Mathematical / Computational / Theoretical physics Books

Book SynopsisWritten by two PhDs in nuclear engineering, this book includes practical examples drawn from a working knowledge of physics concepts. You'll learn how to use the Python programming language to perform everything from collecting and analyzing data to building software and publishing your results.

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Book SynopsisTable of Contents1. The Statistical Basis of Thermodynamics 2. Elements of Ensemble Theory 3. The Canonical Ensemble 4. The Grand Canonical Ensemble 5. Formulation of Quantum Statistics 6. The Theory of Simple Gases 7. Ideal Bose Systems 8. Ideal Fermi Systems 9. Thermodynamics of the Early Universe 10. Statistical Mechanics of Interacting Systems: The Method of Cluster Expansions 11. Statistical Mechanics of Interacting Systems: The Method of Quantized Fields 12. Phase Transitions: Criticality, Universality, and Scaling 13. Phase Transitions: Exact (or Almost Exact) Results for Various Models 14. Phase Transitions: The Renormalization Group Approach 15. Fluctuations and Nonequilibrium Statistical Mechanics 16. Computer Simulations

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Book SynopsisA distinctive and accessible introduction to quantum information science and quantum computing, this textbook provides a solid conceptual and formal understanding of quantum states and entanglement for undergraduate students and upper-level secondary school students with little or no background in physics, computer science, or mathematics.Trade ReviewWhile broadly accessible, the textbook does not dodge providing a solid conceptual and formal understanding of quantum states and entanglement - the key ingredients in quantum computing. The authors dish up a hearty meal for the readers, disentangling and explaining many of the classic quantum algorithms that demonstrate how and when QC has an advantage over classical computers. The book is spiced with Try Its, brief exercises that engage the readers in problem solving (both with and without mathematics) and help them digest the many counter-intuitive quantum information science and quantum computing concepts. * zb Math Open *This is a refreshing, pedagogical, and timely overview of quantum computing for non-experts, by two well-qualified authors. * Shimon Kolkowitz, University of Wisconsin-Madison *This is a much needed bridge between popular and technical texts that provides easy access to the topic of quantum computing for curious readers who aim to go further and deeper in their understanding. * Dieter Jaksch, University of Oxford *The reader gets to avoid the complexity of technical quantum-computing books, yet gets more depth and rigor than in the popular writing on the topic...the book is written in a very conversational rather than academic tone. * Bogdan Hoanca, University of Alaska Anchorage *Table of Contents1: Introduction 2: Traditional Computing 3: Traditional Bits in New Clothes 4: Qubits and Quantum States 5: Quantum Measurements 6: Quantum Gates 7: Putting a Spin on Spin 8: My Basis, Your Basis 9: Multi-qubit Systems, Entanglement, and Quantum Weirdness 10: Quantum Circuits and Multi-qubit Applications 11: Quantum Computing Algorithms 12: More Quantum Algorithms 13: RSA Encryption and the Shor Factoring Algorithm 14: Fundamental Quantum Issues 15: Complexifying Quantum States 16: Present and Future QIS and QC

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Book SynopsisQuantum Computing: From Alice to Bob provides a distinctive and accessible introduction to the rapidly growing fields of quantum information science and quantum computing. The textbook is designed for undergraduate students and upper-level secondary school students with little or no background in physics, computer science, or mathematics beyond secondary school algebra and a bit of trigonometry. Higher education faculty members and secondary school mathematics, physics, and computer science educators who want to learn about quantum computing and perhaps teach a course accessible to students with wide ranging backgrounds will also find the book useful and enjoyable. While broadly accessible, the textbook does not dodge providing a solid conceptual and formal understanding of quantum states and entanglement - the key ingredients in quantum computing. The authors dish up a hearty meal for the readers, disentangling and explaining many of the classic quantum algorithms that demonstrate how and when QC has an advantage over classical computers. The book is spiced with Try Its, brief exercises that engage the readers in problem solving (both with and without mathematics) and help them digest the many counter-intuitive quantum information science and quantum computing concepts.Trade ReviewWhile broadly accessible, the textbook does not dodge providing a solid conceptual and formal understanding of quantum states and entanglement - the key ingredients in quantum computing. The authors dish up a hearty meal for the readers, disentangling and explaining many of the classic quantum algorithms that demonstrate how and when QC has an advantage over classical computers. The book is spiced with Try Its, brief exercises that engage the readers in problem solving (both with and without mathematics) and help them digest the many counter-intuitive quantum information science and quantum computing concepts. * zb Math Open *This is a refreshing, pedagogical, and timely overview of quantum computing for non-experts, by two well-qualified authors. * Shimon Kolkowitz, University of Wisconsin-Madison *This is a much needed bridge between popular and technical texts that provides easy access to the topic of quantum computing for curious readers who aim to go further and deeper in their understanding. * Dieter Jaksch, University of Oxford *The reader gets to avoid the complexity of technical quantum-computing books, yet gets more depth and rigor than in the popular writing on the topic...the book is written in a very conversational rather than academic tone. * Bogdan Hoanca, University of Alaska Anchorage *Table of Contents1: Introduction 2: Traditional Computing 3: Traditional Bits in New Clothes 4: Qubits and Quantum States 5: Quantum Measurements 6: Quantum Gates 7: Putting a Spin on Spin 8: My Basis, Your Basis 9: Multi-qubit Systems, Entanglement, and Quantum Weirdness 10: Quantum Circuits and Multi-qubit Applications 11: Quantum Computing Algorithms 12: More Quantum Algorithms 13: RSA Encryption and the Shor Factoring Algorithm 14: Fundamental Quantum Issues 15: Complexifying Quantum States 16: Present and Future QIS and QC

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Book SynopsisThe Physics of Quantum Mechanics aims to give students a good understanding of how quantum mechanics describes the material world. The text stresses the continuity between the quantum world and the classical world, which is merely an approximation to the quantum world.Trade ReviewThis book is a deep, well-explained and beautiful text on the foundations and applications of quantum mechanics. It is eminently suitable for advanced undergraduates and graduates who wish to study the subject. Some precious jewels can be found within after building up the Dirac representation of quantum mechanics: scattering theory and condensed matter applications, for example. * Ben Allanach, Department of Applied Mathematics and Theoretical Physics, University of Cambridge *The extensive discussion of the physics behind the mathematical manipulations of the theory, coupled with the smooth, colloquial writing style and delightful historical footnotes makes this book somewhat unique in the field. It devotes large sections to the more modern topics of quantum computing and quantum measurement theory, which are active areas of current research. In addition, there is a copious selection of problems, at all levels of difficulty, which should prove extremely useful to anyone teaching the course. * Harold S. Zapolsky, Rutgers University *Binney and Skinners introductory book on quantum mechanics approaches the subject in a unique way ... The text is very well written for the target audience of second or third year University students in Physics, Chemistry, or certain Engineering specialties and I would highly recommend it for anyone who might be considering teaching or tutoring such a course. * Brian Todd Huffman, University of Oxford *Table of Contents1. Introduction ; 2. Operators, measurement and time evolution ; 3. Oscillators ; 4. Transformations & Observables ; 5. Motion in step potentials ; 6. Composite systems ; 7. Angular Momentum ; 8. Hydrogen ; 9. Motion in a magnetic field ; 10. Perturbation theory ; 11. Helium and the periodic table ; 12. Adiabatic principle ; 13. Scattering Theory ; Appendices

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Book SynopsisIntended primarily for graduate students and researchers in theoretical high-energy physics, mathematical physics, condensed matter theory, statistical physics, the book will also be of interest in other areas of theoretical physics and mathematics.Table of Contents1. Introduction; 2. Quantum Field Theory; 3. Statistical Mechanics; 4. Global Conformal Invariance; 5. Conformal Invariance in Two Dimensions; 6. The Operator Formalism I; 7. The Operator Formalism II; 8. Minimal Models; 9. The Coulomb Gas Formalism; 10. Modular Invariance; 11. Finite Size Scaling; 12. The Two-Dimensional Ising Model; 13. Simple Lie Algebras; 14. Affine Lie Algebras; 15. The WZNW Model; 16. Fusion Rules; 17. Modular Invariants; 18. The Coset Construction

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Book SynopsisHypersonic turbulent boundary layers are a fundamental phenomenon in high-speed flight. The interaction of shock waves with hypersonic turbulent boundary layers has a critical impact on vehicle aerothermodynamic loading including surface heat transfer, pressure and skin friction. This book provides a comprehensive exposition of hypersonic turbulent boundary layers, including the fundamental mathematical theory, structure of equilibrium boundary layers, and extensive surveys of Direct Numerical Simulation (DNS), Large Eddy Simulation (LES) and experiments. It also provides a roadmap for both future experiments and DNS and LES simulations. Descriptions of hypersonic ground test facilities is included as an appendix. As a research and reference text, this book would appeal to graduate students and researchers in hypersonics and could be the basis for professional training courses.Key FeaturesProvides a summary of the state-of-th

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Book SynopsisThis book offers a practical introduction to computational physics for undergraduates, teaching essential numerical methods and programming skills to solve real-world physics problems across various domains.

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Book SynopsisThis book adopts a novel, physics-first approach to quantum measurement, using physical experiments as the basis to describe the underlying mathematical formalism. The text is an excellent introduction for students wanting to learn more about measurement theory, and the wide selection of exercises make this book ideal for courses.Trade Review'There is a spot in the great John Archibald Wheeler's autobiography where he writes, 'Many students entering upon their study of quantum mechanics are told that [the theory] shows its essence in the equation Erwin Schrödinger published in 1926. … But, to my mind, the Schrödinger wave fails to capture the true essence of quantum mechanics. That essence is measurement.' Were Wheeler but alive today to see this marvelous book! His outlook shaped my own approach to the foundations of quantum theory, but this book is the first living instantiation of Wheeler's deep thought to physical practice itself. It will be a standard reference for years to come.' Christopher Fuchs, University of Massachusetts Boston'This is a fascinating exploration of quantum measurement, going far beyond the standard textbook coverage and guided by the most recent experiments. Essential reading for quantum physicists and engineers and a valuable reference for all those seeking an in-depth understanding of fundamental quantum processes and solid-state quantum devices.' Jean-Michel Raimond, Sorbonne Université'Theoretical and experimental physicists mean different things when they refer to the quantum measurement problem. In this book two world leading quantum physicists, one a theoretician and one an experimentalist, give a comprehensive treatment of the real measurement problem: how to intervene and control the quantum world. This problem is at the foundation of the rapidly developing quantum technology industry. In so doing, they recast moribund questions in quantum foundations and provide the tools for more effective quantum technology.' Gerard Milburn, The University of QueenslandTable of Contents1. Introduction to quantum physics and measurement; 2. Projective measurement; 3. Generalized measurement; 4. Weak measurement; 5. Continuous measurement – diffusive case; 6. Continuous measurement – quantum jump case; 7. Linear detectors; 8. Quantum amplifcation; 9. Measurement-related phenomena and applications; 10. Feedback and control; 11. Epilogue – what does it all mean?

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Book SynopsisThis is a how to guide for making beginning calculations in modern physics. The academic level is second year college physical science and engineering students. The calculations are performed in Mathematica, and stress graphical visualization, units, and numerical answers. The techniques show the student how to learn the physics without being hung up on the math. There is a continuing movement to introduce more advanced computational methods into lower-level physics courses. Mathematica is a unique tool in that code is written as human readable much like one writes a traditional equation on the board.Key Features:Concise summary of the physics concepts.Over 300 worked examples in Mathematica.Tutorial to allow a beginner to produce fast results.The companion code for this book can be found here:Table of Contents1. Basis of Modern Physics 2. Thermal Radiation 3. Key Processes 4. Special Relativity 5. Bohr Model 6. Particle in a Box 7. Quantum Harmonic Oscillator 8. Hydrogen Atom 9. Statistical Physics 10. Astrophysics Appendix A: Mathematica Starter Appendix B: Physical Constants

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Book SynopsisA pedagogical introduction to a set of mathematical ideas associated with Berry phases that have revolutionized understanding of key aspects of the behavior of electrons in solids. Including practical examples and exercises throughout to test understanding, this book covers electric polarization, orbital magnetization and topological insulators.Trade Review'This book brings together almost forty years of progress in understanding how the wavefunctions of electrons in a crystal, and in particular their continuous evolution with momentum, determine important physical properties. David Vanderbilt is one of the creators of this field, and nearly every chapter includes topics where his contributions were decisive. In addition to its scope, one way in which this book differs from others on related topics is the clear path from physical insight, through theoretical understanding, to practical methods for specific materials. This book can be read profitably by those interested in the fundamental theory of topological phases as well as those seeking to understand modern electronic structure approaches.' Joel Moore, Chern-Simons Professor of Physics, University of California, Berkeley'The geometric phase and related concepts provide a unified framework for describing many fundamental properties of electrons in solids, from electric polarization to quantized effects in topological materials. Readers wishing to become familiar with these notions will find David Vanderbilt's excellent book to be an invaluable resource.' Ivo Souza, University of the Basque Country, San Sebastián'Berry phases and associated geometric and topological concepts have transformed our understanding of electronic properties. This book provides a much needed pedagogical exposition with computational instructions which will be very valuable for students and researchers in solid state physics and materials science.' Qian Niu, University of Texas'David Vanderbilt explicates a new exciting frontier in solid state physics and materials theory, and does so in a clear and interesting to read way. Not only does he cover every nook and cranny of this new area, but in the process clearly explains the basics of electronic structure theory, such as density functional theory (DFT) and tight-binding, that will be extremely useful and important to any student of condensed matter theory. The subject of the book is how the phases of the wave functions, neglected for decades, affect important measurable properties of materials. He covers everything from the mathematical theory of geometric phases, applications to polarization and orbital magnetism, all the way to complex applications such as three-dimensional topological insulators and beyond. To be able to write about such seemingly esoteric matters in such a clear and gripping way is the mark of a great teacher. I look forward to my second reading of the book!' Ronald Cohen, Extreme Materials Initiative, Geophysical Laboratory, Carnegie Institution for Science'For anyone who wants to learn about Berry phases in electronic structure and the exciting recent developments in topological insulators, I heartily recommend this book. David Vanderbilt is uniquely poised to present the concepts and practical developments in this field that has revolutionized our understanding of condensed matter. He has made some of the most important advances in electronic structure theory in the last twenty years, including the original work that has made Berry phases a central part the field, and he is known for lucid presentations. In this book Vanderbilt introduces the concepts in a way that is accessible to a nonexpert, with clear explanations and instructive examples, and yet he presents the material in the depth that it deserves. I recommend this book for anyone who wants to be a part of condensed matter theory in the twenty-first century or just to appreciate the basic ideas and phenomena of this exciting field.' Richard M. Martin, University of Illinois, Urbana Champaign'This is a well-structured book which will serve admirably as a text for advanced students as well as a means for more mature readers to gain an appreciation of the recent developments in this area of activity.' K. Alan Shore, Contemporary Physics'Its author, Rutgers University physicist David Vanderbilt, is eminently qualified for the task: he is the senior author of a large part of the research at the book's core. That literature is now fundamental knowledge for any scientist working on modern electronic structure. … The book's presentation combines mathematical rigor with illuminating discussions and examples … the ideal textbook for any special-topics course that broadly covers geometry and topology in electronic structure.' Physics Today'… I would like to recommend this book to crystallographers, and more generally to condensed-matter physicists who wish to learn about the physics of Berry phases. The pedagogical presentation used throughout will allow careful readers to start working on the more detailed literature with a solid basis and a clear view of recent results.' Laurent Chaput, Acta CrystallographicaTable of ContentsPreface; Acronyms; Introduction; 1. Invariance and quantization of charges and currents; 2. Review of electronic structure theory; 3. Berry phases and curvatures; 4. Electric polarization; 5. Topological insulators and semimetals; 6. Orbital magnetization and axion magnetoelectric coupling; Appendix A. Fourier transform conventions; Appendix B. Optimal alignment and the singular value decomposition; Appendix C. Gauge transformation of the Chern–Simons axion coupling; Appendix D. The PythTB package; References; Index.

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Book SynopsisGinzburgLandau theory is an important tool in condensed matter physics research, describing the ordered phases of condensed matter, including the dynamics, elasticity, and thermodynamics of the condensed configurations. In this systematic introduction to GinzbergLandau theory, both common and topological excitations are considered on the same footing (including their thermodynamics and dynamical phenomena). The role of the topological versus energetic considerations is made clear. Required mathematics (symmetry, including lattice translation, topology, and perturbative techniques) are introduced as needed. The results are illustrated using arguably the most fascinating class of such systems, high Tc superconductors subject to magnetic field. This book is an important reference for both researchers and graduate students working in condensed matter physics or can act as a textbook for those taking advanced courses on these topics.Trade Review'Baruch Rosenstein and Dingping Li, renowned experts in the theory of superconductivity, will guide readers, like Dante's Virgil, through the circles of the fascinating world of Topological Matter.' Andrey Varlamov, CNR-SPIN and University of Tor VergataTable of ContentsPreface. 1. Introduction and overview; Part I. Ordered Phases of Condensed Matter Disrupted by Topological Defects: 2. The phenomenological (Landau) description of the ordered condensed matter from magnets to Bose condensates; 3. Simplest topological defects; 4. Topological defects and their classification; Part II. Structure of the Topological Matter Created by Gauge Field: 5. Repulsion between solitons and viable vortex matter created by a gauge field; 6. Abrikosov vortices created by the magnetic field; 7. Structure and magnetization of the vortex lattice within London approximation; 8. Structure and megnetization of the vortex lattice within Abrikosov approximation; Part III. Excitation Modes of Condensate: Elasticity and Stability of the Topological Matter: 9. Linear stability analysis of the homogenous states; 10. Stability and the excitation spectrum of the single soliton and the vortex lattice; 11. Forces of solitons, pinning and elasticity of the vortex matter; Part IV. Dynamics of Condensates and Solitary Waves: 12. Dynamics of the order parameter field; 13. Solitary waves; 14. Viscous flow of the Abrikosov flux lattice; Part V. Thermal Fluctuations. 15. Statistical physics of mesoscopic degrees of freedom; 16. The Landau-Wilson approach to statistical physics of the interacting field fluctuations; 17. Thermal fluctuations in the vortex matter; Appendix; Index.

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Book SynopsisThis monograph is the first to present the theory of global attractors of Hamiltonian partial differential equations. A particular focus is placed on the results obtained in the last three decades, with chapters on the global attraction to stationary states, to solitons, and to stationary orbits. The text includes many physically relevant examples and will be of interest to graduate students and researchers in both mathematics and physics. The proofs involve novel applications of methods of harmonic analysis, including Tauberian theorems, Titchmarsh''s convolution theorem, and the theory of quasimeasures. As well as the underlying theory, the authors discuss the results of numerical simulations and formulate open problems to prompt further research.Table of ContentsIntroduction; 1. Global attraction to stationary states; 2. Global attraction to solitons; 3. Global attraction to stationary orbits; 4. Asymptotic stability of stationary orbits and solitons; 5. Adiabatic effective dynamics of solitons; 6. Numerical simulation of solitons; 7. Dispersive decay; 8. Attractors and quantum mechanics; References; Index.

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Book SynopsisThis compact guide presents the key features of general relativity, to support and supplement the presentation in mainstream, more comprehensive undergraduate textbooks, or as a re-cap of essentials for graduate students pursuing more advanced studies. It helps students plot a careful path to understanding the core ideas and basics of differential geometry, as applied to general relativity, without overwhelming them. While the guide doesn''t shy away from necessary technicalities, it emphasises the essential simplicity of the main physical arguments. Presuming a familiarity with special relativity (with a brief account in an appendix), it describes how general covariance and the equivalence principle motivate Einstein''s theory of gravitation. It then introduces differential geometry and the covariant derivative as the mathematical technology which allows us to understand Einstein''s equations of general relativity. The book is supported by numerous worked exampled and problems, and imTrade Review'The strength of Gray's book lies in his concern to provide friendly, pedagogical explanations for many tricky features of the theory, starting from a basic level, and his informal style will be welcomed by the less confident reader.' Peter J. Bussey, Contemporary Physics'... this book marks a welcome move to shorter, more focussed introductions to General Relativity aimed at undergraduate students. As the mathematical half of a full GR course it works well, but perhaps a less abstract approach and greater emphasis on the geometrical nature of the theory might appeal more to some readers.' Andrew Taylor, The Observatory'This book is part of the Cambridge 'Student's Guide' series. It is based on a 10 lecture course the author taught at the University of Glasgow. The book is mostly about introducing the math needed to reach the discussion of the Einstein equation.' Jorge Pullin, zbMATHTable of ContentsPreface; 1. Introduction; 2. Vectors, tensors and functions; 3. Manifolds, vectors and differentiation; 4. Energy, momentum and Einstein's equations; Appendix A. Special relativity – a brief introduction; Appendix B. Solutions to Einstein's equations; Appendix C. Notation; Bibliography; Index.

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Book SynopsisI Fundamentals.- 1 Ordinary Differential Equations.- 2 Difference Equations.- II Local Analysis.- 3 Approximate Solution of Linear Differential Equations.- 4 Approximate Solution of Nonlinear Differential Equations.- 5 Approximate Solution of Difference Equations.- 6 Asymptotic Expansion of Integrals.- III Perturbation Methods.- 7 Perturbation Series.- 8 Summation of Series.- IV Global Analysis.- 9 Boundary Layer Theory.- 10 WKB Theory.- 11 Multiple-Scale Analysis.Trade Review"This book is a reprint of the original published by McGraw-Hill \ref [MR0538168 (80d:00030)]. The only changes are the addition of the Roman numeral I to the title and the provision of a subtitle, "Asymptotic methods and perturbation theory". This latter improvement is much needed, as the original title suggested that this was a teaching book for undergraduate scientists and engineers. It is not, but is an excellent introduction to asymptotic and perturbation methods for master's degree students or beginning research students. Certain parts of it could be used for a course in asymptotics for final year undergraduates in applied mathematics or mathematical physics. This is a book that has stood the test of time and I cannot but endorse the remarks of the original reviewer. It is written in a fresh and lively style and the many graphs and tables, comparing the results of exact and approximate methods, were in advance of its time. I have owned a copy of the original for over twenty years, using it on a regular basis, and, after the original had gone out of print, lending it to my research students. Springer-Verlag has done a great service to users of, and researchers in, asymptotics and perturbation theory by reprinting this classic." (A.D. Wood, Mathematical Reviews) Table of ContentsI Preface. 1 Ordinary Differential Equations. 2 Difference Equations. 3 Approximate Solution of Linear Differential Equations. 4 Approximate Solution of Nonlinear Equations. 5 Approximate Solution of Difference Equations. 6 Asymptotic Expansion of Integrals. 7 Perturbation Series. 8 Summation of Series. 9 Boundary Layer Theory. 10 WKB Theory. 11 Multiple Scales Analysis. Appendix, References, Index

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Book SynopsisThis book demonstrates some of the ways in which Microsoft Excel® may be used to solve numerical problems in the field of physics. But why use Excel in the first place? Certainly, Excel is never going to out-perform the wonderful symbolic algebra tools that we have today – Mathematica, Mathcad, Maple, MATLAB, etc. However, from a pedagogical stance, Excel has the advantage of not being a ‘black box’ approach to problem solving. The user must do a lot more work than just call up a function. The intermediate steps in a calculation are displayed on the worksheet. Another advantage is the somewhat less steep learning curve. This book shows Excel in action in various areas within physics. Some Visual Basic for Applications (VBA) has been introduced, the purpose here is to show how the power of Excel can be greatly extended and hopefully to whet the appetite of a few readers to get familiar with the power of VBA. Those with programming experience in any other language should be able to follow the code.

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Book SynopsisMetrological data is known to be blurred by the imperfections of the measuring process. In retrospect, for about two centuries regular or constant errors were no focal point of experimental activities, only irregular or random error were. Today's notation of unknown systematic errors is in line with this. Confusingly enough, the worldwide practiced approach to belatedly admit those unknown systematic errors amounts to consider them as being random, too. This book discusses a new error concept dispensing with the common practice to randomize unknown systematic errors. Instead, unknown systematic errors will be treated as what they physically are- namely as constants being unknown with respect to magnitude and sign. The ideas considered in this book issue a proceeding steadily localizing the true values of the measurands and consequently traceability.Table of Contents Preface Acknowledgements Author biography 1. Basics of metrology 2. Some statistics 3. Measurement uncertainties 4. Method of least squares 5. Fitting of straight lines 6. Features of least squares estimators 7. Prospects 8. Epilogue References and suggested reading

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Book SynopsisThis book demonstrates Microsoft EXCEL-based Fourier transform of selected physics examples. Spectral density of the auto-regression process is also described in relation to Fourier transform. Rather than offering rigorous mathematics, readers will "try and feel" Fourier transform for themselves through the examples. Readers can also acquire and analyze their own data following the step-by-step procedure explained in this book. A hands-on acoustic spectral analysis can be one of the ideal long-term student projects.Table of Contents Preface Acknowledgments Author biography 1. The principle of superposition and the Fourier series 2. The Fourier transform 3. The EXCEL-based Fourier transform 4. The Fourier transform in physics 5. Beyond the Fourier transform spectroscopy Appendix

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Book SynopsisThis is a companion textbook for an introductory course in physics. It aims to link the theories and models that students learn in class with practical problem-solving techniques. In other words, it should address the common complaint that 'I understand the concepts but I can't do the homework or tests'. The fundamentals of introductory physics courses are addressed in simple and concise terms, with emphasis on how the fundamental concepts and equations should be used to solve physics problems.

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Book SynopsisThe world of single-board computing puts powerful coding tools in the palm of your hand. The portable Raspberry Pi computing platform with the power of Linux yields an exciting exploratory tool for beginning scientific computing.Science and Computing with Raspberry Pi takes the enterprising researcher, student, or hobbyist through explorations in a variety of computing exercises with the physical sciences. The book has tutorials and exercises for a wide range of scientific computing problems while guiding the user through: Configuring your Raspberry Pi and Linux operating system Understanding the software requirements while using the Pi for scientific computing Computing exercises in physics, astronomy, chaos theory, and machine learning Table of Contents Preface Acknowledgements Author biography 1. Raspberry Pi 2. Setting up your system 3. Chaos and non-linear dynamics 4. Physics and astronomy 5. Machine learning 6. Image combination and analysis Appendices

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Book SynopsisThis primer begins with a brief introduction to the main ideas underlying Effective Field Theory (EFT) and describes how nuclear forces are obtained from first principles by introducing a Euclidean space-time lattice for chiral EFT. It subsequently develops the related technical aspects by addressing the two-nucleon problem on the lattice and clarifying how it fixes the numerical values of the low-energy constants of chiral EFT. In turn, the spherical wall method is introduced and used to show how improved lattice actions render higher-order corrections perturbative. The book also presents Monte Carlo algorithms used in actual calculations. In the last part of the book, the Euclidean time projection method is introduced and used to compute the ground-state properties of nuclei up to the mid-mass region. In this context, the construction of appropriate trial wave functions for the Euclidean time projection is discussed, as well as methods for determining the energies of the low-lying excitations and their spatial structure. In addition, the so-called adiabatic Hamiltonian, which allows nuclear reactions to be precisely calculated, is introduced using the example of alpha-alpha scattering. In closing, the book demonstrates how Nuclear Lattice EFT can be extended to studies of unphysical values of the fundamental parameters, using the triple-alpha process as a concrete example with implications for the anthropic view of the Universe. Nuclear Lattice Effective Field Theory offers a concise, self-contained, and introductory text suitable for self-study use by graduate students and newcomers to the field of modern computational techniques for atomic nuclei and nuclear reactions.Trade Review“Nuclear Lattice Effective Field Theory … is a great practical advantage to the reader. … Lähde and Meißner’s helpful primer has the potential to stimulate increased efforts by serving newcomers as an essential guide to the field.” (Ruprecht Machleidt, Physics Today, Vol. 72 (10), October, 2019)Table of ContentsIntroduction to Effective Field Theory.- Nuclear Forces in Chiral EFT.- Lattice Formulations.- Lattice Chiral Effective Field Theory.- Two and Three Nucleons on the Lattice.- Lattice Monte Carlo.- LIght and Medium-Mass Nuclei on the Lattice.- Further Developments.- Notations and Conventions.- Basics of the Nucleon-Nucleon Interaction.- Study of Rotational Symmetry Breaking Effects in an A Cluster Model.- Monte Carlo Sampling.- Hybrid Monte Carlo Action and Force.- Monte Carlo Calculation of Observables.-

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Book SynopsisThis book explains and develops the Dirac equation in the context of general relativistic quantum mechanics in a range of spacetime dimensions. It clarifies the subject by carefully pointing out the various conventions used and explaining how they are related to each other. The prerequisites are familiarity with general relativity and an exposure to the Dirac equation at the level of special relativistic quantum mechanics, but a review of this latter topic is given in the first chapter as a reference and framework for the physical interpretations that follow. Worked examples and exercises with solutions are provided. Appendices include reviews of topics used in the body of the text. This book should benefit researchers and graduate students in general relativity and in condensed matter.Trade Review“Ultimately, this short monograph will be of interest as a quick guide to researchers who need a notation reference, well organized overview of the literature, or an introduction to the subject, looking for connection with their own field; also for graduate students who are looking for a bird's eye view or need help with determining the learning path. It must be added that students especially will appreciate that the authors provide solutions to the exercises.” (Tomasz Artur Stachowiak, Mathematical Reviews, December, 2019)“The book represents a very useful tool for graduate students and beginning researchers in a large area of the theory and applications of the Dirac equation. It can be useful for all the stages of learning: from the initial acknowledgement to deep investigations. … The book will be very useful to everybody desiring to make an economy with special articles from various journals.” (Alex B. Gaina, zbMath 1416.81003, 2019)Table of ContentsIntroduction.- The Dirac equation in special relativity.- The spinorial covariant derivative.- Examples in (3+1) GR.- The Dirac equation in (1+1) GR.- The Dirac equation in (2+1) GR.- Scalar product.- Appendices.

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Book SynopsisThis book develops analytical methods for studying the dynamical chaos, synchronization, and dynamics of structures in various models of coupled rotators. Rotators and their systems are defined in a cylindrical phase space, and, unlike oscillators, which are defined in Rn, they have a wider “range” of motion: There are vibrational and rotational types for cyclic variables, as well as their combinations (rotational-vibrational) if the number of cyclic variables is more than one. The specificity of rotator phase space poses serious challenges in terms of selecting methods for studying the dynamics of related systems. The book chiefly focuses on developing a modified form of the method of averaging, which can be used to study the dynamics of rotators. In general, the book uses the “language” of the qualitative theory of differential equations, point mappings, and the theory of bifurcations, which helps authors to obtain new results on dynamical chaos in systems with few degrees of freedom. In addition, a special section is devoted to the study and classification of dynamic structures that can occur in systems with a large number of interconnected objects, i.e. in lattices of rotators and/or oscillators. Given its scope and format, the book can be used both in lectures and courses on nonlinear dynamics, and in specialized courses on the development and operation of relevant systems that can be represented by a large number of various practical systems: interconnected grids of various mechanical systems, various types of networks including not only mechanical but also biological systems, etc. Table of ContentsIntroduction.- Autonomous and non-autonomous systems with one degrees-of-freedom. Autonomous and non-autonomous systems with one and a half degrees-of-freedom.- Autonomous systems with two degrees-of-freedom.- Vibration of shafts.- Synchronization in homogeneous lattices.- Physics, existence, fusion and stability Of cluster structures.- Appendix I.- Appendix II.

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Book SynopsisThis book, now in its third edition, offers a practical guide to the use of probability and statistics in experimental physics that is of value for both advanced undergraduates and graduate students. Focusing on applications and theorems and techniques actually used in experimental research, it includes worked problems with solutions, as well as homework exercises to aid understanding. Suitable for readers with no prior knowledge of statistical techniques, the book comprehensively discusses the topic and features a number of interesting and amusing applications that are often neglected. Providing an introduction to neural net techniques that encompasses deep learning, adversarial neural networks, and boosted decision trees, this new edition includes updated chapters with, for example, additions relating to generating and characteristic functions, Bayes’ theorem, the Feldman-Cousins method, Lagrange multipliers for constraints, estimation of likelihood ratios, and unfolding problems.Trade Review“The depth and the manner in which the material is treated will make it easy for the students to transition to more advanced topics such as deep learning, machine learning and artificial intelligence after perusing the book. … Roe’s book is a wonderful, forward looking introduction to probability and statistics and its applications. Hence, I have no hesitations whatsoever in recommending the book – both to the students and instructors.” (Mogadalai P Gururajan, Contemporary Physics, August 19, 2021)Table of Contents1. Front Matter Pages i-xi 2. Basic Probability Concepts 3. Some Initial Definitions 4. Some Results Independent of Specific Distributions 5. Discrete Distributions and Combinatorials 6. Specific Discrete Distributions 7. The Normal (or Gaussian) Distribution and Other Continuous Distributions 8. Generating Functions and Characteristic Functions 9. The Monte Carlo Method: Computer Simulation of Experiments 10. Queueing Theory and Other Probability Questions 11. Two-Dimensional and Multidimensional Distributions 12. The Central Limit Theorem 13. Inverse Probability; Confidence Limits 14. Methods for Estimating Parameters. Least Squares and Maximum Likelihood 15. Curve Fitting 16. Bartlett S Function; Estimating Likelihood Ratios Needed for an Experiment 17. Interpolating Functions and Unfolding Problems 18. Fitting Data with Correlations and Constraints 19. Beyond Maximum Likelihood and Least Squares; Robust Methods 20. Back Matter

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Book SynopsisThis book presents the state-of-the-art in supercomputer simulation. It includes the latest findings from leading researchers using systems from the High Performance Computing Center Stuttgart (HLRS) in 2019. The reports cover all fields of computational science and engineering ranging from CFD to computational physics and from chemistry to computer science with a special emphasis on industrially relevant applications. Presenting findings of one of Europe’s leading systems, this volume covers a wide variety of applications that deliver a high level of sustained performance.The book covers the main methods in high-performance computing. Its outstanding results in achieving the best performance for production codes are of particular interest for both scientists and engineers. The book comes with a wealth of color illustrations and tables of results.Table of ContentsPart 1, Physics.- Part 2, Solid State Physics.- Part 3, Chemistry.- Part 4, Material Science.- Part 5, Reactive Flows.- Part 6, Computational Fluid Dynamics.- Part 7, Transport and Climate.- Part 8, Computer Science.- Part 9, Miscellaneous Topics.

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Book SynopsisThis book provides a solid foundation in the Python programming language, numerical methods, and data analysis, all embedded within the context of astronomy and astrophysics. It not only enables students to learn programming with the aid of examples from these fields but also provides ample motivation for engagement in independent research. The book opens by outlining the importance of computational methods and programming algorithms in contemporary astronomical and astrophysical research, showing why programming in Python is a good choice for beginners. The performance of basic calculations with Python is then explained with reference to, for example, Kepler’s laws of planetary motion and gravitational and tidal forces. Here, essential background knowledge is provided as necessary. Subsequent chapters are designed to teach the reader to define and use important functions in Python and to utilize numerical methods to solve differential equations and landmark dynamical problems in astrophysics. Finally, the analysis of astronomical data is discussed, with various hands-on examples as well as guidance on astronomical image analysis and applications of artificial neural networks.Table of ContentsChapter 1. Introduction.- Chapter 2. Getting Started with Python.- Chapter 3. Computing and Displaying Data.- Chapter 4. Functions and Numerical Methods.- Chapter 5. Solving Differential Equations.- Chapter 6. Astronomical Data Analysis.

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Book SynopsisThis book offers an informal, easy-to-understand account of topics in modern physics and mathematics. The focus is, in particular, on statistical mechanics, soft matter, probability, chaos, complexity, and models, as well as their interplay. The book features 28 key entries and it is carefully structured so as to allow readers to pursue different paths that reflect their interests and priorities, thereby avoiding an excessively systematic presentation that might stifle interest. While the majority of the entries concern specific topics and arguments, some relate to important protagonists of science, highlighting and explaining their contributions. Advanced mathematics is avoided, and formulas are introduced in only a few cases. The book is a user-friendly tool that nevertheless avoids scientific compromise. It is of interest to all who seek a better grasp of the world that surrounds us and of the ideas that have changed our perceptions.Trade Review“Each topic is discussed in a brief chapter, at a technical level that could be followed by first-year students of physics and mathematics, but also by wider parts of the public. Each chapter contains a statement of the topic, a brief history, and describes a number of examples … . The book makes a pleasant reading, full of wit and of surprising turns. I think that it can be useful to the general reader … motivate students … .” (Luca Peliti, Journal of Statistical Physics, Vol. 185, 2021)Table of ContentsChapter 1 - Introduction.- Chapter 2 - Atoms, Irreversibility, Probability, Statistical Mechanics, Entropy.- Chapter 3 - Probability, Entropy, Chaos.- Chapter 4 - Chaos, Prediction.- Chapter 5 - Prediction, Turbulence, Models.- Chapter 6 - Models, Richardson.- Chapter 7 - Boltzmann, Statistical Mechanics, Brownian Motion.- Chapter 8 - Boltzmann, Atoms, Statistical Mechanics, Mesoscale Systems.- Chapter 9 - Prediction: Chaos, Poincaré, Richardson, Models, Big data.- Chapter 10 - Statistical Mechanics: Atoms, Boltzmann, Maxwell.

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Book SynopsisThis book introduces the phenomenology of gravitational lensing in an accessible manner and provides a thorough discussion of the related astrophysical applications. It is intended for advanced undergraduates and graduate students who want to start working in this rapidly evolving field. This includes also senior researchers who are interested in ongoing or future surveys and missions such as DES, Euclid, WFIRST, LSST. The reader is guided through many fascinating topics related to gravitational lensing like the structure of our galaxy, the searching for exoplanets, the investigation of dark matter in galaxies and galaxy clusters, and several aspects of cosmology, including dark energy and the cosmic microwave background. The author, who has gained valuable experience as academic teacher, guides the readers towards the comprehension of the theory of gravitational lensing and related observational techniques by using simple codes written in python. This approach, beyond facilitating the understanding of gravitational lensing, is preparatory for learning the python programming language which is gaining large popularity both in academia and in the private sector.Table of ContentsPART I: Generalities1. Light deflection1.1. Deflection of a light corpuscle1.2. Deflection of light according to General Relativity1.3. Deflection by an ensable of point masses1.4. Deflection by an extended mass distribution1.5. Light propagation through an inhomogeneous universe1.6. Python examples2. The general lens2.1. Lens equation2.2. Lensing potential2.3. First order lens mapping2.4 Magnification2.5 Lensing to the second order2.6 Time delay surface2.7 Python examplesPART II: Applications of gravitational lensing1. Microlensing1.1 The point mass lens1.2 Standard microlensing light curve1.3 Microlensing parallax1.4 Optical depth and event rate1.5 Astrometric microlensing1.6 Multiple point lenses1.7 Planetary microlensing1.8 Python examples2. Strong lensing by galaxies and galaxy clusters2.1 Axially symmetric lenses2.2 Power-law lens2.3 Softened lenses2.4 Elliptical lenses2.5 Substructures2.6 External shear2.7 Parametric lens modeling2.8 Non-parametric lens modeling2.9 Searches for strong lenses2.10 Cosmic telescopes2.11 Strong lensing cosmography2.12 Time-delay cosmology2.13 Python examples3. Weak lensing by virialized structures3.1 Shear measurements3.2 Tangential and cross component of the shear3.3 Lens mass measurements3.4 Two-dimensional mass mapping3.5 Mass-sheet degeneracy3.6 Python examples4. Weak lensing by the large-scale-structure4.1 Effective convergence4.2 Limber’s equation4.3 Shear correlation functions4.4 Shear in apertures and aperture mass4.5 E- and B-modes4.6 Python examples5. Lensing of the Cosmic Microwave Background5.1 Lensing of the CMB temperature5.2 Gravitational lensing of the CMB polarization5.3 Recovery of the gravitational potential5.4 Python examples

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Book SynopsisIn this undergraduate textbook, now in its 2nd edition, the author develops the quantum theory from first principles based on very simple experiments: a photon traveling through beam splitters to detectors, an electron moving through magnetic fields, and an atom emitting radiation. From the physical description of these experiments follows a natural mathematical description in terms of matrices and complex numbers.The first part of the book examines how experimental facts force us to let go of some deeply held preconceptions and develops this idea into a description of states, probabilities, observables, and time evolution. The quantum mechanical principles are illustrated using applications such as gravitational wave detection, magnetic resonance imaging, atomic clocks, scanning tunneling microscopy, and many more. The first part concludes with an overview of the complete quantum theory.The second part of the book covers more advanced topics, including the concept of entanglement, the process of decoherence or how quantum systems become classical, quantum computing and quantum communication, and quantum particles moving in space. Here, the book makes contact with more traditional approaches to quantum physics. The remaining chapters delve deeply into the idea of uncertainty relations and explore what the quantum theory says about the nature of reality.The book is an ideal accessible introduction to quantum physics, tested in the classroom, with modern examples and plenty of end-of-chapter exercises.Table of ContentsChapter 1: Three simple experiments.- The purpose of physical theories.- A laser and a detector.- A laser and a beam splitter.- A Mach-Zehnder interferometer.- The breakdown of classical concepts.- Chapter 2: Photons and Interference.- Photon paths and superpositions.- The beam splitter as a matrix.- The phase in an interferometer.- How to calculate probabilities.- Gravitational wave detection.- Chapter 3: Electrons with Spin.- The Stern-Gerlach experiment.- The spin observable.- The Bloch sphere.- The uncertainty principle.- Magnetic resonance imaging.- Chapter 4: Atoms and Energy.- The energy spectrum of atoms.- Changes over time.- The Hamiltonian.- Interactions.- Atomic clocks.- Chapter 5: Operators.- Eigenvalue problems.- Observables.- Evolution.- The commutator.- Projectors.- Chapter 6: Entanglement.- The state of two electrons.- Entanglement.- Quantum teleportation.- Quantum computers.- Chapter 7: Decoherence.- Classical and quantum uncertainty.- The density matrix.- Interactions with the environment.- Entropy and Landauer’s principle.- Chapter 8: The Motion of Particles.- A particle in a box.- The momentum of a particle.- The energy of a particle.- The scanning tunneling microscope.- Chemistry.- Chapter 9: Uncertainty Relations.- Quantum uncertainty revisited.- Position-momentum uncertainty.- The energy-time uncertainty relation.- The quantum mechanical pendulum.- Precision measurements.- Chapter 10: The Nature of Reality.- The emergent classical world.- The quantum state revisited.- Nonlocality.- Contextuality.- A compendium of interpretations.

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Book SynopsisIn these lecture notes, we will analyze the behavior of random walk on disordered media by means of both probabilistic and analytic methods, and will study the scaling limits. We will focus on the discrete potential theory and how the theory is effectively used in the analysis of disordered media. The first few chapters of the notes can be used as an introduction to discrete potential theory.Recently, there has been significant progress on the theory of random walk on disordered media such as fractals and random media. Random walk on a percolation cluster(‘the ant in the labyrinth’)is one of the typical examples. In 1986, H. Kesten showed the anomalous behavior of a random walk on a percolation cluster at critical probability. Partly motivated by this work, analysis and diffusion processes on fractals have been developed since the late eighties. As a result, various new methods have been produced to estimate heat kernels on disordered media. These developments are summarized in the notes.Table of ContentsIntroduction.- Weighted graphs and the associated Markov chains.- Heat kernel estimates – General theory.- Heat kernel estimates using effective resistance.- Heat kernel estimates for random weighted graphs.- Alexander-Orbach conjecture holds when two-point functions behave nicely.- Further results for random walk on IIC.- Random conductance model.

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Book SynopsisCollating different aspects of Vector-valued Partial Differential Equations and Applications, this volume is based on the 2013 CIME Course with the same name which took place at Cetraro, Italy, under the scientific direction of John Ball and Paolo Marcellini. It contains the following contributions: The pullback equation (Bernard Dacorogna), The stability of the isoperimetric inequality (Nicola Fusco), Mathematical problems in thin elastic sheets: scaling limits, packing, crumpling and singularities (Stefan Müller), and Aspects of PDEs related to fluid flows (Vladimir Sverák). These lectures are addressed to graduate students and researchers in the field.Table of ContentsPreface.- Bernard Dacorogna: The pullback equation.- Nicola Fusco: The stability of the isoperimetric inequality.- Stefan Müller: Mathematical problems in thin elastic sheets: scaling limits.-packing, crumpling and singularities.- Vladimir Sverák: Aspects of PDEs related to Fluid Flows.

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Book SynopsisUnderstanding and controlling the physics of space charge effects in linear and circular proton and ion accelerators are essential to their operation, and to future high-intensity facilities. This book presents the status quo of this field from a theoretical perspective, compares analytical approaches with multi-particle computer simulations and – where available – with experiments. It discusses fundamental concepts of phase space motion, matched beams and modes of perturbation, along with mathematical models of analysis – from envelope to Vlasov-Poisson equations. The main emphasis is on providing a systematic description of incoherent and coherent resonance phenomena; parametric instabilities and sum modes; mismatch and halo; error driven resonances; and emittance exchange due to anisotropy, as well as the role of Landau damping. Their distinctive features are elaborated in the context of numerous sample simulations, and their potential impacts on beam quality degradation and beam loss are discussed. The book is intended for advanced beginners in accelerator research, and for experts interested in the mechanisms of direct space charge interaction and their modeling.Table of ContentsDedication.- Preface.- Introduction.- Phase Space Dynamics in Theory and Simulation.- Vlasov and Envelope Analysis.- Matched Beams.- Modes of Space Charge Interaction.- Beam Mismatch and Halo.- Coherent Parametric Instabilities.- Magnet Error Driven Coherent Resonances.- Emittance Exchange in Anisotropic Beams.- Discussion of Space Charge in Accelerator Design.- Epilogue.- Glossary.

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Book SynopsisThe purpose of this book is twofold: first, it sets out to equip the reader with a sound understanding of the foundations of probability theory and stochastic processes, offering step-by-step guidance from basic probability theory to advanced topics, such as stochastic differential equations, which typically are presented in textbooks that require a very strong mathematical background. Second, while leading the reader on this journey, it aims to impart the knowledge needed in order to develop algorithms that simulate realistic physical systems. Connections with several fields of pure and applied physics, from quantum mechanics to econophysics, are provided. Furthermore, the inclusion of fully solved exercises will enable the reader to learn quickly and to explore topics not covered in the main text. The book will appeal especially to graduate students wishing to learn how to simulate physical systems and to deepen their knowledge of the mathematical framework, which has very deep connections with modern quantum field theory.Table of Contents1 Review of Probability Theory.- 2 Applications to Mathematical Statistics.- 3 Conditional Probability and Conditional Expectation.- 4 Markov Chains.- 5 Sampling of Random Variables and Simulation.- 6 Brownian Motion.- 7 Introduction to Stochastic Calculus and Ito Integral.- 8 Introduction to Stochastic Differential Equations and Applications.- Bibliography.- Solutions.

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Book SynopsisThe book assumes next to no prior knowledge of the topic. The first part introduces the core mathematics, always in conjunction with the physical context. In the second part of the book, a series of examples showcases some of the more conceptually advanced areas of physics, the presentation of which draws on the developments in the first part. A large number of problems helps students to hone their skills in using the presented mathematical methods. Solutions to the problems are available to instructors on an associated password-protected website for lecturers.Table of ContentsPreface xv Part I Mathematics 1 1 Functions of One Variable 3 1.1 Limits 3 1.2 Elementary Calculus 5 1.2.1 Differentiation Products and Quotients 6 1.2.2 Chain Rule 7 1.2.3 Inverse Functions 8 1.3 Integration 10 1.4 The Binomial Expansion 14 1.5 Taylor’s Series 15 1.6 Extrema 17 1.7 Power Series 17 1.8 Basic Functions 19 1.8.1 Exponential 19 1.8.2 Logarithm 22 1.9 First-Order Ordinary Differential Equations 24 1.10 Trigonometric Functions 25 1.10.1 L’Hôpital’s Rule 27 Problems 27 2 Complex Numbers 29 2.1 Exponential Function of a Complex Variable 30 2.2 Argand Diagrams and the Complex Plane 32 2.3 Complex Logarithm 34 2.4 Hyperbolic Functions 34 2.5 The Simple Harmonic Oscillator 36 2.5.1 Mechanics in One Dimension 38 2.5.2 Damped and Driven Oscillations 40 Problems 47 3 VectorsinR 3 51 3.1 Basic Operation 51 3.1.1 Scalar Triple Product 55 3.1.2 Vector Equations of Lines and Planes 56 3.2 Kinematics in Three Dimensions 57 3.2.1 Differentiation 57 3.2.2 Motion in a Uniform Magnetic Field 57 3.3 Coordinate Systems 59 3.3.1 Polar Coordinates 59 3.4 Central Forces 60 3.5 Rotating Frames 64 3.5.1 Larmor Effect 66 Problems 67 4 VectorSpaces 71 4.1 Formal Definition of a Vector Space 71 4.2 Fourier Series 75 4.3 Linear Operators 78 4.4 Change of Basis 89 Problems 91 5 Functions of Several Variables 95 5.1 Partial Derivatives 95 5.1.1 Definition of the Partial Derivative 95 5.1.2 Total Derivatives 98 5.1.3 Elementary Numerical Methods 104 5.1.4 Change of Variables 107 5.1.5 Mechanics Again 109 5.2 Extrema under Constraint 111 5.3 Multiple Integrals 113 5.3.1 Triple Integrals 116 5.3.2 Change of Variables 117 Problems 121 6 Vector Fields and Operators 125 6.1 The Gradient Operator 125 6.1.1 Coordinate Systems 127 6.2 Work and Energy in Vectorial Mechanics 130 6.2.1 Line Integrals 133 6.3 A Little Fluid Dynamics 135 6.3.1 Rotational Motion 138 6.3.2 Fields 141 6.4 Surface Integrals 142 6.5 The Divergence Theorem 146 6.6 Stokes’ Theorem 149 6.6.1 Conservative Forces 153 Problems 154 7 Generalized Functions 159 7.1 The Dirac Delta Function 159 7.2 Green’s Functions 163 7.3 Delta Function in Three Dimensions 165 Problems 169 8 Functions of a Complex Variable 173 8.1 Limits 174 8.2 Power Series 178 8.3 Fluids Again 179 8.4 Complex Integration 180 8.4.1 Application of the Residue Theorem 186 Problems 192 Part II Physics 195 9 Maxwell’s Equations: A Very Short Introduction 197 9.1 Electrostatics: Gauss’s Law 197 9.1.1 Conductors 203 9.2 The No Magnetic Monopole Rule 204 9.3 Current 205 9.4 Faraday’s Law 206 9.5 Ampère’s Law 208 9.6 The Wave Equation 210 9.7 Gauge Conditions 211 Problems 213 10 Special Relativity: Four-Vector Formalism 217 10.1 Lorentz Transformation 217 10.1.1 Inertial Frames 217 10.1.2 Properties and Consequences of the Lorentz Transformation 220 10.2 Minkowski Space 220 10.2.1 Four Vectors 220 10.2.2 Time Dilation 226 10.3 Four-Velocity 227 10.3.1 Four-Momentum 229 10.4 Electrodynamics 234 10.4.1 Maxwell’s Equations in Four-Vector Form 234 10.4.2 Field of a Moving Point Charge 237 10.5 Transformation of the Electromagnetic Fields 239 Problems 240 11 Quantum Theory 243 11.1 Bohr Atom 243 11.2 The de Broglie Hypothesis 246 11.3 The Schrödinger Wave Equation 246 11.4 Interpretation of the Wave function 249 11.5 Atom 251 11.5.1 The Delta Function Potential 252 11.5.2 Molecules 254 11.6 Formalism 257 11.6.1 Dirac Notation 257 11.7 Probabilistic Interpretation 258 11.7.1 Commutator Relations 259 11.7.2 Functions of Observables 261 11.7.3 Block’s Theorem 261 11.7.4 Band Structure 263 11.8 Time Evolution 266 11.9 The Stern–Gerlach Experiment 269 11.9.1 Successive Measurements 270 11.9.2 Spin Space 271 11.9.3 Explicit Matrix Representation 272 11.9.4 Larmor Precession 274 11.9.5 EPR Paradox 275 11.9.6 Bell’s Theorem 276 11.9.7 The Harmonic Oscillator 279 Problems 280 12 An Informal Treatment of Variational Principles and their History 287 12.1 Sin and Death 287 12.2 The Calculus of Variations 288 12.3 Constrained Variations 293 12.4 Hamilton’s Equations 293 12.5 Phase Space 296 12.6 Fixed Points 296 Problems 298 A Conic Sections 301 A.1 Polar Coordinates 303 A.2 Intersection of a Cone and a Plane 304 B Vector Relations 305 B.1 Products 305 B.2 Differential Operator Relations 305 B.3 Coordinates 306 Cylindrical Polar 306 Spherical Polar 307 Bibliography 309 Index 311

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Book SynopsisSince the early 70's, mixed finite elements have been the object of a wide and deep study by the mathematical and engineering communities. The fundamental role of this method for many application fields has been worldwide recognized and its use has been introduced in several commercial codes. An important feature of mixed finite elements is the interplay between theory and application. Discretization spaces for mixed schemes require suitable compatibilities, so that simple minded approximations generally do not work and the design of appropriate stabilizations gives rise to challenging mathematical problems. This volume collects the lecture notes of a C.I.M.E. course held in Summer 2006, when some of the most world recognized experts in the field reviewed the rigorous setting of mixed finite elements and revisited it after more than 30 years of practice. Applications, in this volume, range from traditional ones, like fluid-dynamics or elasticity, to more recent and active fields, like electromagnetism.Table of ContentsMixed Finite Element Methods.- Finite Elements for the Stokes Problem.- Polynomial Exact Sequences and Projection-Based Interpolation with Application to Maxwell Equations.- Finite Element Methods for Linear Elasticity.- Finite Elements for the Reissner–Mindlin Plate.

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a huge range and FREE tracked UK delivery on ALL orders.

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a huge range and FREE tracked UK delivery on ALL orders.

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