Eine komplett neu geschriebene Auflage. Es wurden neue Übungen ausgewählt, verschiedene Themen, wie z. B. Stabilität und Turbulenz, wurden auf den neuesten Stand der Forschung gebracht und es wurden ganz neue Themen hinzugefügt. Das Thema wird unter Aspekten der angewandten Mathematik behandelt und führt den Leser in weit verzweigte theoretische Studien der Flüssigkeitsdynamik ein. Dabei wird in umfassender und verständlicher Weise fast der gesamte Themenkomplex der klassischen Flüssigkeitsdynamik abgedeckt. (10/97)
INTRODUCTION TO THEORETICAL AND MATHEMATICAL FLUID DYNAMICS A practical treatment of mathematical fluid dynamics In Introduction to Theoretical and Mathematical Fluid Dynamics, distinguished researcher Dr. Bhimsen K. Shivamoggi delivers a comprehensive and insightful exploration of fluid dynamics from a mathematical point of view. The book introduces readers to the mathematical study of fluid behavior and highlights areas of active research in fluid dynamics. With coverage of advances in the field over the last 15 years, this book provides in-depth examinations of theoretical and mathematical fluid dynamics with a particular focus on incompressible and compressible fluid flows. Introduction to Theoretical and Mathematical Fluid Dynamics includes practical applications and exercises to illustrate the concepts discussed within, and real-world examples are explained throughout the text. Clear and explanatory material accompanies the rigorous mathematics, making the book perfect for students seeking to learn and retain this complex subject. The book also offers: A thorough introduction to the basic concepts and equations of fluid dynamics, including an introduction to the fluid model, the equations of fluid flows, and surface tension effects Comprehensive explorations of the dynamics of incompressible fluid flows, fluid kinematics and dynamics, the complex-variable method, and three-dimensional irrotational flows Practical discussions of the dynamics of compressible fluid flows, including a review of thermodynamics, isentropic fluid flows, potential flows, and nonlinear theory of plane sound waves Ideal for graduate-level students taking courses on mathematical fluid dynamics as part of a program in mathematics, engineering, or physics, Introduction to Theoretical and Mathematical Fluid Dynamics is also an indispensable resource for practicing applied mathematicians, engineers, and physicists.
Although there are many texts and monographs on fluid dynamics, I do not know of any which is as comprehensive as the present book. It surveys nearly the entire field of classical fluid dynamics in an advanced, compact, and clear manner, and discusses the various conceptual and analytical models of fluid flow." - Foundations of Physics on the first edition Theoretical Fluid Dynamics functions equally well as a graduate-level text and a professional reference. Steering a middle course between the empiricism of engineering and the abstractions of pure mathematics, the author focuses on those ideas and formulations that will be of greatest interest to students and researchers in applied mathematics and theoretical physics. Dr. Shivamoggi covers the main branches of fluid dynamics, with particular emphasis on flows of incompressible fluids. Readers well versed in the physical and mathematical prerequisites will find enlightening discussions of many lesser-known areas of study in fluid dynamics. This thoroughly revised, updated, and expanded Second Edition features coverage of recent developments in stability and turbulence, additional chapter-end exercises, relevant experimental information, and an abundance of new material on a wide range of topics, including: * Hamiltonian formulation * Nonlinear water waves and sound waves * Stability of a fluid layer heated from below * Equilibrium statistical mechanics of turbulence * Two-dimensional turbulence
Integral transform methods provide effective ways to solve a variety of problems arising in the engineering, optical, and physical sciences. Suitable as a self-study for practicing engineers and applied mathematicians and as a textbook in graduate-level courses in optics, engineering sciences, physics, and mathematics.
This book starts with a discussion of nonlinear ordinary differential equations, bifurcation theory and Hamiltonian dynamics. It then embarks on a systematic discussion of the traditional topics of modern nonlinear dynamics -- integrable systems, Poincaré maps, chaos, fractals and strange attractors. The Baker’s transformation, the logistic map and Lorenz system are discussed in detail in view of their central place in the subject. There is a detailed discussion of solitons centered around the Korteweg-deVries equation in view of its central place in integrable systems. Then, there is a discussion of the Painlevé property of nonlinear differential equations which seems to provide a test of integrability. Finally, there is a detailed discussion of the application of fractals and multi-fractals to fully-developed turbulence -- a problem whose understanding has been considerably enriched by the application of the concepts and methods of modern nonlinear dynamics. On the application side, there is a special emphasis on some aspects of fluid dynamics and plasma physics reflecting the author’s involvement in these areas of physics. A few exercises have been provided that range from simple applications to occasional considerable extension of the theory. Finally, the list of references given at the end of the book contains primarily books and papers used in developing the lecture material this volume is based on. This book has grown out of the author’s lecture notes for an interdisciplinary graduate-level course on nonlinear dynamics. The basic concepts, language and results of nonlinear dynamical systems are described in a clear and coherent way. In order to allow for an interdisciplinary readership, an informal style has been adopted and the mathematical formalism has been kept to a minimum. This book is addressed to first-year graduate students in applied mathematics, physics, and engineering, and is useful also to any theoretically inclined researcher in the physical sciences and engineering. This second edition constitutes an extensive rewrite of the text involving refinement and enhancement of the clarity and precision, updating and amplification of several sections, addition of new material like theory of nonlinear differential equations, solitons, Lagrangian chaos in fluids, and critical phenomena perspectives on the fluid turbulence problem and many new exercises.
Perturbation methods are widely used in the study of physically significant differential equations, which arise in Applied Mathematics, Physics and Engineering.; Background material is provided in each chapter along with illustrative examples, problems, and solutions.; A comprehensive bibliography and index complete the work.; Covers an important field of solutions for engineering and the physical sciences.; To allow an interdisciplinary readership, the book focuses almost exclusively on the procedures and the underlying ideas and soft pedal the proofs; Dr. Bhimsen K. Shivamoggi has authored seven successful books for various publishers like John Wiley & Sons and Kluwer Academic Publishers.
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