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Mathematical Physical Chemistry: Practical and Intuitive Methodology
by Shu HottaThe third edition of this book has been updated so that both advanced physics and advanced chemistry can be overviewed from a modern mathematical perspective in a single integrated book. Nowadays key research arears in physics and chemistry such as materials science, molecular science, and device physics are drawing closer and closer together and becoming more and more mathematical. Hence, while retaining the basic feature, the contents are targeted at graduate and undergraduate students majoring in not only chemistry but also physics and engineering. The book covers topics ranging from classical physics (e.g., electromagnetism and analytical mechanics) to quantum science. The latter topic includes an introduction to the quantum theory of fields as well as standard quantum mechanics and quantum chemistry. Tangible examples help readers to understand abstract concepts about the topics covered. Several major revisions have been made and they contain: (a) constitution of the Dirac equation; (b) quantization of the fields; (c) interaction between the quantum fields; (d) basic formalism related to the extended vector spaces and the transformation properties of the Dirac equation; (e) advanced topics of Lie algebra. The new edition thus supplies chemists, physicists, and engineers with fundamental knowledge and calculation methodology of mathematical physics.
Mathematical Physics: Applications and Problems
by V. BalakrishnanThis textbook is aimed at advanced undergraduate and graduate students interested in learning the fundamental mathematical concepts and tools widely used in different areas of physics. The author draws on a vast teaching experience, and presents a comprehensive and self-contained text which explains how mathematics intertwines with and forms an integral part of physics in numerous instances. Rather than emphasizing rigorous proofs of theorems, specific examples and physical applications (such as fluid dynamics, electromagnetism, quantum mechanics, etc.) are invoked to illustrate and elaborate upon the relevant mathematical techniques. The early chapters of the book introduce different types of functions, vectors and tensors, vector calculus, and matrices. In the subsequent chapters, more advanced topics like linear spaces, operator algebras, special functions, probability distributions, stochastic processes, analytic functions, Fourier series and integrals, Laplace transforms, Green's functions and integral equations are discussed. The book also features about 400 exercises and solved problems interspersed throughout the text at appropriate junctures, to facilitate the logical flow and to test the key concepts. Overall this book will be a valuable resource for a wide spectrum of students and instructors of mathematical physics.
Mathematical Physics (Chicago Lectures in Physics)
by Robert GerochMathematical Physics is an introduction to such basic mathematical structures as groups, vector spaces, topological spaces, measure spaces, and Hilbert space. Geroch uses category theory to emphasize both the interrelationships among different structures and the unity of mathematics. Perhaps the most valuable feature of the book is the illuminating intuitive discussion of the "whys" of proofs and of axioms and definitions. This book, based on Geroch's University of Chicago course, will be especially helpful to those working in theoretical physics, including such areas as relativity, particle physics, and astrophysics.
Mathematical Physics: A Modern Introduction to Its Foundations
by Sadri HassaniThe goal of this book is to expose the reader to the indispensable role that mathematics---often very abstract---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 fiber bundles and their applications to differential geometry and gauge theories. This second edition is a substantial revision of the first one with a complete rewriting of many chapters and the addition of new ones, including chapters on algebras, representation of Clifford algebras and spinors, fiber bundles, and gauge theories. The spirit of the first edition, namely the balance between rigor 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. Einstein has famously said, "The most incomprehensible thing about nature is that it is comprehensible." What he had in mind was reiterated in another one of his famous quotes concerning the question of how " ... mathematics, being after all a product of human thought, is so admirably appropriate to the objects of reality." It is a question that comes to everyone's mind when encountering the highly abstract mathematics required for a deep understanding of modern physics. It is the experience that Eugene Wigner so profoundly described as "the unreasonable effectiveness of mathematics in the natural sciences." Some praise for the previous edition: PAGEOPH [Pure and Applied Geophysics] Review by Daniel Wojcik, University of Maryland "This volume should be a welcome addition to any collection. The book is well written and explanations are usually clear. Lives of famous mathematicians and physicists are scattered within the book. They are quite extended, often amusing, making nice interludes. Numerous exercises help the student practice the methods introduced. ... I have recently been using this book for an extended time and acquired a liking for it. Among all the available books treating mathematical methods of physics this one certainly stands out and assuredly it would suit the needs of many physics readers." ZENTRALBLATT MATH Review by G.Roepstorff, University of Aachen, Germany "... Unlike most existing texts with the same emphasis and audience, which are merely collections of facts and formulas, the present book is more systematic, self-contained, with a level of presentation that tends to be more formal and abstract. This entails proving a large number of theorems, lemmas, and corollaries, deferring most of the applications that physics students might be interested in to the example sections in small print. Indeed, there are 350 worked-out examples and about 850 problems. ... A very nice feature is the way the author intertwines the formalism with the life stories and anecdotes of some mathematicians and physicists, leading at their times. As is often the case, the historical view point helps to understand and appreciate the ideas presented in the text. ... For the physics student in the middle of his training, it will certainly prove to be extremely useful." THE PHYSICIST Review by Paul Davies, Orion Productions, Adelaide, Australia "I am pleased to have so many topics collected in a single volume. All the tricks are there of course, but supported by sufficient rigour and substantiation to make the dedicated mathematical physicist sigh with delight." EMS [EUROPEAN MATHEMATICAL SOCIETY] NEWSLETTER "This book is a condensed exposition of the mathematics that is met in most parts of physics. The presentation attains a very good balance between the formal introduction of concepts, theorems and proofs on one hand, and the applied approach on the other, with many examples, fully...
Mathematical Physics: Classical Mechanics (UNITEXT #109)
by Andreas Knauf Jochen DenzlerAs a limit theory of quantum mechanics, classical dynamics comprises a large variety of phenomena, from computable (integrable) to chaotic (mixing) behavior. This book presents the KAM (Kolmogorov-Arnold-Moser) theory and asymptotic completeness in classical scattering. Including a wealth of fascinating examples in physics, it offers not only an excellent selection of basic topics, but also an introduction to a number of current areas of research in the field of classical mechanics. Thanks to the didactic structure and concise appendices, the presentation is self-contained and requires only knowledge of the basic courses in mathematics.The book addresses the needs of graduate and senior undergraduate students in mathematics and physics, and of researchers interested in approaching classical mechanics from a modern point of view.
Mathematical Physics and Its Interactions: In Honor of the 60th Birthday of Tohru Ozawa, Tokyo, Japan, August 2021 (Springer Proceedings in Mathematics & Statistics #451)
by Shuji MachiharaThis publication comprises research papers contributed by the speakers, primarily based on their planned talks at the meeting titled 'Mathematical Physics and Its Interactions,' initially scheduled for the summer of 2021 in Tokyo, Japan. It celebrates Tohru Ozawa's 60th birthday and his extensive contributions in many fields.The works gathered in this volume explore interactions between mathematical physics, various types of partial differential equations (PDEs), harmonic analysis, and applied mathematics. They are authored by research leaders in these fields, and this selection honors the spirit of the workshop by showcasing cutting-edge results and providing a forward-looking perspective through discussions of problems, with the goal of shaping future research directions.Originally planned as an in-person gathering, this conference had to change its format due to limitations imposed by COVID, more precisely to avoid inducing people into unnecessary vaccinations.
Mathematical Physics for Nuclear Experiments
by Andrew E. EkpenyongMathematical Physics for Nuclear Experiments presents an accessible introduction to the mathematical derivations of key equations used in describing and analysing results of typical nuclear physics experiments. Instead of merely showing results and citing texts, crucial equations in nuclear physics such as the Bohr’s classical formula, Bethe’s quantum mechanical formula for energy loss, Poisson, Gaussian and Maxwellian distributions for radioactive decay, and the Fermi function for beta spectrum analysis, among many more, are presented with the mathematical bases of their derivation and with their physical utility. This approach provides readers with a greater connection between the theoretical and experimental sides of nuclear physics. The book also presents connections between well-established results and ongoing research. It also contains figures and tables showing results from the author’s experiments and those of his students to demonstrate experimental outcomes. This is a valuable guide for advanced undergraduates and early graduates studying nuclear instruments and methods, medical and health physics courses as well as experimental particle physics courses. Key features Contains over 500 equations connecting theory with experiments. Presents over 80 examples showing physical intuition and illustrating concepts. Includes 80 exercises, with solutions, showing applications in nuclear and medical physics.
A Mathematical Primer on Quantum Mechanics (UNITEXT for Physics)
by Alessandro TetaThis book offers a rigorous yet elementary approach to quantum mechanics that will meet the needs of Master’s-level Mathematics students and is equally suitable for Physics students who are interested in gaining a deeper understanding of the mathematical structure of the theory. Throughout the coverage, which is limited to single-particle quantum mechanics, the focus is on formulating theory and developing applications in a mathematically precise manner. Following a review of selected key concepts in classical physics and the historical background, the basic elements of the theory of operators in Hilbert spaces are presented and used to formulate the rules of quantum mechanics. The discussion then turns to free particles, harmonic oscillators, delta potential, and hydrogen atoms, providing rigorous proofs of the corresponding dynamical properties. Starting from an analysis of these applications, readers are subsequently introduced to more advanced topics such as the classical limit, scattering theory, and spectral analysis of Schrödinger operators. The main content is complemented by numerous exercises that stimulate interactive learning and help readers check their progress.
Mathematical Problems in Meteorological Modelling
by András Bátkai Petra Csomós István Faragó András Horányi Gabriella SzépszóThis book deals with mathematical problems arising in the context of meteorological modelling. It gathers and presents some of the most interesting and important issues from the interaction of mathematics and meteorology. It is unique in that it features contributions on topics like data assimilation, ensemble prediction, numerical methods, and transport modelling, from both mathematical and meteorological perspectives. The derivation and solution of all kinds of numerical prediction models require the application of results from various mathematical fields. The present volume is divided into three parts, moving from mathematical and numerical problems through air quality modelling, to advanced applications in data assimilation and probabilistic forecasting. The book arose from the workshop "Mathematical Problems in Meteorological Modelling" held in Budapest in May 2014 and organized by the ECMI Special Interest Group on Numerical Weather Prediction. Its main objective is to highlight the beauty of the development fields discussed, to demonstrate their mathematical complexity and, more importantly, to encourage mathematicians to contribute to the further success of such practical applications as weather forecasting and climate change projections. Written by leading experts in the field, the book provides an attractive and diverse introduction to areas in which mathematicians and modellers from the meteorological community can cooperate and help each other solve the problems that operational weather centres face, now and in the near future. Readers engaged in meteorological research will become more familiar with the corresponding mathematical background, while mathematicians working in numerical analysis, partial differential equations, or stochastic analysis will be introduced to further application fields of their research area, and will find stimulation and motivation for their future research work.
Mathematical Problems of Classical Nonlinear Electromagnetic Theory (Monographs And Surveys In Pure And Applied Mathematics Ser. #Vol. 63)
by Frederick BloomA survey of some problems of current interest in the realm of classical nonlinear electromagnetic theory.
Mathematical Problems of the Dynamics of Incompressible Fluid on a Rotating Sphere
by Yuri N. SkibaThis book presents selected mathematical problems involving the dynamics of a two-dimensional viscous and ideal incompressible fluid on a rotating sphere. In this case, the fluid motion is completely governed by the barotropic vorticity equation (BVE), and the viscosity term in the vorticity equation is taken in its general form, which contains the derivative of real degree of the spherical Laplace operator.This work builds a bridge between basic concepts and concrete outcomes by pursuing a rich combination of theoretical, analytical and numerical approaches, and is recommended for specialists developing mathematical methods for application to problems in physics, hydrodynamics, meteorology and geophysics, as well for upper undergraduate or graduate students in the areas of dynamics of incompressible fluid on a rotating sphere, theory of functions on a sphere, and flow stability.
Mathematical Quantization (Studies in Advanced Mathematics)
by null Nik WeaverWith a unique approach and presenting an array of new and intriguing topics, Mathematical Quantization offers a survey of operator algebras and related structures from the point of view that these objects are quantizations of classical mathematical structures. This approach makes possible, with minimal mathematical detail, a unified treatment of a
The Mathematical Structure of Classical and Relativistic Physics: A General Classification Diagram
by Enzo TontiThe theories describing seemingly unrelated areas of physics have surprising analogies that have aroused the curiosity of scientists and motivated efforts to identify reasons for their existence. Comparative study of physical theories has revealed the presence of a common topological and geometric structure. The Mathematical Structure of Classical and Relativistic Physics is the first book to analyze this structure in depth, thereby exposing the relationship between (a) global physical variables and (b) space and time elements such as points, lines, surfaces, instants, and intervals. Combining this relationship with the inner and outer orientation of space and time allows one to construct a classification diagram for variables, equations, and other theoretical characteristics. The book is divided into three parts. The first introduces the framework for the above-mentioned classification, methodically developing a geometric and topological formulation applicable to all physical laws and properties; the second applies this formulation to a detailed study of particle dynamics, electromagnetism, deformable solids, fluid dynamics, heat conduction, and gravitation. The third part further analyses the general structure of the classification diagram for variables and equations of physical theories. Suitable for a diverse audience of physicists, engineers, and mathematicians, The Mathematical Structure of Classical and Relativistic Physics offers a valuable resource for studying the physical world. Written at a level accessible to graduate and advanced undergraduate students in mathematical physics, the book can be used as a research monograph across various areas of physics, engineering and mathematics, and as a supplemental text for a broad range of upper-level scientific coursework.
Mathematical Theory of Black Holes in Higher Dimensions (Lecture Notes in Physics #1031)
by Petya Nedkova Stoytcho YazadjievThis book portraits the mathematical theory which lies behind black hole solutions in spacetimes with an extra dimension. Step by step the authors build a comprehensive picture of the main concepts and tools necessary to understand these geometries. In this way the book addresses questions like: How do we describe black holes in higher dimensions? How can we construct such geometries explicitly as exact solutions to the field equations? How many independent solutions can exist and how are they classified?The book concentrates on five-dimensional stationary and axisymmetric spacetimes in electro-vacuum and systematically introduces the most important black geometries which can arise in these settings. The authors follow the natural progress of the research area by initially describing the first results that were obtained intuitively and sparkled interest in the community. Then the elaborate mathematical techniques are introduced which allow to systematically construct exact black hole solutions. Topics like the integrability of the theory, the hidden symmetries of the field equations, the available Bäcklund transformations and solution generation techniques based on the inverse scattering method are covered. The last part of the book is devoted to uniqueness theorems showing how to classify the black hole spacetimes and distinguish the non-equivalent ones.The book is not just a mere collection of facts but a methodological description of the most important mathematical techniques and constructions in an active research area. The discussion is pedagogical and all the methods are demonstrated on a variety of examples. Most of the book is adapted to the level of a graduate student possessing a basic knowledge of general relativity and differential equations, and can serve as a practical guide for quickly acquiring the specific concepts and calculation techniques. Both authors have contributed to the research area by their original results, and share their own experience and perspective.
Mathematical Theory of Compressible Fluids on Moving Domains (Advances in Mathematical Fluid Mechanics)
by Ondřej Kreml Václav Mácha Šárka Nečasová Tomasz Piasecki Aneta Wróblewska-KamińskaThis monograph presents the existence and properties of both weak and strong solutions to the problems of the flow of a compressible fluid in a domain whose motion is prescribed. Chapters build upon the research of Lions and Feireisl with regards to weak solutions to the compressible version of the Navier-Stokes system, and extend it to problems on moving domains. The authors also show the existence of strong solutions to the compressible Navier-Stokes system for either a small time interval or small data. The opening chapters introduce the notation, tools, and problems covered in the rest of the book, emphasizing pedagogy and accessibility throughout. Mathematical Theory of Compressible Fluids on Moving Domains will be suitable for graduate students and researchers interested in mathematical fluid mechanics.
The Mathematical Theory of Cosmic Strings: Cosmic Strings in the Wire Approximation (Series in High Energy Physics, Cosmology and Gravitation)
by null M.R. AndersonThis book is a comprehensive survey of the current state of knowledge about the dynamics and gravitational properties of cosmic strings treated in the idealized classical approximation as line singularities described by the Nambu-Goto action. The author's purpose is to provide a standard reference to all work that has been published since the mid-1
Mathematical Theory of Elasticity of Quasicrystals and Its Applications
by Tian-You FanThis interdisciplinary work on condensed matter physics, the continuum mechanics of novel materials, and partial differential equations, discusses the mathematical theory of elasticity and hydrodynamics of quasicrystals, as well as its applications. By establishing new partial differential equations of higher order and their solutions under complicated boundary value and initial value conditions, the theories developed here dramatically simplify the solution of complex elasticity problems. Comprehensive and detailed mathematical derivations guide readers through the work. By combining theoretical analysis and experimental data, mathematical studies and practical applications, readers will gain a systematic, comprehensive and in-depth understanding of condensed matter physics, new continuum mechanics and applied mathematics. This new edition covers the latest developments in quasicrystal studies. In particular, it pays special attention to the hydrodynamics, soft-matter quasicrystals, and the Poisson bracket method and its application in deriving hydrodynamic equations. These new sections make the book an even more useful and comprehensive reference guide for researchers working in Condensed Matter Physics, Chemistry and Materials Science.
Mathematical Thermodynamics of Complex Fluids: Cetraro, Italy 2015 (Lecture Notes in Mathematics #2200)
by Elisabetta Rocca Felix OttoEduard Feireisl Eduard Feireisl John M. BallThe main goal of this book is to provide an overview of the state of the art in the mathematical modeling of complex fluids, with particular emphasis on its thermodynamical aspects. The central topics of the text, the modeling, analysis and numerical simulation of complex fluids, are of great interest and importance both for the understanding of various aspects of fluid dynamics and for its applications to special real-world problems. New emerging trends in the subject are highlighted with the intent to inspire and motivate young researchers and PhD students.
Mathematical Topics in Fluid Mechanics: Proceedings Of The Summer Course Held In Lisbon, Portugal, September 9-13, 1991 (Pitman Research Notes In Mathematics Ser.)
by Jose Francisco Rodrigues Adelia SequeiraThis Research Note presents several contributions and mathematical studies in fluid mechanics, namely in non-Newtonian and viscoelastic fluids and on the Navier-Stokes equations in unbounded domains. It includes review of the mathematical analysis of incompressible and compressible flows and results in magnetohydrodynamic and electrohydrodynamic stability and thermoconvective flow of Boussinesq-Stefan type. These studies, along with brief communications on a variety of related topics comprise the proceedings of a summer course held in Lisbon, Portugal in 1991. Together they provide a set of comprehensive survey and advanced introduction to problems in fluid mechanics and partial differential equations.
Mathematics: A Simple Tool For Geologists
by Waltham, D.Uses geological examples to illustrate mathematical ideas. Contains a large number of worked examples, and problems for students to attempt themselves. Answers to all the questions are given at the end of the book.
Mathematics for Earth Science and Geography: Introductory Course With Practical Exercises And R/xcas Resources (Springer Textbooks In Earth Sciences, Geography And Environment Ser.)
by Cyril Fleurant Sandrine Bodin-FleurantThis undergraduate textbook presents a unique comprehensive overview on Mathematics in Earth Sciences and Geography. It deals with fundamental theoretical and applied mathematics, needed by bachelor students in a wide range of subjects. The book is illustrated with many examples and over a hundred practical exercises, with solutions included in the book. In addition, this textbook highlights numerical resources by using two free software packages (R and Xcas) and introducing their use.
Mathematics for Engineers and Scientists: Concepts, Applications, and History
by Vinh Phu NguyenA majority of mathematics textbooks are written in a rigorous, concise, dry, and boring way. On the other hands, there exist excellent, engaging, fun-to-read popular math books. The problem with these popular books is the lack of mathematics itself. This book is a blend of both. It provides a mathematics book to read, to engage with, and to understand the whys — the story behind the theorems. Written by an engineer, not a mathematician, who struggled to learn math in high school and in university, this book explains in an informal voice the mathematics that future and current engineering and science students need to acquire. If we learn math to understand it, to enjoy it, not to pass a test or an exam, we all learn math better and there is no such a thing that we call math phobia. With a slow pace and this book, everyone can learn math and use it, as the author did at the age of 40 and with a family to take care of.
Mathematics for Natural Scientists
by Lev KantorovichThis book covers a course of mathematics designed primarily for physics and engineering students. It includes all the essential material on mathematical methods, presented in a form accessible to physics students, avoiding precise mathematical jargon and proofs which are comprehensible only to mathematicians. Instead, all proofs are given in a form that is clear and convincing enough for a physicist. Examples, where appropriate, are given from physics contexts. Both solved and unsolved problems are provided in each section of the book. Mathematics for Natural Scientists: Fundamentals and Basics is the first of two volumes. Advanced topics and their applications in physics are covered in the second volume.
Mathematics for Natural Scientists II
by Lev KantorovichThis book covers the advanced mathematical techniques useful for physics and engineering students, presented in a form accessible to physics students, avoiding precise mathematical jargon and laborious proofs. Instead, all proofs are given in a simplified form that is clear and convincing for a physicist. Examples, where appropriate, are given from physics contexts. Both solved and unsolved problems are provided in each chapter. Mathematics for Natural Scientists II: Advanced Methods is the second of two volumes. It follows the first volume on Fundamentals and Basics.
Mathematics for Natural Scientists II: Advanced Methods (Undergraduate Lecture Notes in Physics)
by Lev KantorovichThis textbook, the second in a series (the first covered fundamentals and basics), seeks to make its material accessible to physics students. Physics/engineering can be greatly enhanced by knowledge of advanced mathematical techniques, but the math-specific jargon and laborious proofs can be off-putting to students not well versed in abstract math. This book uses examples and proofs designed to be clear and convincing from the context of physics, as well as providing a large number of both solved and unsolved problems in each chapter. This is the second edition, and it has been significantly revised and enlarged, with Chapters 1 (on linear algebra) and 2 (on the calculus of complex numbers and functions) having been particularly expanded. The enhanced topics throughout the book include: vector spaces, general (non-Hermitian, including normal and defective) matrices and their right/left eigenvectors/values, Jordan form, pseudoinverse, linearsystems of differential equations, Gaussian elimination, fundamental theorem of algebra, convergence of a Fourie series and Gibbs-Wilbraham phenomenon, careful derivation of the Fourier integral and of the inverse Laplace transform. New material has been added on many physics topics meant to illustrate the maths, such as 3D rotation, properties of the free electron gas, van Hove singularities, and methods for both solving PDEs with a Fourier transform and calculating the width of a domain wall in a ferromagnet, to mention just a few. This textbook should prove invaluable to all of those with an interest in physics/engineering who have previously experienced difficulty processing the math involved.