Download or read book Mathematical Methods of Classical Mechanics written by V.I. Arnol'd and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.
Download or read book Mathematical Methods in Quantum Mechanics written by Gerald Teschl and published by American Mathematical Soc.. This book was released on 2009 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum mechanics and the theory of operators on Hilbert space have been deeply linked since their beginnings in the early twentieth century. States of a quantum system correspond to certain elements of the configuration space and observables correspond to certain operators on the space. This book is a brief, but self-contained, introduction to the mathematical methods of quantum mechanics, with a view towards applications to Schrodinger operators. Part 1 of the book is a concise introduction to the spectral theory of unbounded operators. Only those topics that will be needed for later applications are covered. The spectral theorem is a central topic in this approach and is introduced at an early stage. Part 2 starts with the free Schrodinger equation and computes the free resolvent and time evolution. Position, momentum, and angular momentum are discussed via algebraic methods. Various mathematical methods are developed, which are then used to compute the spectrum of the hydrogen atom. Further topics include the nondegeneracy of the ground state, spectra of atoms, and scattering theory. This book serves as a self-contained introduction to spectral theory of unbounded operators in Hilbert space with full proofs and minimal prerequisites: Only a solid knowledge of advanced calculus and a one-semester introduction to complex analysis are required. In particular, no functional analysis and no Lebesgue integration theory are assumed. It develops the mathematical tools necessary to prove some key results in nonrelativistic quantum mechanics. Mathematical Methods in Quantum Mechanics is intended for beginning graduate students in both mathematics and physics and provides a solid foundation for reading more advanced books and current research literature. It is well suited for self-study and includes numerous exercises (many with hints).
Download or read book Mathematical Methods in Continuum Mechanics of Solids written by Martin Kružík and published by Springer. This book was released on 2019-03-02 with total page 617 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book primarily focuses on rigorous mathematical formulation and treatment of static problems arising in continuum mechanics of solids at large or small strains, as well as their various evolutionary variants, including thermodynamics. As such, the theory of boundary- or initial-boundary-value problems for linear or quasilinear elliptic, parabolic or hyperbolic partial differential equations is the main underlying mathematical tool, along with the calculus of variations. Modern concepts of these disciplines as weak solutions, polyconvexity, quasiconvexity, nonsimple materials, materials with various rheologies or with internal variables are exploited. This book is accompanied by exercises with solutions, and appendices briefly presenting the basic mathematical concepts and results needed. It serves as an advanced resource and introductory scientific monograph for undergraduate or PhD students in programs such as mathematical modeling, applied mathematics, computational continuum physics and engineering, as well as for professionals working in these fields.
Download or read book Mathematical Methods For Physics written by H. W. Wyld and published by CRC Press. This book was released on 2018-03-14 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic book helps students learn the basics in physics by bridging the gap between mathematics and the basic fundamental laws of physics. With supplemental material such as graphs and equations, Mathematical Methods for Physics creates a strong, solid anchor of learning. The text has three parts: Part I focuses on the use of special functions in solving the homogeneous partial differential equations of physics, and emphasizes applications to topics such as electrostatics, wave guides, and resonant cavities, vibrations of membranes, heat flow, potential flow in fluids, plane and spherical waves. Part II deals with the solution of inhomogeneous differential equations with particular emphasis on problems in electromagnetism, Green's functions for Poisson's equation, the wave equation and the diffusion equation, and the solution of integral equations by iteration, eigenfunction expansion and the Fredholm series. Finally, Part II explores complex variable techniques, including evalution of itegrals, dispersion relations, special functions in the complex plane, one-sided Fourier transforms, and Laplace transforms.
Download or read book Mathematical Methods for Mechanics written by Eckart W. Gekeler and published by Springer Science & Business Media. This book was released on 2008-09-26 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is undoubtedly the key to state-of-the-art high technology. It is aninternationaltechnicallanguageandprovestobeaneternallyyoungscience to those who have learned its ways. Long an indispensable part of research thanks to modeling and simulation, mathematics is enjoying particular vit- ity now more than ever. Nevertheless, this stormy development is resulting in increasingly high requirements for students in technical disciplines, while general interest in mathematics continues to wane at the same time. This book and its appendices on the Internet seek to deal with this issue, helping students master the di?cult transition from the receptive to the productive phase of their education. The author has repeatedly held a three-semester introductory course - titled Higher Mathematics at the University of Stuttgart and used a series of “handouts” to show further aspects, make the course contents more motiv- ing, and connect with the mechanics lectures taking place at the same time. One part of the book has more or less evolved from this on its own. True to the original objective, this part treats a variety of separate topics of varying degrees of di?culty; nevertheless, all these topics are oriented to mechanics. Anotherpartofthisbookseekstoo?eraselectionofunderstandablereal- ticmodelsthatcanbeimplementeddirectlyfromthemultitudeofmathema- calresources.TheauthordoesnotattempttohidehispreferenceofNumerical Mathematics and thus places importance on careful theoretical preparation.
Download or read book Mathematical Methods of Classical Physics written by Vicente Cortés and published by Springer. This book was released on 2017-04-26 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: This short primer, geared towards students with a strong interest in mathematically rigorous approaches, introduces the essentials of classical physics, briefly points out its place in the history of physics and its relation to modern physics, and explains what benefits can be gained from a mathematical perspective. As a starting point, Newtonian mechanics is introduced and its limitations are discussed. This leads to and motivates the study of different formulations of classical mechanics, such as Lagrangian and Hamiltonian mechanics, which are the subjects of later chapters. In the second part, a chapter on classical field theories introduces more advanced material. Numerous exercises are collected in the appendix.
Download or read book Mathematical Methods written by Sadri Hassani and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 673 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intended to follow the usual introductory physics courses, this book contains many original, lucid and relevant examples from the physical sciences, problems at the ends of chapters, and boxes to emphasize important concepts to help guide students through the material.
Download or read book Mathematical Methods for Physics and Engineering written by Mattias Blennow and published by CRC Press. This book was released on 2018-01-03 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: Suitable for advanced undergraduate and graduate students, this new textbook contains an introduction to the mathematical concepts used in physics and engineering. The entire book is unique in that it draws upon applications from physics, rather than mathematical examples, to ensure students are fully equipped with the tools they need. This approach prepares the reader for advanced topics, such as quantum mechanics and general relativity, while offering examples, problems, and insights into classical physics. The book is also distinctive in the coverage it devotes to modelling, and to oft-neglected topics such as Green's functions.
Download or read book Mathematical Methods in the Physical Sciences written by Mary L. Boas and published by John Wiley & Sons. This book was released on 2006 with total page 868 pages. Available in PDF, EPUB and Kindle. Book excerpt: Market_Desc: · Physicists and Engineers· Students in Physics and Engineering Special Features: · Covers everything from Linear Algebra, Calculus, Analysis, Probability and Statistics, to ODE, PDE, Transforms and more· Emphasizes intuition and computational abilities· Expands the material on DE and multiple integrals· Focuses on the applied side, exploring material that is relevant to physics and engineering· Explains each concept in clear, easy-to-understand steps About The Book: The book provides a comprehensive introduction to the areas of mathematical physics. It combines all the essential math concepts into one compact, clearly written reference. This book helps readers gain a solid foundation in the many areas of mathematical methods in order to achieve a basic competence in advanced physics, chemistry, and engineering.
Download or read book Mathematical Methods for Physics written by H.W. Wyld and published by CRC Press. This book was released on 2020-11-25 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: From classical mechanics and classical electrodynamics to modern quantum mechanics many physical phenomena are formulated in terms of similar partial differential equations while boundary conditions determine the specifics of the problem. This 45th anniversary edition of the advanced book classic Mathematical Methods for Physics demonstrates how many physics problems resolve into similar inhomogeneous partial differential equations and the mathematical techniques for solving them. The text has three parts: Part I establishes solving the homogenous Laplace and Helmholtz equations in the three main coordinate systems, rectilinear, cylindrical, and spherical and develops the solution space for series solutions to the Sturm-Liouville equation, indicial relations, and the expansion of orthogonal functions including spherical harmonics and Fourier series, Bessel, and Spherical Bessel functions. Many examples with figures are provided including electrostatics, wave guides and resonant cavities, vibrations of membranes, heat flow, potential flow in fluids, and plane and spherical waves. In Part II the inhomogeneous equations are addressed where source terms are included for Poisson's equation, the wave equation, and the diffusion equation. Coverage includes many examples from averaging approaches for electrostatics and magnetostatics, from Green function solutions for time independent and time dependent problems, and from integral equation methods. In Part III complex variable techniques are presented for solving integral equations involving Cauchy Residue theory, contour methods, analytic continuation, and transforming the contour; for addressing dispersion relations; for revisiting special functions in the complex plane; and for transforms in the complex plane including Green’s functions and Laplace transforms. Key Features: · Mathematical Methods for Physics creates a strong, solid anchor of learning and is useful for reference. · Lecture note style suitable for advanced undergraduate and graduate students to learn many techniques for solving partial differential equations with boundary conditions · Many examples across various subjects of physics in classical mechanics, classical electrodynamics, and quantum mechanics · Updated typesetting and layout for improved clarity This book, in lecture note style with updated layout and typesetting, is suitable for advanced undergraduate, graduate students, and as a reference for researchers. It has been edited and carefully updated by Gary Powell.
Download or read book Mathematical Methods in Physics written by Philippe Blanchard and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: Physics has long been regarded as a wellspring of mathematical problems. Mathematical Methods in Physics is a self-contained presentation, driven by historic motivations, excellent examples, detailed proofs, and a focus on those parts of mathematics that are needed in more ambitious courses on quantum mechanics and classical and quantum field theory. Aimed primarily at a broad community of graduate students in mathematics, mathematical physics, physics and engineering, as well as researchers in these disciplines.
Download or read book Mathematical Methods for Physics written by J. R. Claycomb and published by Stylus Publishing, LLC. This book was released on 2018-03-20 with total page 820 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book may be used by students and professionals in physics and engineering that have completed first-year calculus and physics. An introductory chapter reviews algebra, trigonometry, units and complex numbers that are frequently used in physics. Examples using MATLAB and Maple for symbolic and numerical calculations in physics with a variety of plotting features are included in all 16 chapters. The book applies many of mathematical concepts covered in Chapters 1-9 to fundamental physics topics in mechanics, electromagnetics; quantum mechanics and relativity in Chapters 10-16. Companion files are included with MATLAB and Maple worksheets and files, and all of the figures from the text. Features: • Each chapter includes the mathematical development of the concept with numerous examples • MATLAB & Maple examples are integrated in each chapter throughout the book • Applies the mathematical concepts to fundamental physics principles such as relativity, mechanics, electromagnetics, etc. • Introduces basic MATLAB and Maple commands and programming structures • Includes companion files with MATLAB and Maple files and worksheets, and all of the figures from the text
Download or read book Basic Training in Mathematics written by R. Shankar and published by Springer. This book was released on 2013-12-20 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on course material used by the author at Yale University, this practical text addresses the widening gap found between the mathematics required for upper-level courses in the physical sciences and the knowledge of incoming students. This superb book offers students an excellent opportunity to strengthen their mathematical skills by solving various problems in differential calculus. By covering material in its simplest form, students can look forward to a smooth entry into any course in the physical sciences.
Download or read book Mathematical Methods for Physicists written by Tai L. Chow and published by Cambridge University Press. This book was released on 2000-07-27 with total page 575 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is designed for an intermediate-level, two-semester undergraduate course in mathematical physics. It provides an accessible account of most of the current, important mathematical tools required in physics these days. It is assumed that the reader has an adequate preparation in general physics and calculus. The book bridges the gap between an introductory physics course and more advanced courses in classical mechanics, electricity and magnetism, quantum mechanics, and thermal and statistical physics. The text contains a large number of worked examples to illustrate the mathematical techniques developed and to show their relevance to physics. The book is designed primarily for undergraduate physics majors, but could also be used by students in other subjects, such as engineering, astronomy and mathematics.
Download or read book Mathematical Methods of Classical Mechanics written by V. I. Arnold and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many different mathematical methods and concepts are used in classical mechanics: differential equations and phase ftows, smooth mappings and manifolds, Lie groups and Lie algebras, symplectic geometry and ergodic theory. Many modern mathematical theories arose from problems in mechanics and only later acquired that axiomatic-abstract form which makes them so hard to study. In this book we construct the mathematical apparatus of classical mechanics from the very beginning; thus, the reader is not assumed to have any previous knowledge beyond standard courses in analysis (differential and integral calculus, differential equations), geometry (vector spaces, vectors) and linear algebra (linear operators, quadratic forms). With the help of this apparatus, we examine all the basic problems in dynamics, including the theory of oscillations, the theory of rigid body motion, and the hamiltonian formalism. The author has tried to show the geometric, qualitative aspect of phenomena. In this respect the book is closer to courses in theoretical mechanics for theoretical physicists than to traditional courses in theoretical mechanics as taught by mathematicians.
Download or read book Mathematical Methods in Physics and Engineering written by John W. Dettman and published by Courier Corporation. This book was released on 2013-01-23 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intended for college-level physics, engineering, or mathematics students, this volume offers an algebraically based approach to various topics in applied math. It is accessible to undergraduates with a good course in calculus which includes infinite series and uniform convergence. Exercises follow each chapter to test the student's grasp of the material; however, the author has also included exercises that extend the results to new situations and lay the groundwork for new concepts to be introduced later. A list of references for further reading will be found at the end of each chapter. For this second revised edition, Professor Dettman included a new section on generalized functions to help explain the use of the Dirac delta function in connection with Green's functions. In addition, a new approach to series solutions of ordinary differential equations has made the treatment independent of complex variable theory. This means that the first six chapters can be grasped without prior knowledge of complex variables. However, since Chapter 8 depends heavily on analytic functions of a complex variable, a new Chapter 7 on analytic function theory has been written.
Download or read book Introduction to Mathematical Physics written by Chun Wa Wong and published by OUP Oxford. This book was released on 2013-01-24 with total page 731 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical physics provides physical theories with their logical basis and the tools for drawing conclusions from hypotheses. Introduction to Mathematical Physics explains to the reader why and how mathematics is needed in the description of physical events in space. For undergraduates in physics, it is a classroom-tested textbook on vector analysis, linear operators, Fourier series and integrals, differential equations, special functions and functions of a complex variable. Strongly correlated with core undergraduate courses on classical and quantum mechanics and electromagnetism, it helps the student master these necessary mathematical skills. It contains advanced topics of interest to graduate students on relativistic square-root spaces and nonlinear systems. It contains many tables of mathematical formulas and references to useful materials on the Internet. It includes short tutorials on basic mathematical topics to help readers refresh their mathematical knowledge. An appendix on Mathematica encourages the reader to use computer-aided algebra to solve problems in mathematical physics. A free Instructor's Solutions Manual is available to instructors who order the book for course adoption.