Topics covered include topological, low-dimensional, hyperbolic and symbolic dynamics, as well as a brief introduction to ergodic theory. In particular, the authors consider topological recurrence, topological entropy, homeomorphisms and diffeomorphisms of the circle, Sharkovski's ordering, the Poincaré-Bendixson theory, and the construction of stable manifolds, as well as an introduction to geodesic flows and the study of hyperbolicity (the latter is often absent in a first introduction). Moreover, the authors introduce the basics of symbolic dynamics, the construction of symbolic codings, invariant measures, Poincaré's recurrence theorem and Birkhoff's ergodic theorem.
The exposition is mathematically rigorous, concise and direct: all statements (except for some results from other areas) are proven. At the same time, the text illustrates the theory with many examples and 140 exercises of variable levels of difficulty. The only prerequisites are a background in linear algebra, analysis and elementary topology.
This is a textbook primarily designed for a one-semester or two-semesters course at the advanced undergraduate or beginning graduate levels. It can also be used for self-study and as a starting point for more advanced topics.
The text is divided into two parts: part one focuses on complex analysis and part two on differential equations. Each part can be read independently, so in essence this text offers two books in one. In the second part of the book, some emphasis is given to the application of complex analysis to differential equations. Half of the book consists of approximately 200 worked out problems, carefully prepared for each part of theory, plus 200 exercises of variable levels of difficulty.
Tailored to any course giving the first introduction to complex analysis or differential equations, this text assumes only a basic knowledge of linear algebra and differential and integral calculus. Moreover, the large number of examples, worked out problems and exercises makes this the ideal book for independent study.
The book is intended for researchers and graduate students specializing in dynamical systems who wish to have a sufficiently comprehensive view of the theory together with a working knowledge of its main techniques. The discussion of some open problems is also included in the hope that it may lead to further developments. Ideally, readers should have some familiarity with the basic notions and results of ergodic theory and hyperbolic dynamics at the level of an introductory course in the area, though the initial chapters also review all the necessary material.
The volume is primarily intended for graduate students interested in dynamical systems, as well as researchers in other areas who wish to learn about ergodic theory, thermodynamic formalism, or dimension theory of hyperbolic dynamics at an intermediate level in a sufficiently detailed manner. In particular, it can be used as a basis for graduate courses on any of these three subjects. The text can also be used for self-study: it is self-contained, and with the exception of some well-known basic facts from other areas, all statements include detailed proofs.
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Time and again, where Yau has gone, physics has followed. Now for the first time, readers will follow Yau’s penetrating thinking on where we’ve been, and where mathematics will take us next. A fascinating exploration of a world we are only just beginning to grasp, The Shape of Inner Space will change the way we consider the universe on both its grandest and smallest scales.
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Topics include: Numbers; Sequences; Functions, Limits, and Continuity; Derivatives; Integrals; Partial Derivatives; Vectors; Applications of Partial Derivatives; Multiple Integrals; Line Integrals, Surface Integrals, and Integral Theorems; Infinite Series; Improper Integrals; Fourier Series; Fourier Integrals; Gamma and Beta Functions; and Functions of a Complex Variable
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A self-contained text, it presents the necessary background on the limit concept, and the first seven chapters could constitute a one-semester introduction to limits. Subsequent chapters discuss differential calculus of the real line, the Riemann-Stieltjes integral, sequences and series of functions, transcendental functions, inner product spaces and Fourier series, normed linear spaces and the Riesz representation theorem, and the Lebesgue integral. Supplementary materials include an appendix on vector spaces and more than 750 exercises of varying degrees of difficulty. Hints and solutions to selected exercises, indicated by an asterisk, appear at the back of the book.
1001 Calculus Practice Problems For Dummies takes you beyond the instruction and guidance offered in Calculus For Dummies, giving you 1001 opportunities to practice solving problems from the major topics in your calculus course. Plus, an online component provides you with a collection of calculus problems presented in multiple-choice format to further help you test your skills as you go.Gives you a chance to practice and reinforce the skills you learn in your calculus course Helps you refine your understanding of calculus Practice problems with answer explanations that detail every step of every problem
The practice problems in 1001 Calculus Practice Problems For Dummies range in areas of difficulty and style, providing you with the practice help you need to score high at exam time.
Want to "know it ALL" when it comes to pre-calculus? This book gives you the expert, one-on-one instruction you need, whether you're new to pre-calculus or you're looking to ramp up your skills. Providing easy-to-understand concepts and thoroughly explained exercises, math whiz Stan Gibilisco serves as your own private tutor--without the expense! His clear, friendly guidance helps you tackle the concepts and problems that confuse you the most and work through them at your own pace.
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Pre-Calculus Know-It-ALL features:Checkpoints to help you track your knowledge and skill level Problem/solution pairs and chapter-ending quizzes to reinforce learning Fully explained answers to all practice exercises A multiple-choice exam to prepare you for standardized tests "Extra Credit" and "Challenge" problems to stretch your mind
Stan's expert guidance gives you the know-how to:Calculate distance in Cartesian two-and three-space Perform vector multiplication Work with cylindrical and spherical coordinates Understand relations and functions Learn the properties of conic sections Graph exponential, logarithmic, and trigonometric curves Define curves with parametric equations Work with sequences, series, and limits Take college entrance examinations with confidence And much more!
The five main ideas involve (1) insuring that in computing there is an intimate connection between the source of the problem and the usability of the answers (2) avoiding isolated formulas and algorithms in favor of a systematic study of alternate ways of doing the problem (3) avoidance of roundoff (4) overcoming the problem of truncation error (5) insuring the stability of a feedback system.
In this second edition, Professor Hamming (Naval Postgraduate School, Monterey, California) extensively rearranged, rewrote and enlarged the material. Moreover, this book is unique in its emphasis on the frequency approach and its use in the solution of problems. Contents include:
I. Fundamentals and Algorithms
II. Polynomial Approximation- Classical Theory
Ill. Fourier Approximation- Modern Theory
IV. Exponential Approximation ... and more
Highly regarded by experts in the field, this is a book with unlimited applications for undergraduate and graduate students of mathematics, science and engineering. Professionals and researchers will find it a valuable reference they will turn to again and again.
"This is quite a well-done book: very tightly organized, better-than-average exposition, and numerous examples, illustrations, and applications."
—Mathematical Reviews of the American Mathematical Society
An Introduction to Linear Programming and Game Theory, Third Edition presents a rigorous, yet accessible, introduction to the theoretical concepts and computational techniques of linear programming and game theory. Now with more extensive modeling exercises and detailed integer programming examples, this book uniquely illustrates how mathematics can be used in real-world applications in the social, life, and managerial sciences, providing readers with the opportunity to develop and apply their analytical abilities when solving realistic problems.
This Third Edition addresses various new topics and improvements in the field of mathematical programming, and it also presents two software programs, LP Assistant and the Solver add-in for Microsoft Office Excel, for solving linear programming problems. LP Assistant, developed by coauthor Gerard Keough, allows readers to perform the basic steps of the algorithms provided in the book and is freely available via the book's related Web site. The use of the sensitivity analysis report and integer programming algorithm from the Solver add-in for Microsoft Office Excel is introduced so readers can solve the book's linear and integer programming problems. A detailed appendix contains instructions for the use of both applications.
Additional features of the Third Edition include:A discussion of sensitivity analysis for the two-variable problem, along with new examples demonstrating integer programming, non-linear programming, and make vs. buy models
Revised proofs and a discussion on the relevance and solution of the dual problem
A section on developing an example in Data Envelopment Analysis
An outline of the proof of John Nash's theorem on the existence of equilibrium strategy pairs for non-cooperative, non-zero-sum games
Providing a complete mathematical development of all presented concepts and examples, Introduction to Linear Programming and Game Theory, Third Edition is an ideal text for linear programming and mathematical modeling courses at the upper-undergraduate and graduate levels. It also serves as a valuable reference for professionals who use game theory in business, economics, and management science.
Reif first introduces basic probability concepts and statistical methods used throughout all of physics. Statistical ideas are then applied to systems of particles in equilibrium to enhance an understanding of the basic notions of statistical mechanics, from which derive the purely macroscopic general statements of thermodynamics. Next, he turns to the more complicated equilibrium situations, such as phase transformations and quantum gases, before discussing nonequilibrium situations in which he treats transport theory and dilute gases at varying levels of sophistication. In the last chapter, he addresses some general questions involving irreversible processes and fluctuations.
A large amount of material is presented to facilitate students later access to more advanced works, to allow those with higher levels of curiosity to read beyond the minimum given on a topic, and to enhance understanding by presenting several ways of looking at a particular question. Formatting within the text either signals material that instructors can assign at their own discretion or highlights important results for easy reference to them. Additionally, by solving many of the 230 problems contained in the text, students activate and embed their knowledge of the subject matter.
Want to "know it ALL" when it comes to calculus? This book gives you the expert, one-on-one instruction you need, whether you're new to calculus or you're looking to ramp up your skills. Providing easy-to-understand concepts and thoroughly explained exercises, math whiz Stan Gibilisco serves as your own private tutor--without the expense! His clear, friendly guidance helps you tackle the concepts and problems that confuse you the most and work through them at your own pace.
Train your brain with ease! Calculus Know-It-ALL features:Checkpoints to help you track your knowledge and skill level Problem/solution pairs and chapter-ending quizzes to reinforce learning Fully explained answers to all practice exercises A multiple-choice exam to prepare you for standardized tests "Extra Credit" and "Challenge" problems to stretch your mind
Stan's expert guidance gives you the know-how to:Understand mappings, relations, and functions Calculate limits and determine continuity Differentiate and integrate functions Analyze graphs using first and second derivatives Define and evaluate inverse functions Use specialized integration techniques Determine arc lengths, surface areas, and solid volumes Work with multivariable functions Take college entrance examinations with confidence And much more!
At the outset the text explains the various key terms of thermodynamics with suitable examples and then thoroughly deals with the virial and cubic equations of state by showing the P-V-T (pressure, molar volume and temperature) relation of fluids. It elaborates on the first and second laws of thermodynamics and their applications with the help of numerous engineering examples. The text further discusses the concepts of exergy, standard property changes of chemical reactions, thermodynamic property relations and fugacity. The book also includes detailed discussions on residual and excess properties of mixtures, various activity coefficient models, local composition models, and group contribution methods. In addition, the text focuses on vapour-liquid and other phase equilibrium calculations, and analyzes chemical reaction equilibria and adiabatic reaction temperature for systems with complete and incomplete conversion of reactants.
Includes a large number of fully worked-out examples to help students master the concepts discussed.
Provides well-graded problems with answers at the end of each chapter to test and foster students’ conceptual understanding of the subject. The total number of solved examples and end-chapter exercises in the book are over 600.
Contains chapter summaries that review the major concepts covered.
The book is primarily designed for the undergraduate students of chemical engineering and its related disciplines such as petroleum engineering and polymer engineering. It can also be useful to professionals.
The Solution Manual containing the complete worked-out solutions to chapter-end exercises and problems is available for instructors.
This latest edition of Atmospheric Science, has been revamped in terms of content and appearance. It contains new chapters on atmospheric chemistry, the Earth system, the atmospheric boundary layer, and climate, as well as enhanced treatment of atmospheric dynamics, radiative transfer, severe storms, and global warming. The authors illustrate concepts with full-color, state-of-the-art imagery and cover a vast amount of new information in the field. Extensive numerical and qualitative exercises help students apply basic physical principles to atmospheric problems. There are also biographical footnotes summarizing the work of key scientists, along with a student companion website that hosts climate data; answers to quantitative exercises; full solutions to selected exercises; skew-T log p chart; related links, appendices; and more. The instructor website features: instructor’s guide; solutions to quantitative exercises; electronic figures from the book; plus supplementary images for use in classroom presentations.
Meteorology students at both advanced undergraduate and graduate levels will find this book extremely useful.Full-color satellite imagery and cloud photographs illustrate principles throughoutExtensive numerical and qualitative exercises emphasize the application of basic physical principles to problems in the atmospheric sciencesBiographical footnotes summarize the lives and work of scientists mentioned in the text, and provide students with a sense of the long history of meteorologyCompanion website encourages more advanced exploration of text topics: supplementary information, images, and bonus exercises
The first half of the book focuses on water chillers and the second half addresses cooling towers. In both sections, the author includes the following material:
Fundamentals—basic information about systems and equipment, including how they and their various components work Design and Application—equipment sizing, selection, and application; details of piping, control, and water treatment; and special considerations such as noise control, electrical service, fire protection, and energy efficiency Operations and Maintenance—commissioning and programmed maintenance of components and systems, with guidelines and recommended specifications for procurement
This up-to-date book provides HVAC designers, building owners, operating and maintenance staff, architects, and mechanical contractors with definitive and practical guidance on the application, design, purchase, operation, and maintenance of water chillers and cooling towers. It offers helpful information for you to use on a daily basis, including checklists and troubleshooting guidelines.
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Knowledge flow provides learning book of Engineering Thermodynamics. This book is for all engineering students and professionals across the world. Thermodynamics deals with heat and temperature and also their relation with work and energy. This book of thermodynamics describes Carnot engine cycle, entropy and laws of thermodynamics that partly describe a body of matter or radiation.
1. Thermodynamic System and Control Volume
2. Zeroth law of Thermodynamics
3. First law of Thermodynamics
4. Thermodynamic processes
5. Second law of Thermodynamics
6. Entropy and Third Law of Thermodynamics
7. Working Fluids in Thermodynamics
8. Carnot Engine Cycle
9. Refrigeration Cycle
10. Vapour Compression and Absorption System
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Integrated throughout the text are real-world applications that emphasize the relevance of thermodynamics principles to some of the most critical problems and issues of today, including a wealth of coverage of topics related to energy and the environment, biomedical/bioengineering, and emerging technologies.
The Nuclear Engineering Handbook is a response to this global resurgence of interest in commercial nuclear power. A broad overview of nuclear power and engineering and their limitless potential, this basic introduction to the field provides an in-depth discussion of power plants and extensive coverage of the nuclear fuel cycle, waste disposal, and related engineering technologies.
Organized into three sections—Nuclear Power Reactors, Nuclear Fuel Cycle Processes and Facilities, and Engineering and Analytical Applications—this book addresses the entire nuclear fuel cycle and process. Topics include everything from the mining, milling, and enrichment of uranium and thorium fuel resources, to fuel fabrication, nuclear materials transportation, fuel reprocessing, and safe waste disposal. This all-encompassing volume discusses current analytical techniques related to nuclear engineering, addressing safety, heat transfer, shielding, thermo-hydraulics, and heat physics. Covering reactor operation and radiation protection, it also outlines the economic considerations involved in building new nuclear power stations instead of large fossil-fueled plants, and elaborates on concerns regarding the control of emissions from the latter.
A review of past and current nuclear engineering capabilities, this valuable resource covers the gamut of crucial topics, including historical perspectives, a detailed technological review, and an assessment of the field’s future direction. It is an exceptional tool that will help readers to foster optimal understanding and use of nuclear power for electricity generation now and in the future.
The second edition preserves the book’s clear and concise style, illuminating discussions, and simple, well-motivated proofs. New topics include material on the irrationality of pi, the Baire category theorem, Newton's method and the secant method, and continuous nowhere-differentiable functions.
Review from the first edition:
"This book is intended for the student who has a good, but naïve, understanding of elementary calculus and now wishes to gain a thorough understanding of a few basic concepts in analysis.... The author has tried to write in an informal but precise style, stressing motivation and methods of proof, and ... has succeeded admirably."
Opening chapters on classical mechanics examine the laws of particle mechanics; generalized coordinates and differentiable manifolds; oscillations, waves, and Hilbert space; and statistical mechanics. A survey of quantum mechanics covers the old quantum theory; the quantum-mechanical substitute for phase space; quantum dynamics and the Schrödinger equation; the canonical "quantization" of a classical system; some elementary examples and original discoveries by Schrödinger and Heisenberg; generalized coordinates; linear systems and the quantization of the electromagnetic field; and quantum-statistical mechanics.
The final section on group theory and quantum mechanics of the atom explores basic notions in the theory of group representations; perturbations and the group theoretical classification of eigenvalues; spherical symmetry and spin; and the n-electron atom and the Pauli exclusion principle.
An Instructor's Manual presenting detailed solutions to all the problems in the book is available online.
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"This book covers many interesting topics not usually covered in a present day undergraduate course, as well as certain basic topics such as the development of the calculus and the solution of polynomial equations. The fact that the topics are introduced in their historical contexts will enable students to better appreciate and understand the mathematical ideas involved...If one constructs a list of topics central to a history course, then they would closely resemble those chosen here."
(David Parrott, Australian Mathematical Society)
"The book...is presented in a lively style without unnecessary detail. It is very stimulating and will be appreciated not only by students. Much attention is paid to problems and to the development of mathematics before the end of the nineteenth century... This book brings to the non-specialist interested in mathematics many interesting results. It can be recommended for seminars and will be enjoyed by the broad mathematical community."
(European Mathematical Society)
"Since Stillwell treats many topics, most mathematicians will learn a lot from this book as well as they will find pleasant and rather clear expositions of custom materials. The book is accessible to students that have already experienced calculus, algebra and geometry and will give them a good account of how the different branches of mathematics interact."
(Denis Bonheure, Bulletin of the Belgian Society)
This third edition includes new chapters on simple groups and combinatorics, and new sections on several topics, including the Poincare conjecture. The book has also been enriched by added exercises.
This textbook is designed for use in a standard two-semester engineering thermodynamics course sequence, with the goal of helping students develop engineering problem solving skills through the use of structured problem-solving techniques. The first half of the text contains material suitable for a basic Thermodynamics course taken by engineers from all majors. The second half of the text is suitable for an Applied Thermodynamics course in mechanical engineering programs. The Second Law of Thermodynamics is introduced through a basic entropy concept, providing students a more intuitive understanding of this key course topic. Property Values are discussed before the First Law of Thermodynamics to ensure students have a firm understanding of property data before using them. Over 200 worked examples and more than 1,300 end of chapter problems provide an extensive opportunity to practice solving problems. For greater instructor flexibility at exam time, thermodynamic tables are provided in a separate accompanying booklet.
University students in mechanical, chemical, and general engineering taking a thermodynamics course will find this book extremely helpful.Provides the reader with clear presentations of the fundamental principles of basic and applied engineering thermodynamics.Helps students develop engineering problem solving skills through the use of structured problem-solving techniques.Introduces the Second Law of Thermodynamics through a basic entropy concept, providing students a more intuitive understanding of this key course topic.Covers Property Values before the First Law of Thermodynamics to ensure students have a firm understanding of property data before using them.Over 200 worked examples and more than 1,300 end of chapter problems offer students extensive opportunity to practice solving problems.Historical Vignettes, Critical Thinking boxes and Case Studies throughout the book help relate abstract concepts to actual engineering applications. For greater instructor flexibility at exam time, thermodynamic tables are provided in a separate accompanying booklet.
The first three chapters of the book address linear spaces, orthogonal functions, and the Fourier series. Chapter 4 introduces Legendre polynomials and Bessel functions, and Chapter 5 takes up heat and temperature. The concluding Chapter 6 explores waves and vibrations and harmonic analysis. Several topics not usually found in undergraduate texts are included, among them summability theory, generalized functions, and spherical harmonics.
Throughout the text are 570 exercises devised to encourage students to review what has been read and to apply the theory to specific problems. Those preparing for further study in functional analysis, abstract harmonic analysis, and quantum mechanics will find this book especially valuable for the rigorous preparation it provides. Professional engineers, physicists, and mathematicians seeking to extend their mathematical horizons will find it an invaluable reference as well.
Richard Courant's classic text Differential and Integral Calculus is an essential text for those preparing for a career in physics or applied math. Volume 1 introduces the foundational concepts of "function" and "limit", and offers detailed explanations that illustrate the "why" as well as the "how". Comprehensive coverage of the basics of integrals and differentials includes their applications as well as clearly-defined techniques and essential theorems. Multiple appendices provide supplementary explanation and author notes, as well as solutions and hints for all in-text problems.
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Providing the big picture view that other detailed, data-focused resources lack, this book has a strong focus on the information needed to effectively decision-make and plan gas turbine system use for particular applications, taking into consideration not only operational requirements but long-term life-cycle costs in upkeep, repair and future use.
With concise, easily digestible overviews of all important theoretical bases and a practical focus throughout, Gas Turbines is an ideal handbook for those new to the field or in the early stages of their career, as well as more experienced engineers looking for a reliable, one-stop reference that covers the breadth of the field.Covers installation, maintenance, manufacturer's specifications, performance criteria and future trends, offering a rounded view of the area that takes in technical detail as well as well as industry economics and outlookUpdated with the latest industry developments, including new emission and efficiency regulations and their impact on gas turbine technology Over 300 pages of new/revised content, including new sections on microturbines, non-conventional fuel sources for microturbines, emissions, major developments in aircraft engines, use of coal gas and superheated steam, and new case histories throughout highlighting component improvements in all systems and sub-systems.
- Real analysis, Complex analysis, Functional analysis, Lebesgue integration theory, Fourier analysis, Laplace analysis, Wavelet analysis, Differential equations, and Tensor analysis.
This book is essentially self-contained, and assumes only standard undergraduate preparation such as elementary calculus and linear algebra. It is thus well suited for graduate students in physics and engineering who are interested in theoretical backgrounds of their own fields. Further, it will also be useful for mathematics students who want to understand how certain abstract concepts in mathematics are applied in a practical situation. The readers will not only acquire basic knowledge toward higher-level mathematics, but also imbibe mathematical skills necessary for contemporary studies of their own fields.
This new edition of the widely used analysis book continues to cover real analysis in greater detail and at a more advanced level than most books on the subject. Encompassing several subjects that underlie much of modern analysis, the book focuses on measure and integration theory, point set topology, and the basics of functional analysis. It illustrates the use of the general theories and introduces readers to other branches of analysis such as Fourier analysis, distribution theory, and probability theory.
This edition is bolstered in content as well as in scope-extending its usefulness to students outside of pure analysis as well as those interested in dynamical systems. The numerous exercises, extensive bibliography, and review chapter on sets and metric spaces make Real Analysis: Modern Techniques and Their Applications, Second Edition invaluable for students in graduate-level analysis courses. New features include:
* Revised material on the n-dimensional Lebesgue integral.
* An improved proof of Tychonoff's theorem.
* Expanded material on Fourier analysis.
* A newly written chapter devoted to distributions and differential equations.
* Updated material on Hausdorff dimension and fractal dimension.
Now you can turn to Corrosion Engineering for expert coverage of the theory and current practices you need to understand water, atmospheric, and high-temperature corrosion processes. This comprehensive resource explains step-by-step how to prevent and control corrosion in all types of metallic materials and applications-from steel and aluminum structures to pipelines.
Filled with 300 illustrations, this skills-building guide shows you how to utilize advanced inspection and monitoring methods for corrosion problems in infrastructure, process and food industries, manufacturing, and military industries. Authoritative and complete, Corrosion Engineering features:Expert guidance on corrosion prevention and control techniques Hands-on methods for inspection and monitoring of corrosion problems New methods for dealing with corrosion A review of current practice, with numerous examples and calculations
Inside This Cutting-Edge Guide to Corrosion Prevention and Control• Introduction: Scope and Language of Corrosion • Electrochemistry of Corrosion • Environments: Atmospheric Corrosion • Corrosion by Water and Steam • Corrosion in Soils • Reinforced Concrete • High-Temperature Corrosion • Materials and How They Corrode: Engineering Materials • Forms of Corrosion • Methods of Control: Protective Coatings • Cathodic Protection • Corrosion Inhibitors • Failure Analysis and Design Considerations • Testing and Monitoring: Corrosion Testing and Monitoring
Volume III concentrates on the classical aspects of gauge theory, describing the four fundamental forces by the curvature of appropriate fiber bundles. This must be supplemented by the crucial, but elusive quantization procedure.
The book is arranged in four sections, devoted to realizing the universal principle force equals curvature:
Part I: The Euclidean Manifold as a Paradigm
Part II: Ariadne's Thread in Gauge Theory
Part III: Einstein's Theory of Special Relativity
Part IV: Ariadne's Thread in Cohomology
For students of mathematics the book is designed to demonstrate that detailed knowledge of the physical background helps to reveal interesting interrelationships among diverse mathematical topics. Physics students will be exposed to a fairly advanced mathematics, beyond the level covered in the typical physics curriculum.
Quantum Field Theory builds a bridge between mathematicians and physicists, based on challenging questions about the fundamental forces in the universe (macrocosmos), and in the world of elementary particles (microcosmos).
The second edition yet. Each chapter presents its subject matter consistently, based on the classification of thermodynamic systems, properties, and derivations that illustrate important relationships among variables for finding the conditions for equilibrium. Each chapter also contains a summary of important concepts and relationships as well as examples and sample problems that apply appropriate strategies for solving real-world problems.
The up-to-date and complete coverage ofthermodynamic data, laws, definitions, strategies, and tools in Thermodynamics in Materials Science, Second Edition provides students and practicing engineers a valuable guide for producing and applying maps of equilibrium states to everyday applications in materials sciences.
Beginning with a view of the conditions that permit a mathematical-numerical analysis, the text explores Poisson and renewal processes, Markov chains in discrete and continuous time, semi-Markov processes, and queuing processes. Each chapter opens with an illustrative case study, and comprehensive presentations include formulation of models, determination of parameters, analysis, and interpretation of results. Programming language–independent algorithms appear for all simulation and numerical procedures.
* Assumes prior knowledge of Naive set theory, linear algebra, point set topology, basic complex variable, and real variables.
* Includes an appendix on the Riesz representation theorem.
In addition to the Szego and Killip-Simon theorems for orthogonal polynomials on the unit circle (OPUC) and orthogonal polynomials on the real line (OPRL), Simon covers Toda lattices, the moment problem, and Jacobi operators on the Bethe lattice. Recent work on applications of universality of the CD kernel to obtain detailed asymptotics on the fine structure of the zeros is also included. The book places special emphasis on OPRL, which makes it the essential companion volume to the author's earlier books on OPUC.
This book is suitable for researchers and graduate students working in complex approximation and its applications, mathematical analysis and numerical analysis.
The contributors are Jean Bourgain, Luis Caffarelli, Michael Christ, Guy David, Charles Fefferman, Alexandru D. Ionescu, David Jerison, Carlos Kenig, Sergiu Klainerman, Loredana Lanzani, Sanghyuk Lee, Lionel Levine, Akos Magyar, Detlef Müller, Camil Muscalu, Alexander Nagel, D. H. Phong, Malabika Pramanik, Andrew S. Raich, Fulvio Ricci, Keith M. Rogers, Andreas Seeger, Scott Sheffield, Luis Silvestre, Christopher D. Sogge, Jacob Sturm, Terence Tao, Christoph Thiele, Stephen Wainger, and Steven Zelditch.
New in the Third Edition:
Computer-aided calculation of phase diagrams Recent developments in metallic glasses The Scheil method of calculating a CCT diagram from a TTT diagram Expanded treatment of the nucleation and growth of polygonal ferrite and bainite New case studies covering copper precipitation hardening of very low carbon bainitic steel and very fine carbide-free bainite Detailed treatment of strain-induced martensite provides a theoretical background to transformation-induced plasticity (TRIP) steels
Unique Presentation Links Theory to Application
Adding new case studies, detailed examples, and exercises drawn from current applications, the third edition keeps the previous editions’ popular easy-to -follow style and excellent mix of basic and advanced information, making it ideal for those new to the field. The book’s unique presentation links basic understanding of theory with application in a gradually progressive yet exciting manner. Based on the author’s teaching notes, the book takes a pedagogical approach and provides examples for applications and problems that can be readily used for exercises.
PowerPoint© illustrations available with qualifying course adoptions