explorations in mathematical physics

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Explorations In Mathematical Physics

Author : Don Koks
ISBN : 9780387309439
Genre : Science
File Size : 83. 87 MB
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Have you ever wondered why the language of modern physics centres on geometry? Or how quantum operators and Dirac brackets work? What a convolution really is? What tensors are all about? Or what field theory and lagrangians are, and why gravity is described as curvature? This book takes you on a tour of the main ideas forming the language of modern mathematical physics. Here you will meet novel approaches to concepts such as determinants and geometry, wave function evolution, statistics, signal processing, and three-dimensional rotations. You will see how the accelerated frames of special relativity tell us about gravity. On the journey, you will discover how tensor notation relates to vector calculus, how differential geometry is built on intuitive concepts, and how variational calculus leads to field theory. You will meet quantum measurement theory, along with Green functions and the art of complex integration, and finally general relativity and cosmology. The book takes a fresh approach to tensor analysis built solely on the metric and vectors, with no need for one-forms. This gives a much more geometrical and intuitive insight into vector and tensor calculus, together with general relativity, than do traditional, more abstract methods. Don Koks is a physicist at the Defence Science and Technology Organisation in Adelaide, Australia. His doctorate in quantum cosmology was obtained from the Department of Physics and Mathematical Physics at Adelaide University. Prior work at the University of Auckland specialised in applied accelerator physics, along with pure and applied mathematics.

Ill Posed Problems Of Mathematical Physics And Analysis

Author : Mikhail Mikha_lovich Lavrent_ev
ISBN : 0821898140
Genre : Mathematics
File Size : 47. 60 MB
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Physical formulations leading to ill-posed problems Basic concepts of the theory of ill-posed problems Analytic continuation Boundary value problems for differential equations Volterra equations Integral geometry Multidimensional inverse problems for linear differential equations

Mathematical Explorations With Matlab

Author : K. Chen
ISBN : 0521639204
Genre : Computers
File Size : 61. 81 MB
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This book is about the kind of mathematics usually encountered in first year university courses. A key feature of the book is that this mathematics is explored in depth using the popular and powerful package Matlab. The emphasis is on understanding and investigating the mathematics, and putting it into practice in a wide variety of modelling situations. In the process, the reader will gain some fluency with Matlab, no starting knowledge of the package being assumed.

A Unified Grand Tour Of Theoretical Physics Third Edition

Author : Ian D. Lawrie
ISBN : 9781439884461
Genre : Science
File Size : 38. 92 MB
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A Unified Grand Tour of Theoretical Physics invites its readers to a guided exploration of the theoretical ideas that shape our contemporary understanding of the physical world at the fundamental level. Its central themes, comprising space-time geometry and the general relativistic account of gravity, quantum field theory and the gauge theories of fundamental forces, and statistical mechanics and the theory of phase transitions, are developed in explicit mathematical detail, with an emphasis on conceptual understanding. Straightforward treatments of the standard models of particle physics and cosmology are supplemented with introductory accounts of more speculative theories, including supersymmetry and string theory. This third edition of the Tour includes a new chapter on quantum gravity, focusing on the approach known as Loop Quantum Gravity, while new sections provide extended discussions of topics that have become prominent in recent years, such as the Higgs boson, massive neutrinos, cosmological perturbations, dark energy and matter, and the thermodynamics of black holes. Designed for those in search of a solid grasp of the inner workings of these theories, but who prefer to avoid a full-scale assault on the research literature, the Tour assumes as its point of departure a familiarity with basic undergraduate-level physics, and emphasizes the interconnections between aspects of physics that are more often treated in isolation. The companion website at www.unifiedgrandtours.org provides further resources, including a comprehensive manual of solutions to the end-of-chapter exercises.

Some Mathematical Methods Of Physics

Author : Gerald Goertzel
ISBN : 9780486793320
Genre : Science
File Size : 85. 58 MB
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Well-rounded, thorough treatment introduces basic concepts of mathematical physics involved in the study of linear systems, with emphasis on eigenvalues, eigenfunctions, and Green's functions. Topics include discrete and continuous systems and approximation methods. 1960 edition.

Explorations In Complex And Riemannian Geometry

Author : Robert Everist Greene
ISBN : 9780821832738
Genre : Mathematics
File Size : 20. 42 MB
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This book contains contributions by an impressive list of leading mathematicians. The articles include high-level survey and research papers exploring contemporary issues in geometric analysis, differential geometry, and several complex variables. Many of the articles will provide graduate students with a good entry point into important areas of modern research. The material is intended for researchers and graduate students interested in several complex variables and complex geometry.

Physical Theory In Biology

Author : Charles J Lumsden
ISBN : 9789814546331
Genre : Science
File Size : 46. 32 MB
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What is the physics of life and why does it matter? The essays in this book probe this question, celebrating modern biology's vibrant dialog with theoretical physics — a scientific adventure in which biological understanding is enriched by physical theory without losing its own inherent traditions and perspectives. The book explores organic complexity and self-organization through research applications to embryology, cell biology, behavioral neuroscience, and evolution. The essays will excite the interest of physics students in thinking about biology's “grand challenges”, in part by means of self-contained introductions to theoretical computer science, symmetry methods in bifurcation theory, and evolutionary games. Seasoned investigators in both the physical and life sciences will also find challenging ideas and applications presented in this volume. This is a Print On Demand title. We no longer stock the original but will recreate a copy for you. While all efforts are made to ensure that quality is the same as the original, there may be differences in some areas of the design and packaging. Contents:Foundations:Emergence in Physics and Biology (L E H Trainor)Holism and Reduction (C J Lumsden)Complexity: A Pluralistic Approach (W A M Brandts)Dynamics, Complexity and Computation (P A Dufort & C J Lumsden)Development: Field Approaches to Pattern Formation:Vector Field Models of Morphogenesis (W A M Brandts & J Totafurno)Symmetry Breaking Bifurcations (T M Hart & L E H Trainor)Development: Principles of Self-Organization:Generic Dynamics of Morphogenesis (B Goodwin)Toward a Model of Growth and Form in Living Systems (F Cummings)Living Organization, the Coherence of Organisms and the Morphogenetic Field (M W Ho et al.)Is Spatial Pattern Formation Homologous in Unicellular and Multicellular Organisms? (J Frankel)Cellular and Organismic Biology:Statistical Mechanics of the Main Phase Transition in Lipid Bilayers (F P Jones & P Tevlin)Multi-Neuron Interactions in Neural Network Models of Associative Memory (A E Busch & L E H Trainor)Network Hierarchies in Neural Organization, Development and Pathology (J P Sutton)Category Switching — A Neural Network Approach (L E H Trainor et al.)Evolution:A Model of Molecular Evolution Based on the Statistical Analysis of Nucleotide Sequences (L Luo)Codon Space: Exploring the Origins and Development of the Genetic Code (L E H Trainor et al.)Evolution of Development: The Shuffling of Ancient Modules by Ubiquitous Bureaucracies (E W Larsen)Game Theory in Biology (G W A Rowe) Readership: Physicial scientists, biologists, engineers, applied mathematicians and philosophers. keywords:Holism and Reductionism;Complexity;Symmetry;Emergent Property;Patterns;Neural Interactions;Statistical Models;Game Theory;Biology;Morphogenesis;Morphogens;Pattern Formation;Development;Epithelia Folding;Biological Modeling;Complexity;Physical Theory;Biological Regulation;Pattern Formation;Nonlinear Dynamics;Evolution;Developmental Field;Neural Networks;Collective Behavior;Genetic Code;Emergence;Reductionism;Holism;Self-Organization;Bifurcation Theory;Morphogenetic Field;Regeneration;Phase Transitions in Bilayers;Task Switching;Nucleotide Sequences;Molecular Evolution “The important issue here is not what physics theory has done for biology (which is not very much), but what it can do in the future, and to this end the book does a marvellous job of defining the arena.” Nature “… the scope of the articles is broad … The book should be of interest to scientists coming from biological, physical and mathematical sciences.”Bulletin for Mathematical Biology

Computer Algebra Recipes For Mathematical Physics

Author : Richard H. Enns
ISBN : 0817632239
Genre : Mathematics
File Size : 37. 46 MB
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"Hundreds of novel and innovative computer algebra ""recipes"" will enable readers starting at the third year undergraduate level to easily and rapidly solve and explore most problems they encounter in their mathematical physics studies. While the aim is not to try to teach the fundamentals of the subject, the recipes are organized to correlate with topics found in traditional mathematical physics texts. The recipes are presented in the form of stories and anecdotes, a pedagogical approach that makes a mathematically challenging subject easier and more fun to learn. A good working knowledge of ODEs is a prerequisite."

Explorations In Quantum Computing

Author : Colin P. Williams
ISBN : 1846288878
Genre : Computers
File Size : 76. 14 MB
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By the year 2020, the basic memory components of a computer will be the size of individual atoms. At such scales, the current theory of computation will become invalid. "Quantum computing" is reinventing the foundations of computer science and information theory in a way that is consistent with quantum physics - the most accurate model of reality currently known. Remarkably, this theory predicts that quantum computers can perform certain tasks breathtakingly faster than classical computers – and, better yet, can accomplish mind-boggling feats such as teleporting information, breaking supposedly "unbreakable" codes, generating true random numbers, and communicating with messages that betray the presence of eavesdropping. This widely anticipated second edition of Explorations in Quantum Computing explains these burgeoning developments in simple terms, and describes the key technological hurdles that must be overcome to make quantum computers a reality. This easy-to-read, time-tested, and comprehensive textbook provides a fresh perspective on the capabilities of quantum computers, and supplies readers with the tools necessary to make their own foray into this exciting field. Topics and features: concludes each chapter with exercises and a summary of the material covered; provides an introduction to the basic mathematical formalism of quantum computing, and the quantum effects that can be harnessed for non-classical computation; discusses the concepts of quantum gates, entangling power, quantum circuits, quantum Fourier, wavelet, and cosine transforms, and quantum universality, computability, and complexity; examines the potential applications of quantum computers in areas such as search, code-breaking, solving NP-Complete problems, quantum simulation, quantum chemistry, and mathematics; investigates the uses of quantum information, including quantum teleportation, superdense coding, quantum data compression, quantum cloning, quantum negation, and quantum cryptography; reviews the advancements made towards practical quantum computers, covering developments in quantum error correction and avoidance, and alternative models of quantum computation. This text/reference is ideal for anyone wishing to learn more about this incredible, perhaps "ultimate," computer revolution. Dr. Colin P. Williams is Program Manager for Advanced Computing Paradigms at the NASA Jet Propulsion Laboratory, California Institute of Technology, and CEO of Xtreme Energetics, Inc. an advanced solar energy company. Dr. Williams has taught quantum computing and quantum information theory as an acting Associate Professor of Computer Science at Stanford University. He has spent over a decade inspiring and leading high technology teams and building business relationships with and Silicon Valley companies. Today his interests include terrestrial and Space-based power generation, quantum computing, cognitive computing, computational material design, visualization, artificial intelligence, evolutionary computing, and remote olfaction. He was formerly a Research Scientist at Xerox PARC and a Research Assistant to Prof. Stephen W. Hawking, Cambridge University.

Analysis And Mathematical Physics

Author : Bjorn Gustafsson
ISBN : 3764399066
Genre : Mathematics
File Size : 22. 36 MB
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Our knowledge of objects of complex and potential analysis has been enhanced recently by ideas and constructions of theoretical and mathematical physics, such as quantum field theory, nonlinear hydrodynamics, material science. These are some of the themes of this refereed collection of papers, which grew out of the first conference of the European Science Foundation Networking Programme 'Harmonic and Complex Analysis and Applications' held in Norway 2007.

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