Author:
Publisher: Krishna Prakashan Media
ISBN:
Category :
Languages : en
Pages : 326

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Book Description

Author: Joel Franklin
Publisher: Cambridge University Press
ISBN: 1108864279
Category : Science
Languages : en
Pages : 275

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Book Description
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.

Author: Arnt Inge Vistnes
Publisher: Springer
ISBN: 3319723146
Category : Science
Languages : en
Pages : 584

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Book Description
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.

Author: Walter Fox Smith
Publisher: Oxford University Press
ISBN: 019539349X
Category : Science
Languages : en
Pages : 416

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Book Description
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.

Author: Russell L. Herman
Publisher: CRC Press
ISBN: 1000687260
Category : Mathematics
Languages : en
Pages : 776

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Book Description
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

Author: Y. Kuramoto
Publisher: Springer Science & Business Media
ISBN: 3642696899
Category : Science
Languages : en
Pages : 165

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Book Description
Tbis book is intended to provide a few asymptotic methods which can be applied to the dynamics of self-oscillating fields of the reaction-diffusion type and of some related systems. Such systems, forming cooperative fields of a large num of interacting similar subunits, are considered as typical synergetic systems. ber Because each local subunit itself represents an active dynamical system function ing only in far-from-equilibrium situations, the entire system is capable of showing a variety of curious pattern formations and turbulencelike behaviors quite unfamiliar in thermodynamic cooperative fields. I personally believe that the nonlinear dynamics, deterministic or statistical, of fields composed of similar active (Le., non-equilibrium) elements will form an extremely attractive branch of physics in the near future. For the study of non-equilibrium cooperative systems, some theoretical guid ing principle would be highly desirable. In this connection, this book pushes for ward a particular physical viewpoint based on the slaving principle. The dis covery of tbis principle in non-equilibrium phase transitions, especially in lasers, was due to Hermann Haken. The great utility of this concept will again be dem onstrated in tbis book for the fields of coupled nonlinear oscillators.

Author: William Thomson Baron Kelvin
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 506

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Author: Ingram Bloch
Publisher: Springer Science & Business Media
ISBN: 1489900500
Category : Science
Languages : en
Pages : 326

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Book Description
Except for digressions in Chapters 8 and 17, this book is a highly unified treatment of simple oscillations and waves. The phenomena treated are "simple" in that they are de scribable by linear equations, almost all occur in one dimension, and the dependent variables are scalars instead of vectors or something else (such as electromagnetic waves) with geometric complications. The book omits such complicated cases in order to deal thoroughly with properties shared by all linear os cillations and waves. The first seven chapters are a sequential treatment of electrical and mechanical oscillating systems, starting with the simplest and proceeding to systems of coupled oscillators subjected to ar bitrary driving forces. Then, after a brief discussion of nonlinear oscillations in Chapter 8, the concept of normal modes of motion is introduced and used to show the relationship between os cillations and waves. After Chapter 12, properties of waves are explored by whatever mathematical techniques are applicable. The book ends with a short discussion of three-dimensional vii viii Preface problems (in Chapter 16), and a study of a few aspects of non linear waves (in Chapter 17).

Author: G.A. Leonov
Publisher: Springer Science & Business Media
ISBN: 9400901933
Category : Mathematics
Languages : en
Pages : 415

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Book Description
This book is devoted to nonlocal theory of nonlinear oscillations. The frequency methods of investigating problems of cycle existence in multidimensional analogues of Van der Pol equation, in dynamical systems with cylindrical phase space and dynamical systems satisfying Routh-Hurwitz generalized conditions are systematically presented here for the first time. To solve these problems methods of Poincaré map construction, frequency methods, synthesis of Lyapunov direct methods and bifurcation theory elements are applied. V.M. Popov's method is employed for obtaining frequency criteria, which estimate period of oscillations. Also, an approach to investigate the stability of cycles based on the ideas of Zhukovsky, Borg, Hartmann, and Olech is presented, and the effects appearing when bounded trajectories are unstable are discussed. For chaotic oscillations theorems on localizations of attractors are given. The upper estimates of Hausdorff measure and dimension of attractors generalizing Doudy-Oesterle and Smith theorems are obtained, illustrated by the example of a Lorenz system and its different generalizations. The analytical apparatus developed in the book is applied to the analysis of oscillation of various control systems, pendulum-like systems and those of synchronization. Audience: This volume will be of interest to those whose work involves Fourier analysis, global analysis, and analysis on manifolds, as well as mathematics of physics and mechanics in general. A background in linear algebra and differential equations is assumed.

Author: Victor Henner
Publisher: CRC Press
ISBN: 1439865167
Category : Mathematics
Languages : en
Pages : 852

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Book Description
This book is a text on partial differential equations (PDEs) of mathematical physics and boundary value problems, trigonometric Fourier series, and special functions. This is the core content of many courses in the fields of engineering, physics, mathematics, and applied mathematics. The accompanying software provides a laboratory environment that