A Guide to Mathematical Methods for Physicists

With Problems and Solutions

Author: Michela Petrini,Gianfranco Pradisi,Alberto Zaffaroni

Publisher: World Scientific Publishing Company

ISBN: 1786343460

Category: Science

Page: 340

View: 9384

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Mathematics plays a fundamental role in the formulation of physical theories. This textbook provides a self-contained and rigorous presentation of the main mathematical tools needed in many fields of Physics, both classical and quantum. It covers topics treated in mathematics courses for final-year undergraduate and graduate physics programmes, including complex function: distributions, Fourier analysis, linear operators, Hilbert spaces and eigenvalue problems. The different topics are organised into two main parts — complex analysis and vector spaces — in order to stress how seemingly different mathematical tools, for instance the Fourier transform, eigenvalue problems or special functions, are all deeply interconnected. Also contained within each chapter are fully worked examples, problems and detailed solutions. A companion volume covering more advanced topics that enlarge and deepen those treated here is also available. Contents:Complex Analysis:Holomorphic FunctionsIntegrationTaylor and Laurent SeriesResiduesFunctional Spaces:Vector SpacesSpaces of FunctionsDistributionsFourier AnalysisLinear Operators in Hilbert Spaces I: The Finite-Dimensional CaseLinear Operators in Hilbert Spaces II: The Infinite-Dimensional CaseAppendices:Complex Numbers, Series and IntegralsSolutions of the Exercises Readership: Students of undergraduate mathematics and postgraduate students of physics or engineering.
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Application-Driven Quantum and Statistical Physics

A Short Course for Future Scientists and EngineersVolume 2: Equilibrium

Author: Jean-Michel Gillet

Publisher: World Scientific Publishing

ISBN: 1786345595

Category: Science

Page: 336

View: 2892

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Bridging the gap between traditional books on quantum and statistical physics, this series is an ideal introductory course for students who are looking for an alternative approach to the traditional academic treatment. This pedagogical approach relies heavily on scientific or technological applications from a wide range of fields. For every new concept introduced, an application is given to connect the theoretical results to a real-life situation. Each volume features in-text exercises and detailed solutions, with easy-to-understand applications. Building on the principles introduced in Volume 1, this second volume explains the structure of atoms, the vibration and rotation of molecules. It describes how this is related to thermodynamics through statistical physics. It is shown that these fundamental achievements help to understand how explosives and CO₂ can be detected, what makes a gecko stick to the ceiling, why old stars do not necessarily collapse, where nuclear energy comes from, and more. remove
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Mathematical Methods for Physicists

A Comprehensive Guide

Author: George Brown Arfken,Hans-Jurgen Weber,Frank E. Harris

Publisher: Academic Press

ISBN: 0123846544

Category: Mathematics

Page: 1205

View: 7855

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Providing coverage of the mathematics necessary for advanced study in physics and engineering, this text focuses on problem-solving skills and offers a vast array of exercises, as well as clearly illustrating and proving mathematical relations.
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Student Solution Manual for Essential Mathematical Methods for the Physical Sciences

Author: K. F. Riley,M. P. Hobson

Publisher: Cambridge University Press

ISBN: 1139491962

Category: Science

Page: 250

View: 5916

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This Student Solution Manual provides complete solutions to all the odd-numbered problems in Essential Mathematical Methods for the Physical Sciences. It takes students through each problem step-by-step, so they can clearly see how the solution is reached, and understand any mistakes in their own working. Students will learn by example how to select an appropriate method, improving their problem-solving skills.
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Mathematical Physics

A Modern Introduction to Its Foundations

Author: Sadri Hassani

Publisher: Springer Science & Business Media

ISBN: 3319011952

Category: Science

Page: 1205

View: 8732

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The goal of this book is to expose the reader to the indispensable role that mathematics plays in modern physics. Starting with the notion of vector spaces, the first half of the book develops topics as diverse as algebras, classical orthogonal polynomials, Fourier analysis, complex analysis, differential and integral equations, operator theory, and multi-dimensional Green's functions. The second half of the book introduces groups, manifolds, Lie groups and their representations, Clifford algebras and their representations, and fibre bundles and their applications to differential geometry and gauge theories. This second edition is a substantial revision with a complete rewriting of many chapters and the addition of new ones, including chapters on algebras, representation of Clifford algebras, fibre bundles, and gauge theories. The spirit of the first edition, namely the balance between rigour and physical application, has been maintained, as is the abundance of historical notes and worked out examples that demonstrate the "unreasonable effectiveness of mathematics" in modern physics.
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The Mathematics Companion

Mathematical Methods for Physicists and Engineers

Author: Anthony Craig Fischer-Cripps

Publisher: CRC Press

ISBN: 9781420050769

Category: Science

Page: 210

View: 5579

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Following the style of The Physics Companion and The Electronics Companion, this book is a revision aid and study guide for undergraduate students in physics and engineering. It consists of a series of one-page-per-topic descriptions of the key concepts covered in a typical first-year "mathematics for physics" course. The emphasis is placed on relating the mathematical principles being introduced to real-life physical problems. In common with the other companions, there is strong use of figures throughout to help in understanding of the concepts under consideration. The book will be an essential reference and revision guide, particularly for those students who do not have a strong background in mathematics when beginning their degree.
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Mathematics for Physicists

Introductory Concepts and Methods

Author: Alexander Altland,Jan von Delft

Publisher: Cambridge University Press

ISBN: 1108471226

Category: Mathematics

Page: 600

View: 7964

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Introduces fundamental concepts and computational methods of mathematics from the perspective of physicists.
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Essentials of Math Methods for Physicists

Author: Hans J. Weber,George B. Arfken

Publisher: Academic Press

ISBN: 1483225623

Category: Science

Page: 960

View: 529

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Essentials of Math Methods for Physicists aims to guide the student in learning the mathematical language used by physicists by leading them through worked examples and then practicing problems. The pedagogy is that of introducing concepts, designing and refining methods and practice them repeatedly in physics examples and problems. Geometric and algebraic approaches and methods are included and are more or less emphasized in a variety of settings to accommodate different learning styles of students. Comprised of 19 chapters, this book begins with an introduction to the basic concepts of vector algebra and vector analysis and their application to classical mechanics and electrodynamics. The next chapter deals with the extension of vector algebra and analysis to curved orthogonal coordinates, again with applications from classical mechanics and electrodynamics. These chapters lay the foundations for differential equations, variational calculus, and nonlinear analysisin later discussions. High school algebra of one or two linear equations is also extended to determinants and matrix solutions of general systems of linear equations, eigenvalues and eigenvectors, and linear transformations in real and complex vector spaces. The book also considers probability and statistics as well as special functions and Fourier series. Historical remarks are included that describe some physicists and mathematicians who introduced the ideas and methods that were perfected by later generations to the tools routinely used today. This monograph is intended to help undergraduate students prepare for the level of mathematics expected in more advanced undergraduate physics and engineering courses.
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Mathematical Models of Physics Problems

Author: Luis Alfredo Anchordoqui,Thomas Cantzon Paul

Publisher: Nova Science Pub Incorporated

ISBN: 9781626186002

Category: Science

Page: 213

View: 7035

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This textbook is intended to provide a foundation for a one-semester introductory course on the advanced mathematical methods that form the cornerstones of the hard sciences and engineering. The work is suitable for first year graduate or advanced undergraduate students in the fields of Physics, Astronomy and Engineering. This text therefore employs a condensed narrative sufficient to prepare graduate and advanced undergraduate students for the level of mathematics expected in more advanced graduate physics courses, without too much exposition on related but non-essential material. In contrast to the two semesters traditionally devoted to mathematical methods for physicists, the material in this book has been quite distilled, making it a suitable guide for a one-semester course. The assumption is that the student, once versed in the fundamentals, can master more esoteric aspects of these topics on his or her own if and when the need arises during the course of conducting research. The book focuses on two core subjects: complex analysis and classical techniques for the solution of ordinary and partial differential equations. These topics are complemented with occasional terse reviews of other material, including linear algebra, to the extent required to ensure the book can be followed from end-to-end. This textbook is designed to provide a framework for a roughly 12 week course, with 3 weeks devoted to complex variables, a 1 week refresher on linear algebra, followed by 5 and 3 weeks devoted to ordinary and partial differential equations, respectively. This schedule leaves time for a couple of exams. The narrative is complemented with ample problem sets, including detailed guides to solving the problems.
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From Nucleons to the Atomic Nucleus

Perspectives in Nuclear Physics

Author: Kris Heyde

Publisher: Springer Science & Business Media

ISBN: 3662036339

Category: Science

Page: 194

View: 6445

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The present text grew out of a number of lecture courses for advanced under graduate and new graduate students in nuclear physics. They were given at summer schools in Leuven, Melbourne, and at study weeks for Dutch grad uate students which aimed to emphasize fundamental and topical aspects of nuclear physics. On occasion, part of the present text was presented to stu dents from a much wider field than just nuclear physics and also within a number of general physics colloquia, where, in addition to nuclear physicists, physicists from many other fields were present. In this respect, the intention is to present, in an amply illustrated form, the key quest ions that arise in nuclear physics. At the same time we try to show why a better understanding of the atomic nucleus is not only important in itself, but also yields essential insights into the many connections to other fields of physics. We thus concen trate on the unifying themes rather than addressing in great detail particular subfields of nuclear physics. The present project does not aim to be another comprehensive textbook on nuclear physics: Many of the detailed technical arguments that enter into the picture are not developed here as they would be in a more standard textbook. Instead they are presented using analogies, quite often with simple pictures and arguments that try to convey the general line of thinking and working in nuclear physics.
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