A Mathematical Journey Through Differential Equations Of Physics PDF Download
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| Author | : Max Lein |
| Publisher | : World Scientific |
| Total Pages | : 478 |
| Release | : 2022-09-16 |
| Genre | : Science |
| ISBN | : 9811225397 |
Download A Mathematical Journey Through Differential Equations Of Physics Book in PDF, ePub and Kindle
Mathematics is the language of physics, and over time physicists have developed their own dialect. The main purpose of this book is to bridge this language barrier, and introduce the readers to the beauty of mathematical physics. It shows how to combine the strengths of both approaches: physicists often arrive at interesting conjectures based on good intuition, which can serve as the starting point of interesting mathematics. Conversely, mathematicians can more easily see commonalities between very different fields (such as quantum mechanics and electromagnetism), and employ more advanced tools.Rather than focusing on a particular topic, the book showcases conceptual and mathematical commonalities across different physical theories. It translates physical problems to concrete mathematical questions, shows how to answer them and explains how to interpret the answers physically. For example, if two Hamiltonians are close, why are their dynamics similar?The book alternates between mathematics- and physics-centric chapters, and includes plenty of concrete examples from physics as well as 76 exercises with solutions. It exploits that readers from either end are familiar with some of the material already. The mathematics-centric chapters provide the necessary background to make physical concepts mathematically precise and establish basic facts. And each physics-centric chapter introduces physical theories in a way that is more friendly to mathematicians.As the book progresses, advanced material is sprinkled in to showcase how mathematics and physics augment one another. Some of these examples are based on recent publications and include material which has not been covered in other textbooks. This is to keep it interesting for the readers.
| Author | : James Kirkwood |
| Publisher | : Academic Press |
| Total Pages | : 494 |
| Release | : 2018-02-26 |
| Genre | : Mathematics |
| ISBN | : 0128147601 |
Download Mathematical Physics with Partial Differential Equations Book in PDF, ePub and Kindle
Mathematical Physics with Partial Differential Equations, Second Edition, is designed for upper division undergraduate and beginning graduate students taking mathematical physics taught out by math departments. The new edition is based on the success of the first, with a continuing focus on clear presentation, detailed examples, mathematical rigor and a careful selection of topics. It presents the familiar classical topics and methods of mathematical physics with more extensive coverage of the three most important partial differential equations in the field of mathematical physics—the heat equation, the wave equation and Laplace’s equation. The book presents the most common techniques of solving these equations, and their derivations are developed in detail for a deeper understanding of mathematical applications. Unlike many physics-leaning mathematical physics books on the market, this work is heavily rooted in math, making the book more appealing for students wanting to progress in mathematical physics, with particularly deep coverage of Green’s functions, the Fourier transform, and the Laplace transform. A salient characteristic is the focus on fewer topics but at a far more rigorous level of detail than comparable undergraduate-facing textbooks. The depth of some of these topics, such as the Dirac-delta distribution, is not matched elsewhere. New features in this edition include: novel and illustrative examples from physics including the 1-dimensional quantum mechanical oscillator, the hydrogen atom and the rigid rotor model; chapter-length discussion of relevant functions, including the Hermite polynomials, Legendre polynomials, Laguerre polynomials and Bessel functions; and all-new focus on complex examples only solvable by multiple methods. Introduces and evaluates numerous physical and engineering concepts in a rigorous mathematical framework Provides extremely detailed mathematical derivations and solutions with extensive proofs and weighting for application potential Explores an array of detailed examples from physics that give direct application to rigorous mathematics Offers instructors useful resources for teaching, including an illustrated instructor's manual, PowerPoint presentations in each chapter and a solutions manual
| Author | : Edward K Blum |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 498 |
| Release | : 2006-07-07 |
| Genre | : Science |
| ISBN | : 981310662X |
Download Mathematics Of Physics And Engineering Book in PDF, ePub and Kindle
Aimed at scientists and engineers, this book is an exciting intellectual journey through the mathematical worlds of Euclid, Newton, Maxwell, Einstein, and Schrodinger-Dirac.While similar books present the required mathematics in a piecemeal manner with tangential references to the relevant physics and engineering, this textbook serves the interdisciplinary needs of engineers, scientists and applied mathematicians by unifying the mathematics and physics into a single systematic body of knowledge but preserving the rigorous logical development of the mathematics.The authors take an unconventional approach by integrating the mathematics with its motivating physical phenomena and, conversely, by showing how the mathematical models predict new physical phenomena.
| Author | : A. N. Tikhonov |
| Publisher | : Courier Corporation |
| Total Pages | : 802 |
| Release | : 2013-09-16 |
| Genre | : Mathematics |
| ISBN | : 0486173364 |
Download Equations of Mathematical Physics Book in PDF, ePub and Kindle
Mathematical physics plays an important role in the study of many physical processes — hydrodynamics, elasticity, and electrodynamics, to name just a few. Because of the enormous range and variety of problems dealt with by mathematical physics, this thorough advanced undergraduate- or graduate-level text considers only those problems leading to partial differential equations. Contents: I. Classification of Partial Differential Equations II. Evaluations of the Hyperbolic Type III. Equations of the Parabolic Type IV. Equations of Elliptic Type V. Wave Propagation in Space VI. Heat Conduction in Space VII. Equations of Elliptic Type (Continuation) The authors — two well-known Russian mathematicians — have focused on typical physical processes and the principal types of equations dealing with them. Special attention is paid throughout to mathematical formulation, rigorous solutions, and physical interpretation of the results obtained. Carefully chosen problems designed to promote technical skills are contained in each chapter, along with extremely useful appendixes that supply applications of solution methods described in the main text. At the end of the book, a helpful supplement discusses special functions, including spherical and cylindrical functions.
| Author | : Huaiyu Wang |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 752 |
| Release | : 2017-03-02 |
| Genre | : |
| ISBN | : 9813146508 |
Download Mathematics for Physicists Book in PDF, ePub and Kindle
This book covers the necessary aspects of mathematics for graduate students in physics and engineering. Advanced undergraduate students and researchers who intend to enter the field of theoretical physics can also pick up this book. The first eight chapters include variational method, Hilbert space and operators, ordinary linear differential equations, Bessel functions, Dirac delta function, the Green's function in mathematical physics, norm, integral equations. Beside these traditional contents, the last two chapters introduce some recent achievements of scientific research while presenting their mathematical background. Like the basis of number theory and its application in physics, material science and other scientific fields, the fundamental equations in spaces with arbitrary dimensions, not limited to Euclid space; Pseudo spherical coordinates. Plain terminologies were used to present the concept of metric, as well as new and interesting work on the Klein-Gorden equation and Maxwell equation. Request Inspection Copy
| Author | : Victor Henner |
| Publisher | : CRC Press |
| Total Pages | : 859 |
| Release | : 2009-06-18 |
| Genre | : Mathematics |
| ISBN | : 1439865167 |
Download Mathematical Methods in Physics Book in PDF, ePub and Kindle
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
| Author | : Ronald B. Guenther |
| Publisher | : Courier Corporation |
| Total Pages | : 576 |
| Release | : 2012-09-19 |
| Genre | : Mathematics |
| ISBN | : 0486137627 |
Download Partial Differential Equations of Mathematical Physics and Integral Equations Book in PDF, ePub and Kindle
Superb treatment for math and physical science students discusses modern mathematical techniques for setting up and analyzing problems. Discusses partial differential equations of the 1st order, elementary modeling, potential theory, parabolic equations, more. 1988 edition.
| Author | : Grigori N. Milstein |
| Publisher | : Springer Nature |
| Total Pages | : 754 |
| Release | : 2021-12-03 |
| Genre | : Computers |
| ISBN | : 3030820408 |
Download Stochastic Numerics for Mathematical Physics Book in PDF, ePub and Kindle
This book is a substantially revised and expanded edition reflecting major developments in stochastic numerics since the first edition was published in 2004. The new topics, in particular, include mean-square and weak approximations in the case of nonglobally Lipschitz coefficients of Stochastic Differential Equations (SDEs) including the concept of rejecting trajectories; conditional probabilistic representations and their application to practical variance reduction using regression methods; multi-level Monte Carlo method; computing ergodic limits and additional classes of geometric integrators used in molecular dynamics; numerical methods for FBSDEs; approximation of parabolic SPDEs and nonlinear filtering problem based on the method of characteristics. SDEs have many applications in the natural sciences and in finance. Besides, the employment of probabilistic representations together with the Monte Carlo technique allows us to reduce the solution of multi-dimensional problems for partial differential equations to the integration of stochastic equations. This approach leads to powerful computational mathematics that is presented in the treatise. Many special schemes for SDEs are presented. In the second part of the book numerical methods for solving complicated problems for partial differential equations occurring in practical applications, both linear and nonlinear, are constructed. All the methods are presented with proofs and hence founded on rigorous reasoning, thus giving the book textbook potential. An overwhelming majority of the methods are accompanied by the corresponding numerical algorithms which are ready for implementation in practice. The book addresses researchers and graduate students in numerical analysis, applied probability, physics, chemistry, and engineering as well as mathematical biology and financial mathematics.
| Author | : |
| Publisher | : |
| Total Pages | : 1 |
| Release | : 2002 |
| Genre | : |
| ISBN | : |
Download Provisional Agenda for the 4510th Meeting of the Security Council, to be Held on Monday, 8 April 2002 Book in PDF, ePub and Kindle
| Author | : Lopez Velazquez Gustavo |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 200 |
| Release | : 2012-03-21 |
| Genre | : Science |
| ISBN | : 9814397504 |
Download Partial Differential Equations Of First Order And Their Applications To Physics (2nd Edition) Book in PDF, ePub and Kindle
This book tries to point out the mathematical importance of the Partial Differential Equations of First Order (PDEFO) in Physics and Applied Sciences. The intention is to provide mathematicians with a wide view of the applications of this branch in physics, and to give physicists and applied scientists a powerful tool for solving some problems appearing in Classical Mechanics, Quantum Mechanics, Optics, and General Relativity. This book is intended for senior or first year graduate students in mathematics, physics, or engineering curricula.This book is unique in the sense that it covers the applications of PDEFO in several branches of applied mathematics, and fills the theoretical gap between the formal mathematical presentation of the theory and the pure applied tool to physical problems that are contained in other books.Improvements made in this second edition include corrected typographical errors; rewritten text to improve the flow and enrich the material; added exercises in all chapters; new applications in Chapters 1, 2, and 5 and expanded examples.
