Download or read book Mathematical Methods for Oscillations and Waves written by Joel Franklin and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Anchored in simple and familiar physics problems, the author provides a focused introduction to mathematical methods in a narrative driven and structured manner. Ordinary and partial differential equation solving, linear algebra, vector calculus, complex variables and numerical methods are all introduced and bear relevance to a wide range of physical problems. Expanded and novel applications of these methods highlight their utility in less familiar areas, and advertise those areas that will become more important as students continue. This highlights both the utility of each method in progressing with problems of increasing complexity while also allowing students to see how a simplified problem becomes 're-complexified'. Advanced topics include nonlinear partial differential equations, and relativistic and quantum mechanical variants of problems like the harmonic oscillator. Physics, mathematics and engineering students will find 300 problems treated in a sophisticated manner. The insights emerging from Franklin's treatment make it a valuable teaching resource.
Download or read book Mathematical Methods Oscillations Waves written by and published by Krishna Prakashan Media. This book was released on with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Methods for Oscillations and Waves written by Joel Franklin and published by Cambridge University Press. This book was released on 2020-03-05 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: Anchored in simple and familiar physics problems, the author provides a focused introduction to mathematical methods in a narrative driven and structured manner. Ordinary and partial differential equation solving, linear algebra, vector calculus, complex variables and numerical methods are all introduced and bear relevance to a wide range of physical problems. Expanded and novel applications of these methods highlight their utility in less familiar areas, and advertise those areas that will become more important as students continue. This highlights both the utility of each method in progressing with problems of increasing complexity while also allowing students to see how a simplified problem becomes 're-complexified'. Advanced topics include nonlinear partial differential equations, and relativistic and quantum mechanical variants of problems like the harmonic oscillator. Physics, mathematics and engineering students will find 300 problems treated in a sophisticated manner. The insights emerging from Franklin's treatment make it a valuable teaching resource.
Download or read book Oscillations and Waves written by Fritz K. Kneubühl and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: This very comprehensive and practical textbook presents a clear, systematic and comprehensive introduction to the relevant mathematics and physics of linear and nonlinear oscillations and waves. It explains even the most complicated cases clearly, with numerous illustrations for further clarification.
Download or read book Physics of Oscillations and Waves written by Arnt Inge Vistnes and published by Springer. This book was released on 2018-08-21 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this textbook a combination of standard mathematics and modern numerical methods is used to describe a wide range of natural wave phenomena, such as sound, light and water waves, particularly in specific popular contexts, e.g. colors or the acoustics of musical instruments. It introduces the reader to the basic physical principles that allow the description of the oscillatory motion of matter and classical fields, as well as resulting concepts including interference, diffraction, and coherence. Numerical methods offer new scientific insights and make it possible to handle interesting cases that can’t readily be addressed using analytical mathematics; this holds true not only for problem solving but also for the description of phenomena. Essential physical parameters are brought more into focus, rather than concentrating on the details of which mathematical trick should be used to obtain a certain solution. Readers will learn how time-resolved frequency analysis offers a deeper understanding of the interplay between frequency and time, which is relevant to many phenomena involving oscillations and waves. Attention is also drawn to common misconceptions resulting from uncritical use of the Fourier transform. The book offers an ideal guide for upper-level undergraduate physics students and will also benefit physics instructors. Program codes in Matlab and Python, together with interesting files for use in the problems, are provided as free supplementary material.
Download or read book A Course in Mathematical Methods for Physicists written by Russell L. Herman and published by CRC Press. This book was released on 2013-12-04 with total page 776 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the author's junior-level undergraduate course, this introductory textbook is designed for a course in mathematical physics. Focusing on the physics of oscillations and waves, A Course in Mathematical Methods for Physicists helps students understand the mathematical techniques needed for their future studies in physics. It takes a bottom-u
Download or read book Waves and Oscillations written by Walter Fox Smith and published by Oxford University Press. This book was released on 2010-05-20 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: This lively textbook differs from others on the subject by its usefulness as a conceptual and mathematical preparation for the study of quantum mechanics, by its emphasis on a variety of learning tools aimed at fostering the student's self-awareness of learning, and by its frequent connections to current research.
Download or read book Handbook of Mathematical Techniques for Wave Structure Interactions written by C.M. Linton and published by CRC Press. This book was released on 2001-02-26 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although a wide range of mathematical techniques can apply to solving problems involving the interaction of waves with structures, few texts discuss those techniques within that context-most often they are presented without reference to any applications. Handbook of Mathematical Techniques for Wave/Structure Interactions brings together some of the
Download or read book Rays Waves and Scattering written by John A. Adam and published by Princeton University Press. This book was released on 2017-05-30 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: This one-of-a-kind book presents many of the mathematical concepts, structures, and techniques used in the study of rays, waves, and scattering. Panoramic in scope, it includes discussions of how ocean waves are refracted around islands and underwater ridges, how seismic waves are refracted in the earth's interior, how atmospheric waves are scattered by mountains and ridges, how the scattering of light waves produces the blue sky, and meteorological phenomena such as rainbows and coronas. Rays, Waves, and Scattering is a valuable resource for practitioners, graduate students, and advanced undergraduates in applied mathematics, theoretical physics, and engineering. Bridging the gap between advanced treatments of the subject written for specialists and less mathematical books aimed at beginners, this unique mathematical compendium features problems and exercises throughout that are geared to various levels of sophistication, covering everything from Ptolemy's theorem to Airy integrals (as well as more technical material), and several informative appendixes. Provides a panoramic look at wave motion in many different contexts Features problems and exercises throughout Includes numerous appendixes, some on topics not often covered An ideal reference book for practitioners Can also serve as a supplemental text in classical applied mathematics, particularly wave theory and mathematical methods in physics and engineering Accessible to anyone with a strong background in ordinary differential equations, partial differential equations, and functions of a complex variable
Download or read book Slowly Varying Oscillations And Waves From Basics To Modernity written by Lev Ostrovsky and published by World Scientific. This book was released on 2022-02-23 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: The beauty of the theoretical science is that quite different physical, biological, etc. phenomena can often be described as similar mathematical objects, by similar differential (or other) equations. In the 20th century, the notion of 'theory of oscillations' and later 'theory of waves' as unifying concepts, meaning the application of similar methods and equations to quite different physical problems, came into being. In the variety of applications (quite possibly in most of them), the oscillatory process is characterized by a slow (as compared with the characteristic period) variation of its parameters, such as the amplitude and frequency. The same is true for the wave processes.This book describes a variety of problems associated with oscillations and waves with slowly varying parameters. Among them the nonlinear and parametric resonances, self-synchronization, attenuated and amplified solitons, self-focusing and self-modulation, and reaction-diffusion systems. For oscillators, the physical examples include the van der Pol oscillator and a pendulum, models of a laser. For waves, examples are taken from oceanography, nonlinear optics, acoustics, and biophysics. The last chapter of the book describes more formal asymptotic perturbation schemes for the classes of oscillators and waves considered in all preceding chapters.
Download or read book An Introduction to the Mathematical Theory of Waves written by Roger Knobel and published by American Mathematical Soc.. This book was released on 2000 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on an undergraduate course taught at the IAS/Park City Mathematics Institute (Utah) on linear and nonlinear waves. The first part of the text overviews the concept of a wave, describes one-dimensional waves using functions of two variables, provides an introduction to partial differential equations, and discusses computer-aided visualization techniques. The second part of the book discusses traveling waves, leading to a description of solitary waves and soliton solutions of the Klein-Gordon and Korteweg-deVries equations. The wave equation is derived to model the small vibrations of a taut string, and solutions are constructed via d'Alembert's formula and Fourier series.The last part of the book discusses waves arising from conservation laws. After deriving and discussing the scalar conservation law, its solution is described using the method of characteristics, leading to the formation of shock and rarefaction waves. Applications of these concepts are then given for models of traffic flow. The intent of this book is to create a text suitable for independent study by undergraduate students in mathematics, engineering, and science. The content of the book is meant to be self-contained, requiring no special reference material. Access to computer software such as MathematicaR, MATLABR, or MapleR is recommended, but not necessary. Scripts for MATLAB applications will be available via the Web. Exercises are given within the text to allow further practice with selected topics.
Download or read book Mathematical Methods for Wave Phenomena written by Norman Bleistein and published by Academic Press. This book was released on 2012-12-02 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computer Science and Applied Mathematics: Mathematical Methods for Wave Phenomena focuses on the methods of applied mathematics, including equations, wave fronts, boundary value problems, and scattering problems. The publication initially ponders on first-order partial differential equations, Dirac delta function, Fourier transforms, asymptotics, and second-order partial differential equations. Discussions focus on prototype second-order equations, asymptotic expansions, asymptotic expansions of Fourier integrals with monotonic phase, method of stationary phase, propagation of wave fronts, and variable index of refraction. The text then examines wave equation in one space dimension, as well as initial boundary value problems, characteristics for the wave equation in one space dimension, and asymptotic solution of the Klein-Gordon equation. The manuscript offers information on wave equation in two and three dimensions and Helmholtz equation and other elliptic equations. Topics include energy integral, domain of dependence, and uniqueness, scattering problems, Green's functions, and problems in unbounded domains and the Sommerfeld radiation condition. The asymptotic techniques for direct scattering problems and the inverse methods for reflector imaging are also elaborated. The text is a dependable reference for computer science experts and mathematicians pursuing studies on the mathematical methods of wave phenomena.
Download or read book Waves and Oscillations written by R. N. Chaudhuri and published by New Age International. This book was released on 2001 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Book Explains The Various Dimensions Of Waves And Oscillations In A Simple And Systematic Manner. It Is An Unique Attempt At Presenting A Self-Contained Account Of The Subject With Step-By-Step Solutions Of A Large Number Of Problems Of Different Types. The Book Will Be Of Great Help Not Only To Undergraduate Students, But Also To Those Preparing For Various Competitive Examinations.
Download or read book Applied Wave Mathematics II written by Arkadi Berezovski and published by Springer Nature. This book was released on 2019-11-16 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers contributions on various aspects of the theory and applications of linear and nonlinear waves and associated phenomena, as well as approaches developed in a global partnership of researchers with the national Centre of Excellence in Nonlinear Studies (CENS) at the Department of Cybernetics of Tallinn University of Technology in Estonia. The papers chiefly focus on the role of mathematics in the analysis of wave phenomena. They highlight the complexity of related topics concerning wave generation, propagation, transformation and impact in solids, gases, fluids and human tissues, while also sharing insights into selected mathematical methods for the analytical and numerical treatment of complex phenomena. In addition, the contributions derive advanced mathematical models, share innovative ideas on computing, and present novel applications for a number of research fields where both linear and nonlinear wave problems play an important role. The papers are written in a tutorial style, intended for non-specialist researchers and students. The authors first describe the basics of a problem that is currently of interest in the scientific community, discuss the state of the art in related research, and then share their own experiences in tackling the problem. Each chapter highlights the importance of applied mathematics for central issues in the study of waves and associated complex phenomena in different media. The topics range from basic principles of wave mechanics up to the mathematics of Planet Earth in the broadest sense, including contemporary challenges in the mathematics of society. In turn, the areas of application range from classic ocean wave mathematics to material science, and to human nerves and tissues. All contributions describe the approaches in a straightforward manner, making them ideal material for educational purposes, e.g. for courses, master class lectures, or seminar presentations.
Download or read book Wave Physics written by Stephen Nettel and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classical physics of oscillations and waves is developed here at a more advanced mathematical level than is customary for second-year courses. The detailed explanation of the phenomena provides a sound basis for the introduction to wave mechanics that follows. A chapter on nonlinear waves and solitons, as well as contributions on chaos and associated phenomena broaden the concepts of wave behavior, while introducing the reader to important topics in current wave physics. Directed primarily at undergraduates in physics, mathematics and engineering, this will also be useful as a reference for graduate students, and for professors looking for examination questions. This revised second edition contains a number of new examples and exercises.
Download or read book Wave Physics written by Stephen Nettel and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook gives a detailed explanation of waves and oscillations in classical physics. These classical phenomena are dealt with at a more advanced level than is customary for second-year courses. All aspects of classical wave physics are presented, including the mathematical and physical basis needed for extended understanding. Finally several chapters are devoted to important topics in current wave physics. Special attention is given to nonlinear waves, solitons, chaotic behavior and associated phenomena. The new edition contains improvements such as full development of Greens functions, a broadening of the treatment of wave mechanics and a closer integration with classical mechanics, plus more examples and problems.
Download or read book Oscillations and Waves written by Richard Fitzpatrick and published by CRC Press. This book was released on 2013-01-07 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bridging lower-division physics survey courses with upper-division physics courses, Oscillations and Waves: An Introduction develops a unified mathematical theory of oscillations and waves in physical systems. Emphasizing physics over mathematics, the author includes many examples from discrete mechanical, optical, and quantum mechanical systems; continuous gases, fluids, and elastic solids; electronic circuits; and electromagnetic waves. Assuming familiarity with the laws of physics and college-level mathematics, the book focuses on oscillations and waves whose governing differential equations are linear. The author covers aspects of optics that crucially depend on the wave-like nature of light, such as wave optics. He also introduces the conventional complex representation of oscillations and waves later in the text during the discussion of quantum mechanical waves. This helps students thoroughly understand how to represent oscillations and waves in terms of regular trigonometric functions before using the more convenient, but much more abstract, complex representation. Based on the author’s longstanding course at the University of Texas at Austin, this classroom-tested text helps students acquire a sound physical understanding of wave phenomena. It eases students’ difficult transition between lower-division courses that mostly encompass algebraic equations and upper-division courses that rely on differential equations.
