary Theory & Application of Numerical Analysis

Author: James Edward Miller,David G. Moursund,Charles S. Duris

Publisher: Courier Corporation

ISBN: 0486479064

Category: Mathematics

Page: 315

View: 8015

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This updated introduction to modern numerical analysis is a complete revision of a classic text originally written in Fortran but now featuring the programming language C++. It focuses on a relatively small number of basic concepts and techniques. Many exercises appear throughout the text, most with solutions. An extensive tutorial explains how to solve problems with C++.