The main objective of this book is to give a broad uni?ed introduction to the study of dimension and recurrence inhyperbolic dynamics. It includes a disc- sion of the foundations, main results, and main techniques in the rich interplay of fourmain areas of research: hyperbolic dynamics, dimension theory, multifractal analysis, and quantitative recurrence. It also gives a panorama of several selected topics of current research interest. This includes topics on irregular sets, var- tional principles, applications to number theory, measures of maximal dimension, multifractal rigidity, and quantitative recurrence. The book isdirected to researchersas well as graduate students whowish to have a global view of the theory together with a working knowledgeof its main techniques. It can also be used as a basis for graduatecourses in dimension theory of dynamical systems, multifractal analysis (together with a discussion of several special topics), and pointwise dimension and recurrence in hyperbolic dynamics. I hope that the book may serve as a fast entry point to this exciting and active ?eld of research, and also that it may lead to further developments.

This book is a systematic introduction to smooth ergodic theory. The topics discussed include the general (abstract) theory of Lyapunov exponents and its applications to the stability theory of differential equations, stable manifold theory, absolute continuity, and the ergodic theory of dynamical systems with nonzero Lyapunov exponents (including geodesic flows). The authors consider several nontrivial examples of dynamical systems with nonzero Lyapunov exponents to illustrate some basic methods and ideas of the theory. This book is self-contained. The reader needs a basic knowledge of real analysis, measure theory, differential equations, and topology. The authors present basic concepts of smooth ergodic theory and provide complete proofs of the main results. They also state some more advanced results to give readers a broader view of smooth ergodic theory. This volume may be used by those nonexperts who wish to become familiar with the field.

This textbook provides a comprehensive introduction to the qualitative theory of ordinary differential equations. It includes a discussion of the existence and uniqueness of solutions, phase portraits, linear equations, stability theory, hyperbolicity and equations in the plane. The emphasis is primarily on results and methods that allow one to analyze qualitative properties of the solutions without solving the equations explicitly. The text includes numerous examples that illustrate in detail the new concepts and results as well as exercises at the end of each chapter. The book is also intended to serve as a bridge to important topics that are often left out of a course on ordinary differential equations. In particular, it provides brief introductions to bifurcation theory, center manifolds, normal forms and Hamiltonian systems.

The theory of dynamical systems is a broad and active research subject with connections to most parts of mathematics. Dynamical Systems: An Introduction undertakes the difficult task to provide a self-contained and compact introduction.

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.

This text provides an accessible, self-contained and rigorous introduction to complex analysis and differential equations. Topics covered include holomorphic functions, Fourier series, ordinary and partial differential equations.

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.

This book is a systematic introduction to smooth ergodic theory. The topics discussed include the general (abstract) theory of Lyapunov exponents and its applications to the stability theory of differential equations, stable manifold theory, absolute continuity, and the ergodic theory of dynamical systems with nonzero Lyapunov exponents (including geodesic flows). The authors consider several nontrivial examples of dynamical systems with nonzero Lyapunov exponents to illustrate some basic methods and ideas of the theory. This book is self-contained. The reader needs a basic knowledge of real analysis, measure theory, differential equations, and topology. The authors present basic concepts of smooth ergodic theory and provide complete proofs of the main results. They also state some more advanced results to give readers a broader view of smooth ergodic theory. This volume may be used by those nonexperts who wish to become familiar with the field.

The dimension theory of dynamical systems has progressively developed, especially over the last two decades, into an independent and extremely active field of research. Its main aim is to study the complexity of sets and measures that are invariant under the dynamics. In particular, it is essential to characterizing chaotic strange attractors. To date, some parts of the theory have either only been outlined, because they can be reduced to the case of maps, or are too technical for a wider audience. In this respect, the present monograph is intended to provide a comprehensive guide. Moreover, the text is self-contained and with the exception of some basic results in Chapters 3 and 4, all the results in the book include detailed proofs.

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.

This book is the first comprehensive introduction to smooth ergodic theory. It consists of two parts: the first introduces the core of the theory and the second discusses more advanced topics. In particular, the book describes the general theory of Lyapun

Over the last two decades, the dimension theory of dynamical systems has progressively developed into an independent and extremely active field of research. The main aim of this volume is to offer a unified, self-contained introduction to the interplay of these three main areas of research: ergodic theory, hyperbolic dynamics, and dimension theory. It starts with the basic notions of the first two topics and ends with a sufficiently high-level introduction to the third. Furthermore, it includes an introduction to the thermodynamic formalism, which is an important tool in dimension theory.

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.

Many colleges and universities require students to take at least one math course, and Calculus I is often the chosen option. Calculus Essentials For Dummies provides explanations of key concepts for students who may have taken calculus in high school and want to review the most important concepts as they gear up for a faster-paced college course. Free of review and ramp-up material, Calculus Essentials For Dummies sticks to the point with content focused on key topics only. It provides discrete explanations of critical concepts taught in a typical two-semester high school calculus class or a college level Calculus I course, from limits and differentiation to integration and infinite series. This guide is also a perfect reference for parents who need to review critical calculus concepts as they help high school students with homework assignments, as well as for adult learners headed back into the classroom who just need a refresher of the core concepts.

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String theory says we live in a ten-dimensional universe, but that only four are accessible to our everyday senses. According to theorists, the missing six are curled up in bizarre structures known as Calabi-Yau manifolds. In The Shape of Inner Space, Shing-Tung Yau, the man who mathematically proved that these manifolds exist, argues that not only is geometry fundamental to string theory, it is also fundamental to the very nature of our universe.

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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1,370 fully solved problems Complete review of all course fundamentals Clear, concise explanations of all Advanced Calculus concepts

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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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This classroom-tested volume offers a definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. Upper-level undergraduate students with a background in calculus will benefit from its teachings, along with beginning graduate students seeking a firm grounding in modern analysis.
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.

Practice makes perfect—and helps deepen your understanding of calculus

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.

Master pre-calculus from the comfort of home!

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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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!

Numerical analysis is a subject of extreme interest to mathematicians and computer scientists, who will welcome this first inexpensive paperback edition of a groundbreaking classic text on the subject. In an introductory chapter on numerical methods and their relevance to computing, well-known mathematician Richard Hamming ("the Hamming code," "the Hamming distance," and "Hamming window," etc.), suggests that the purpose of computing is insight, not merely numbers. In that connection he outlines five main ideas that aim at producing meaningful numbers that will be read and used, but will also lead to greater understanding of how the choice of a particular formula or algorithm influences not only the computing but our understanding of the results obtained.
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.

Praise for the Second Edition:

"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.

All macroscopic systems consist ultimately of atoms obeying the laws of quantum mechanics. That premise forms the basis for this comprehensive text, intended for a first upper-level course in statistical and thermal physics. Reif emphasizes that the combination of microscopic concepts with some statistical postulates leads readily to conclusions on a purely macroscopic level. The authors writing style and penchant for description energize interest in condensed matter physics as well as provide a conceptual grounding with information that is crystal clear and memorable.

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.

Master calculus from the comfort of home!

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!

This book offers a full account of thermodynamic systems in chemical engineering. It provides a solid understanding of the basic concepts of the laws of thermodynamics as well as their applications with a thorough discussion of phase and chemical reaction equilibria.

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.

key Features

 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.

Atmospheric Science, Second Edition, is the long-awaited update of the classic atmospheric science text, which helped define the field nearly 30 years ago and has served as the cornerstone for most university curricula. Now students and professionals alike can use this updated classic to understand atmospheric phenomena in the context of the latest discoveries, and prepare themselves for more advanced study and real-life problem solving.

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

Written in a cookbook style, this book offers solutions using a recipe based approach. Each recipe contains step-by-step instructions followed by an analysis of what was done in each task and other useful information. The cookbook approach means you can dive into whatever recipes you want in no particular order. The CryENGINE3 Cookbook is written to be accessible to all developers currently using the CryENGINE3. It also explores the depth and power of the CryENGINE3 and is a useful guide to follow when becoming familiar with this award winning middle-ware game engine. This book is written with the casual and professional developer in mind. Fundamental knowledge of some Digital Content Creation Tools, like Photoshop and 3d Studio Max is required. The Software Development Kit version of the CryENGINE is used for all examples, so the reader should have a version of the development kit to follow the recipes contained in this book.

HVAC Water Chillers and Cooling Towers: Fundamentals, Application, and Operation, Second Edition explores the major improvements in recent years to many chiller and cooling tower components that have resulted in improved performance and lower operating costs. This new edition looks at how climate change and "green" designs have significantly impacted the selection of refrigerants and the application of chilled water systems. It also discusses the expanded use of digital controls and variable frequency drives as well as the re-introduction of some older technologies, especially ammonia-based absorption cooling.

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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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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Fundamentals of Engineering Thermodynamics by Moran, Shapiro, Boettner and Bailey continues its tradition of setting the standard for teaching students how to be effective problem solvers. Now in its eighth edition, this market-leading text emphasizes the authors’ collective teaching expertise as well as the signature methodologies that have taught entire generations of engineers worldwide.    

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.

Nuclear power has, in recent years, undergone a major transformation, resulting in major technical developments and a new generation of nuclear scientists and engineers. A comprehensive book that reflects the latest nuclear technologies has been lacking—until now.

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.

For over three decades, this best-selling classic has been used by thousands of students in the United States and abroad as a must-have textbook for a transitional course from calculus to analysis. It has proven to be very useful for mathematics majors who have no previous experience with rigorous proofs. Its friendly style unlocks the mystery of writing proofs, while carefully examining the theoretical basis for calculus. Proofs are given in full, and the large number of well-chosen examples and exercises range from routine to challenging.

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."

—MATHEMATICAL REVIEWS

Designed for students familiar with abstract mathematical concepts but possessing little knowledge of physics, this text focuses on generality and careful formulation rather than problem-solving. Its author, a member of the distinguished National Academy of Science, based this graduate-level text on the course he taught at Harvard University.
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.

In recent years, with the introduction of new media products, there has been a shift in the use of programming languages from FORTRAN or C to MATLAB for implementing numerical methods. This book makes use of the powerful MATLAB software to avoid complex derivations, and to teach the fundamental concepts using the software to solve practical problems. Over the years, many textbooks have been written on the subject of numerical methods. Based on their course experience, the authors use a more practical approach and link every method to real engineering and/or science problems. The main benefit is that engineers don't have to know the mathematical theory in order to apply the numerical methods for solving their real-life problems.

An Instructor's Manual presenting detailed solutions to all the problems in the book is available online.

Gregory's Classical Mechanics is a major new textbook for undergraduates in mathematics and physics. It is a thorough, self-contained and highly readable account of a subject many students find difficult. The author's clear and systematic style promotes a good understanding of the subject: each concept is motivated and illustrated by worked examples, while problem sets provide plenty of practice for understanding and technique. Computer assisted problems, some suitable for projects, are also included. The book is structured to make learning the subject easy; there is a natural progression from core topics to more advanced ones and hard topics are treated with particular care. A theme of the book is the importance of conservation principles. These appear first in vectorial mechanics where they are proved and applied to problem solving. They reappear in analytical mechanics, where they are shown to be related to symmetries of the Lagrangian, culminating in Noether's theorem.

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In the late 1950s, many of the more refined aspects of Fourier analysis were transferred from their original settings (the unit circle, the integers, the real line) to arbitrary locally compact abelian (LCA) groups. Rudin's book, published in 1962, was the first to give a systematic account of these developments and has come to be regarded as a classic in the field. The basic facts concerning Fourier analysis and the structure of LCA groups are proved in the opening chapters, in order to make the treatment relatively self-contained.

HVAC Water Chillers and Cooling Towers provides fundamental principles and practical techniques for the design, application, purchase, operation, and maintenance of water chillers and cooling towers. Written by a leading expert in the field, the book analyzes topics such as piping, water treatment, noise control, electrical service, and energy efficiency for optimal system and equipment performance and offers extensive checklists, troubleshooting strategies, and reference data, as well as recommended specifications for the procurement of new or replacement equipment. This reference also discusses proper installation and placement of chillers and cooling towers, start-up, and capacity.

Though thermodynamics is a tool used in all sciences and technologies, this book is especially designed to acquaint science students with the whole breadth of the subject covering both equilibrium and non-equilibrium regions. Equilibrium thermodynamics covered in the first-seven chapters caters to the needs of students up to the B.Sc./B.Sc. (Hons.) level. The next three chapters devoted to non-equilibrium thermodynamics and network thermodynamics fulfill the needs of the syllabi on these topics introduced in most universities at the postgraduate level. Chapters on ‘The Question of Ideality’ and ‘The Non-linear Region’ were the new additions to the second edition. In the third edition a new chapter on “Causality Principle in Non-equilibrium Thermodynamics” has been added. The readers may find the new chapter intellectually stimulating. The book is an accessible, straightforward discussion of basic topics, beginning with the laws of thermodynamics and focusing on derivations of basic relations. The text is suitably illustrated throughout with examples of various applications of interest to science students. It explains concepts systematically, teaches problem-solving meaningfully, and includes concept-elucidating questions that are intended to reinforce the student’s understanding of the material.

From the reviews of the second edition:

"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.

Modern Engineering Thermodynamics - Textbook with Tables Booklet offers a problem-solving approach to basic and applied engineering thermodynamics, with historical vignettes, critical thinking boxes and case studies throughout to help relate abstract concepts to actual engineering applications. It also contains applications to modern engineering issues.

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 purpose of a first course in calculus is to teach the student the basic notions of derivative and integral, and the basic techniques and applica tions which accompany them. The very talented students, with an ob vious aptitude for mathematics, will rapidly require a course in functions of one real variable, more or less as it is understood by professional is not primarily addressed to them (although mathematicians. This book I hope they will be able to acquire from it a good introduction at an early age). I have not written this course in the style I would use for an advanced monograph, on sophisticated topics. One writes an advanced monograph for oneself, because one wants to give permanent form to one's vision of some beautiful part of mathematics, not otherwise ac cessible, somewhat in the manner of a composer setting down his sym phony in musical notation. This book is written for the students to give them an immediate, and pleasant, access to the subject. I hope that I have struck a proper com promise, between dwelling too much on special details and not giving enough technical exercises, necessary to acquire the desired familiarity with the subject. In any case, certain routine habits of sophisticated mathematicians are unsuitable for a first course. Rigor. This does not mean that so-called rigor has to be abandoned.

This incisive text deftly combines both theory and practical example to introduce and explore Fourier series and orthogonal functions and applications of the Fourier method to the solution of boundary-value problems. Directed to advanced undergraduate and graduate students in mathematics as well as in physics and engineering, the book requires no prior knowledge of partial differential equations or advanced vector analysis. Students familiar with partial derivatives, multiple integrals, vectors, and elementary differential equations will find the text both accessible and challenging.
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.

The goal of this text is to help students learn to use calculus intelligently for solving a wide variety of mathematical and physical problems. This book is an outgrowth of our teaching of calculus at Berkeley, and the present edition incorporates many improvements based on our use of the first edition. We list below some of the key features of the book. Examples and Exercises The exercise sets have been carefully constructed to be of maximum use to the students. With few exceptions we adhere to the following policies. • The section exercises are graded into three consecutive groups: (a) The first exercises are routine, modelled almost exactly on the exam ples; these are intended to give students confidence. (b) Next come exercises that are still based directly on the examples and text but which may have variations of wording or which combine different ideas; these are intended to train students to think for themselves. (c) The last exercises in each set are difficult. These are marked with a star (*) and some will challenge even the best students. Difficult does not necessarily mean theoretical; often a starred problem is an interesting application that requires insight into what calculus is really about. • The exercises come in groups of two and often four similar ones.

The classic introduction to the fundamentals of calculus

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.

Tough Test Questions? Missed Lectures? Not Enough Time?

Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills.

This Schaum's Outline gives you:

Practice problems with full explanations that reinforce knowledge Coverage of the most up-to-date developments in your course field In-depth review of practices and applications

Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time-and get your best test scores!

Schaum's Outlines-Problem Solved.

This is the dramatic and inspirational first-person story of theoretical physicist, Dr. Ronald Mallett, who recently discovered the basic equations for a working time machine that he believes can be used as a transport vehicle to the past. Combining elements of Rocket Boys and Elegant Universe, Time Traveler follows Mallett's discovery of Einstein's work on space-time, his study of Godel's work on a solution of Einstein's equation that might allow for time travel, and his own research in theoretical physics spanning thirty years that culminated in his recent discovery of the effects of circulating laser light and its application to time travel. The foundation for Mallett's historic time-travel work is Einstein's theory of general relativity, a sound platform for any physicist. Through his years of reading and studying Einstein, Mallett became a buff well before he had any notion of the importance of the grand old relativist's theories to his own career. One interesting subtext to the story is Mallett's identification with, and keen interest in, Einstein. Mallett provides easy-to-understand explanations of the famous physicist's seminal work.

Covering basic theory, components, installation, maintenance, manufacturing, regulation and industry developments, Gas Turbines: A Handbook of Air, Sea and Land Applications is a broad-based introductory reference designed to give you the knowledge needed to succeed in the gas turbine industry, land, sea and air applications.

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.

Due to the rapid expansion of the frontiers of physics and engineering, the demand for higher-level mathematics is increasing yearly. This book is designed to provide accessible knowledge of higher-level mathematics demanded in contemporary physics and engineering. Rigorous mathematical structures of important subjects in these fields are fully covered, which will be helpful for readers to become acquainted with certain abstract mathematical concepts. The selected topics are:

- 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.

The principal aim of this book is to give an introduction to harmonic analysis and the theory of unitary representations of Lie groups. The second edition has been brought up to date with a number of textual changes in each of the five chapters, a new appendix on Fatou's theorem has been added in connection with the limits of discrete series, and the bibliography has been tripled in length.

In-depth, textbook-style coverage combined with an intuitive, low-math approach makes this book particularly appealing to the wireless and networking markets New to this edition: Global wireless services, including 3G; Antenna Options; Error Coding

An in-depth look at real analysis and its applications-now expanded and revised.

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.

The Latest Methods for Preventing and Controlling Corrosion in All Types of Materials and Applications

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

In this third volume of his modern introduction to quantum field theory, Eberhard Zeidler examines the mathematical and physical aspects of gauge theory as a principle tool for describing the four fundamental forces which act in the universe: gravitative, electromagnetic, weak interaction and strong interaction.

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).

Thermodynamics in Materials Science, Second Edition is a clear presentation of how thermodynamic data is used to predict the behavior of a wide range of materials, a crucial component in the decision-making process for many materials science and engineering applications. This primary textbook accentuates the integration of principles, strategies, and thermochemical data to generate accurate “maps” of equilibrium states, such as phase diagrams, predominance diagrams, and Pourbaix corrosion diagrams. It also recommends which maps are best suited for specific real-world scenarios and thermodynamic problems.

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.

A coherent introduction to the techniques for modeling dynamic stochastic systems, this volume also offers a guide to the mathematical, numerical, and simulation tools of systems analysis. Suitable for advanced undergraduates and graduate-level industrial engineers and management science majors, it proposes modeling systems in terms of their simulation, regardless of whether simulation is employed for analysis.
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.

Includes sections on the spectral resolution and spectral representation of self adjoint operators, invariant subspaces, strongly continuous one-parameter semigroups, the index of operators, the trace formula of Lidskii, the Fredholm determinant, and more.
* 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.

This book presents a comprehensive overview of the sum rule approach to spectral analysis of orthogonal polynomials, which derives from Gábor Szego's classic 1915 theorem and its 1920 extension. Barry Simon emphasizes necessary and sufficient conditions, and provides mathematical background that until now has been available only in journals. Topics include background from the theory of meromorphic functions on hyperelliptic surfaces and the study of covering maps of the Riemann sphere with a finite number of slits removed. This allows for the first book-length treatment of orthogonal polynomials for measures supported on a finite number of intervals on the real line.

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.

What a journey writing this text has been. The lengthy voyage started well before the idea hatched of authoring a text that contained the word “thermodynamics”! I was informed by my good friend and sometimes colleague Dr. Jose Antonio that by including that word in the title, nutritionists and exercise physiologists might avoid the subject. But almost every step of my expedition was taken on a rather solid foundation of thermodynamics and as such the topic could not possibly be omitted from the title or the text of a book about bioenergetics and energy expenditure. I am not a physicist. In fact I ?rst went to college to become a football coach. That vocational choice began to deteriorate when taking the mandatory anatomy and physiology courses required of all physical education majors. This information was exciting; my interest in physical education began to wane. During sophomore year, I answered an advertisement in the school newspaper requesting research subjects.

This monograph deals with the quantitative overconvergence phenomenon in complex approximation by various operators. The book is divided into three chapters. First, the results for the Schurer-Faber operator, Beta operators of first kind, Bernstein-Durrmeyer-type operators and Lorentz operator are presented. The main focus is on results for several q-Bernstein kind of operators with q > 1, when the geometric order of approximation 1/qn is obtained not only in complex compact disks but also in quaternion compact disks and in other compact subsets of the complex plane. The focus then shifts to quantitative overconvergence and convolution overconvergence results for the complex potentials generated by the Beta and Gamma Euler's functions. Finally quantitative overconvergence results for the most classical orthogonal expansions (of Chebyshev, Legendre, Hermite, Laguerre and Gegenbauer kinds) attached to vector-valued functions are presented. Each chapter concludes with a notes and open problems section, thus providing stimulation for further research. An extensive bibliography and index complete the text.

This book is suitable for researchers and graduate students working in complex approximation and its applications, mathematical analysis and numerical analysis.

Princeton University's Elias Stein was the first mathematician to see the profound interconnections that tie classical Fourier analysis to several complex variables and representation theory. His fundamental contributions include the Kunze-Stein phenomenon, the construction of new representations, the Stein interpolation theorem, the idea of a restriction theorem for the Fourier transform, and the theory of Hp Spaces in several variables. Through his great discoveries, through books that have set the highest standard for mathematical exposition, and through his influence on his many collaborators and students, Stein has changed mathematics. Drawing inspiration from Stein’s contributions to harmonic analysis and related topics, this volume gathers papers from internationally renowned mathematicians, many of whom have been Stein’s students. The book also includes expository papers on Stein’s work and its influence.

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.

Expanded and revised to cover developments in the field over the past 17 years, and now reprinted to correct errors in the prior printing, Phase Transformation in Metals and Alloys, Third Edition provides information and examples that better illustrate the engineering relevance of this topic. It supplies a comprehensive overview of specific types of phase transformations, supplemented by practical case studies of engineering alloys.

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

This is a collection of exercises in the theory of analytic functions, with completed and detailed solutions. We wish to introduce the student to applications and aspects of the theory of analytic functions not always touched upon in a first course. Using appropriate exercises we wish to show to the students some aspects of what lies beyond a first course in complex variables. We also discuss topics of interest for electrical engineering students (for instance, the realization of rational functions and its connections to the theory of linear systems and state space representations of such systems). Examples of important Hilbert spaces of analytic functions (in particular the Hardy space and the Fock space) are given. The book also includes a part where relevant facts from topology, functional analysis and Lebesgue integration are reviewed.

The second part of the book concludes with Plancherel’s theorem in Chapter 8. This theorem is a generalization of the completeness of the Fourier series, as well as of Plancherel’s theorem for the real line. The third part of the book is intended to provide the reader with a ?rst impression of the world of non-commutative harmonic analysis. Chapter 9 introduces methods that are used in the analysis of matrix groups, such as the theory of the exponential series and Lie algebras. These methods are then applied in Chapter 10 to arrive at a clas- ?cation of the representations of the group SU(2). In Chapter 11 we give the Peter-Weyl theorem, which generalizes the completeness of the Fourier series in the context of compact non-commutative groups and gives a decomposition of the regular representation as a direct sum of irreducibles. The theory of non-compact non-commutative groups is represented by the example of the Heisenberg group in Chapter 12. The regular representation in general decomposes as a direct integral rather than a direct sum. For the Heisenberg group this decomposition is given explicitly. Acknowledgements: I thank Robert Burckel and Alexander Schmidt for their most useful comments on this book. I also thank Moshe Adrian, Mark Pavey, Jose Carlos Santos, and Masamichi Takesaki for pointing out errors in the ?rst edition. Exeter, June 2004 Anton Deitmar LEITFADEN vii Leitfaden 1 2 3 5 4 6

The purpose of this textbook is to present an array of topics in Calculus, and conceptually follow our previous effort Mathematical Analysis I.The present material is partly found, in fact, in the syllabus of the typical second lecture course in Calculus as offered in most Italian universities. While the subject matter known as `Calculus 1' is more or less standard, and concerns real functions of real variables, the topics of a course on `Calculus 2'can vary a lot, resulting in a bigger flexibility. For these reasons the Authors tried to cover a wide range of subjects, not forgetting that the number of credits the current programme specifications confers to a second Calculus course is not comparable to the amount of content gathered here. The reminders disseminated in the text make the chapters more independent from one another, allowing the reader to jump back and forth, and thus enhancing the versatility of the book. On the website: http://calvino.polito.it/canuto-tabacco/analisi 2, the interested reader may find the rigorous explanation of the results that are merely stated without proof in the book, together with useful additional material. The Authors have completely omitted the proofs whose technical aspects prevail over the fundamental notions and ideas. The large number of exercises gathered according to the main topics at the end of each chapter should help the student put his improvements to the test. The solution to all exercises is provided, and very often the procedure for solving is outlined.