Dimensional Analysis

Author: Hans G. Hornung
Publisher: Courier Corporation
ISBN: 048615047X
Size: 64.67 MB
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Derived from a course in fluid mechanics, this text for advanced undergraduates and graduate students employs symmetry arguments to illustrate the principles of dimensional analysis. 2006 edition.

Symmetry

Author: Roy McWeeny
Publisher: Courier Corporation
ISBN: 0486138801
Size: 55.58 MB
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Well-organized volume develops ideas of group and representation theory in progressive fashion. Emphasis on finite groups describing symmetry of regular polyhedra and of repeating patterns, plus geometric illustrations.

Dimensional Analysis

Author: P. W. (Percy Williams) 1882-1 Bridgman
Publisher:
ISBN: 9781361887387
Size: 11.18 MB
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Scaling Self Similarity And Intermediate Asymptotics

Author: G. I. Barenblatt
Publisher: Cambridge University Press
ISBN: 9780521435222
Size: 20.19 MB
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Scaling (power-type) laws reveal the fundamental property of the phenomena--self similarity. Self-similar (scaling) phenomena repeat themselves in time and/or space. The property of self-similarity simplifies substantially the mathematical modeling of phenomena and its analysis--experimental, analytical and computational. The book begins from a non-traditional exposition of dimensional analysis, physical similarity theory and general theory of scaling phenomena. Classical examples of scaling phenomena are presented. It is demonstrated that scaling comes on a stage when the influence of fine details of initial and/or boundary conditions disappeared but the system is still far from ultimate equilibrium state (intermediate asymptotics). It is explained why the dimensional analysis as a rule is insufficient for establishing self-similarity and constructing scaling variables. Important examples of scaling phenomena for which the dimensional analysis is insufficient (self-similarities of the second kind) are presented and discussed. A close connection of intermediate asymptotics and self-similarities of the second kind with a fundamental concept of theoretical physics, the renormalization group, is explained and discussed. Numerous examples from various fields--from theoretical biology to fracture mechanics, turbulence, flame propagation, flow in porous strata, atmospheric and oceanic phenomena are presented for which the ideas of scaling, intermediate asymptotics, self-similarity and renormalization group were of decisive value in modeling.

Group Theory And Quantum Mechanics

Author: Michael Tinkham
Publisher: Courier Corporation
ISBN: 0486131661
Size: 67.12 MB
Format: PDF
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Graduate-level text develops group theory relevant to physics and chemistry and illustrates their applications to quantum mechanics, with systematic treatment of quantum theory of atoms, molecules, solids. 1964 edition.

Introduction To Quantum Mechanics With Applications To Chemistry

Author: Linus Pauling
Publisher: Courier Corporation
ISBN: 0486134938
Size: 57.98 MB
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Classic undergraduate text explores wave functions for the hydrogen atom, perturbation theory, the Pauli exclusion principle, and the structure of simple and complex molecules. Numerous tables and figures.

Thinking About Equations

Author: Matt A. Bernstein
Publisher: John Wiley & Sons
ISBN: 1118210646
Size: 46.40 MB
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An accessible guide to developing intuition and skills for solving mathematical problems in the physical sciences and engineering Equations play a central role in problem solving across various fields of study. Understanding what an equation means is an essential step toward forming an effective strategy to solve it, and it also lays the foundation for a more successful and fulfilling work experience. Thinking About Equations provides an accessible guide to developing an intuitive understanding of mathematical methods and, at the same time, presents a number of practical mathematical tools for successfully solving problems that arise in engineering and the physical sciences. Equations form the basis for nearly all numerical solutions, and the authors illustrate how a firm understanding of problem solving can lead to improved strategies for computational approaches. Eight succinct chapters provide thorough topical coverage, including: Approximation and estimation Isolating important variables Generalization and special cases Dimensional analysis and scaling Pictorial methods and graphical solutions Symmetry to simplify equations Each chapter contains a general discussion that is integrated with worked-out problems from various fields of study, including physics, engineering, applied mathematics, and physical chemistry. These examples illustrate the mathematical concepts and techniques that are frequently encountered when solving problems. To accelerate learning, the worked example problems are grouped by the equation-related concepts that they illustrate as opposed to subfields within science and mathematics, as in conventional treatments. In addition, each problem is accompanied by a comprehensive solution, explanation, and commentary, and numerous exercises at the end of each chapter provide an opportunity to test comprehension. Requiring only a working knowledge of basic calculus and introductory physics, Thinking About Equations is an excellent supplement for courses in engineering and the physical sciences at the upper-undergraduate and graduate levels. It is also a valuable reference for researchers, practitioners, and educators in all branches of engineering, physics, chemistry, biophysics, and other related fields who encounter mathematical problems in their day-to-day work.

Groups Representations And Physics

Author: H.F Jones
Publisher: CRC Press
ISBN: 9781420050295
Size: 71.34 MB
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Illustrating the fascinating interplay between physics and mathematics, Groups, Representations and Physics, Second Edition provides a solid foundation in the theory of groups, particularly group representations. For this new, fully revised edition, the author has enhanced the book's usefulness and widened its appeal by adding a chapter on the Cartan-Dynkin treatment of Lie algebras. This treatment, a generalization of the method of raising and lowering operators used for the rotation group, leads to a systematic classification of Lie algebras and enables one to enumerate and construct their irreducible representations. Taking an approach that allows physics students to recognize the power and elegance of the abstract, axiomatic method, the book focuses on chapters that develop the formalism, followed by chapters that deal with the physical applications. It also illustrates formal mathematical definitions and proofs with numerous concrete examples.

Mathematical Physics

Author: Donald H. Menzel
Publisher: Courier Corporation
ISBN: 0486139107
Size: 39.14 MB
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Useful treatment of classical mechanics, electromagnetic theory, and relativity includes explanations of function theory, vectors, matrices, dyadics, tensors, partial differential equations, other advanced mathematical techniques. Nearly 200 problems with answers.

Symmetry In Mechanics

Author: Stephanie Frank Singer
Publisher: Springer Science & Business Media
ISBN: 1461201896
Size: 37.37 MB
Format: PDF
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"And what is the use," thought Alice, "of a book without pictures or conversations in it?" -Lewis Carroll This book is written for modem undergraduate students - not the ideal stu dents that mathematics professors wish for (and who occasionally grace our campuses), but the students like many the author has taught: talented but ap preciating review and reinforcement of past course work; willing to work hard, but demanding context and motivation for the mathematics they are learning. To suit this audience, the author eschews density of topics and efficiency of presentation in favor of a gentler tone, a coherent story, digressions on mathe maticians, physicists and their notations, simple examples worked out in detail, and reinforcement of the basics. Dense and efficient texts play a crucial role in the education of budding (and budded) mathematicians and physicists. This book does not presume to improve on the classics in that genre. Rather, it aims to provide those classics with a large new generation of appreciative readers. This text introduces some basic constructs of modern symplectic geometry in the context of an old celestial mechanics problem, the two-body problem. We present the derivation of Kepler's laws of planetary motion from Newton's laws of gravitation, first in the style of an undergraduate physics course, and x Preface then again in the language of symplectic geometry. No previous exposure to symplectic geometry is required: we introduce and illustrate all necessary con structs.