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A unique feature of the book is its emphasis on applications. These include mechanical vibrations, lasers, biological rhythms, superconducting circuits, insect outbreaks, chemical oscillators, genetic control systems, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with mathematical theory.

In the twenty years since the first edition of this book appeared, the ideas and techniques of nonlinear dynamics and chaos have found application to such exciting new fields as systems biology, evolutionary game theory, and sociophysics. This second edition includes new exercises on these cutting-edge developments, on topics as varied as the curiosities of visual perception and the tumultuous love dynamics in Gone With the Wind.

If you ever regretted not taking physics in college--or simply want to know how to think like a physicist--this is the book for you. In this bestselling introduction, physicist Leonard Susskind and hacker-scientist George Hrabovsky offer a first course in physics and associated math for the ardent amateur. Challenging, lucid, and concise, The Theoretical Minimum provides a tool kit for amateur scientists to learn physics at their own pace.

The Essentials For Dummies Series

Dummies is proud to present our new series, The Essentials For Dummies. Now students who are prepping for exams, preparing to study new material, or who just need a refresher can have a concise, easy-to-understand review guide that covers an entire course by concentrating solely on the most important concepts. From algebra and chemistry to grammar and Spanish, our expert authors focus on the skills students most need to succeed in a subject.

Math textbooks can be as baffling as the subject they're teaching. Not anymore. The best-selling author of The Complete Idiot's Guide® to Calculus has taken what appears to be a typical calculus workbook, chock full of solved calculus problems, and made legible notes in the margins, adding missing steps and simplifying solutions. Finally, everything is made perfectly clear. Students will be prepared to solve those obscure problems that were never discussed in class but always seem to find their way onto exams.

--Includes 1,000 problems with comprehensive solutions

--Annotated notes throughout the text clarify what's being asked in each problem and fill in missing steps

--Kelley is a former award-winning calculus teacher

Fortunately for you, there's Schaum's.

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

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

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

Schaum's Outlines--Problem Solved.

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 problemThe 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.

Train your brain with ease!

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 mindStan'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!In Pursuit of the Traveling Salesman travels to the very threshold of our understanding about the nature of complexity, and challenges you yourself to discover the solution to this captivating mathematical problem.

Some images inside the book are unavailable due to digital copyright restrictions.

Now updated with 30% new material, Roark Formulas for Stress and Strain, Seventh Edition, is the ultimate resource for designers, engineers, and analysts who need to calculate loads and stress. This landmark reference from Warren Young and Richard Budynas provides you with equations and diagrams of structural properties in an easy-to-use, thumb-through format. Updated, with a user-friendly page layout, this new edition includes expanded coverage of joints, bearing and shear stress, experimental stress analysis, and stress concentrations, as well as material behavior coverage and stress and strain measurement. You’ll also find expanded tables and cases; improved notations and figures in the tables; consistent table and equation numbering; and verification of correction factors.

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 mindStan'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!The first part explores functions of one variable, including numbers and sequences, continuous functions, differentiable functions, integration, and sequences and series of functions. The second part examines functions of several variables: the space of several variables and continuous functions, differentiation, multiple integrals, and line and surface integrals, concluding with a selection of related topics. Complete solutions to the problems appear at the end of the text.

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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

Drawing on physics and mechanical engineering, Steven Vogel looks at how animals swim and fly, modes of terrestrial locomotion, organism responses to winds and water currents, circulatory and suspension-feeding systems, and the relationship between size and mechanical design. He also investigates links between the properties of biological materials--such as spider silk, jellyfish jelly, and muscle--and their structural and functional roles. Early chapters and appendices introduce relevant physical variables for quantification, and problem sets are provided at the end of each chapter. Comparative Biomechanics is useful for physical scientists and engineers seeking a guide to state-of-the-art biomechanics. For a wider audience, the textbook establishes the basic biological context for applied areas--including ergonomics, orthopedics, mechanical prosthetics, kinesiology, sports medicine, and biomimetics--and provides materials for exhibit designers at science museums.

Problem sets at the ends of chapters Appendices cover basic background information Updated and expanded documentation and materials Revised figures and text Increased coverage of friction, viscoelastic materials, surface tension, diverse modes of locomotion, and biomimeticsBut while the importance of the calculus and mathematical analysis ― the core of modern mathematics ― cannot be overemphasized, the value of this first comprehensive critical history of the calculus goes far beyond the subject matter. This book will fully counteract the impression of laymen, and of many mathematicians, that the great achievements of mathematics were formulated from the beginning in final form. It will give readers a sense of mathematics not as a technique, but as a habit of mind, and serve to bridge the gap between the sciences and the humanities. It will also make abundantly clear the modern understanding of mathematics by showing in detail how the concepts of the calculus gradually changed from the Greek view of the reality and immanence of mathematics to the revised concept of mathematical rigor developed by the great 19th century mathematicians, which held that any premises were valid so long as they were consistent with one another. It will make clear the ideas contributed by Zeno, Plato, Pythagoras, Eudoxus, the Arabic and Scholastic mathematicians, Newton, Leibnitz, Taylor, Descartes, Euler, Lagrange, Cantor, Weierstrass, and many others in the long passage from the Greek "method of exhaustion" and Zeno's paradoxes to the modern concept of the limit independent of sense experience; and illuminate not only the methods of mathematical discovery, but the foundations of mathematical thought as well.

All of the material in this user-friendly study guide has been proven to get results. The book arose from Adrian Banner's popular calculus review course at Princeton University, which he developed especially for students who are motivated to earn A's but get only average grades on exams. The complete course will be available for free on the Web in a series of videotaped lectures. This study guide works as a supplement to any single-variable calculus course or textbook. Coupled with a selection of exercises, the book can also be used as a textbook in its own right. The style is informal, non-intimidating, and even entertaining, without sacrificing comprehensiveness. The author elaborates standard course material with scores of detailed examples that treat the reader to an "inner monologue"--the train of thought students should be following in order to solve the problem--providing the necessary reasoning as well as the solution. The book's emphasis is on building problem-solving skills. Examples range from easy to difficult and illustrate the in-depth presentation of theory.

The Calculus Lifesaver combines ease of use and readability with the depth of content and mathematical rigor of the best calculus textbooks. It is an indispensable volume for any student seeking to master calculus.

Serves as a companion to any single-variable calculus textbook Informal, entertaining, and not intimidating Informative videos that follow the book--a full forty-eight hours of Banner's Princeton calculus-review course--is available at Adrian Banner lectures More than 475 examples (ranging from easy to hard) provide step-by-step reasoning Theorems and methods justified and connections made to actual practice Difficult topics such as improper integrals and infinite series covered in detail Tried and tested by students taking freshman calculusHelps Students Better Understand Numerical Methods through Use of MATLAB®

The authors uniquely emphasize both theoretical numerical analysis and practical implementation of the algorithms in MATLAB, making the book useful for students in computational science and engineering. They provide students with simple, clear implementations instead of sophisticated usages of MATLAB functions.

All the Material Needed for a Numerical Analysis Course

Based on the authors’ own courses, the text only requires some knowledge of computer programming, advanced calculus, and difference equations. It includes practical examples, exercises, references, and problems, along with a solutions manual for qualifying instructors. Students can download MATLAB code from www.crcpress.com, enabling them to easily modify or improve the codes to solve their own problems.

Tensor Calculus contains eight chapters. The first four deal with the basic concepts of tensors, Riemannian spaces, Riemannian curvature, and spaces of constant curvature. The next three chapters are concerned with applications to classical dynamics, hydrodynamics, elasticity, electromagnetic radiation, and the theorems of Stokes and Green. In the final chapter, an introduction is given to non-Riemannian spaces including such subjects as affine, Weyl, and projective spaces. There are two appendixes which discuss the reduction of a quadratic form and multiple integration. At the conclusion of each chapter a summary of the most important formulas and a set of exercises are given. More exercises are scattered throughout the text. The special and general theory of relativity is briefly discussed where applicable.

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It will help you cut study time, hone problem-solving skills, and achieve your personal best on exams!

Students love Schaum's Solved Problem Guides because they produce results. Each year, thousands of students improve their test scores and final grades with these indispensable guides. Get the edge on your classmates. Use Schaum's!

If you don't have a lot of time but want to excel in class, use this book to:

Brush up before tests Study quickly and more effectively Learn the best strategies for solving tough problems in step-by-step detail Review what you've learned in class by solving thousands of relevant problems that test your skillCompatible with any classroom text, Schaum's Solved Problem Guides let you practice at your own pace and remind you of all the important problem-solving techniques you need to remember--fast! And Schaum's are so complete, they're perfect for preparing for graduate or professional exams.

Inside you will find:

2,000 solved problems with complete solutions--the largest selection of solved problems yet published on this subject An index to help you quickly locate the types of problems you want to solve Problems like those you'll find on your exams Techniques for choosing the correct approach to problems Guidance toward the quickest, most efficient solutionsIf you want top grades and thorough understanding of discrete mathematics, this powerful study tool is the best tutor you can have!

The most valuable and reader-friendly reference available for engineers concerned with the optimization of liquid transportation through pipelines

About the authors . . .

D. M. PIRRO is the Equipment Builder and OEM Manager, ExxonMobil Corporation, Fairfax, Virginia. The author or contributing editor of several scholarly articles on synthetic lubes, environmental awareness applications, grease technology, lubricant interchangeability, and oil analysis, Mr. Pirro is a Certified Lubrication Specialist and a member of the Society of Tribologists and Lubrication Engineers and the Association of Manufacturing Technology. He received the B.S. degree (1978) in mechanical engineering and the B.A. degree (1978) in business administration from Rutgers University, New Brunswick, New Jersey.

A. A. WESSOL is a part-time Lubrication Consultant for the ExxonMobil Corporation in Manassas, Virginia. Mr. Wessol retired from the Mobil Corporation after 24 years in various advanced technical positions. The author or coauthor of numerous professional papers on the environmental aspects of lubrication, plant engineering, hydraulics, and pneumatics, he received the B.S. degree (1972) in mathematics, physics, and chemistry from the University of Pittsburgh, Pennsylvania.

"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.

"The main object of this book is to dispel the fear of mathematics," declares author W. W. Sawyer, adding that "Many people regard mathematicians as a race apart, possessed of almost supernatural powers. While this is very flattering for successful mathematicians, it is very bad for those who, for one reason or another, are attempting to learn the subject." Now retired, Sawyer won international renown for his innovative teaching methods, which he used at colleges in England and Scotland as well as Africa, New Zealand, and North America. His insights into the pleasures and practicalities of mathematics will appeal to readers of all backgrounds.

The movements of each of the 507 mechanisms are depicted in drawings on the left-hand page, and the facing page presents a brief description of the item's use and operation. Ranging from simple to intricately complex, the mechanisms offer a fascinating view of the variety of small components that constitute complex machinery. A detailed index provides easy reference to specific mechanisms.

Inventors, tinkerers, and anyone with an interest in the history of invention and technology will find this volume a treasury of information and inspiration.

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.

The first five chapters consist of a systematic development of many of the important properties of the real number system, plus detailed treatment of such concepts as mappings, sequences, limits, and continuity. The sixth and final chapter discusses metric spaces and generalizes many of the earlier concepts and results involving arbitrary metric spaces.

An index of axioms and key theorems appears at the end of the book, and more than 300 problems amplify and supplement the material within the text. Geared toward students who have taken several semesters of basic calculus, this volume is an ideal prerequisite for mathematics majors preparing for a two-semester course in advanced calculus.

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 applicationsFully 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.

--Hans Camenzind, inventor of the 555 timer (the world's most successful integrated circuit), and author of Much Ado About Almost Nothing: Man's Encounter with the Electron (Booklocker.com)

"A fabulous book: well written, well paced, fun, and informative. I also love the sense of humor. It's very good at disarming the fear. And it's gorgeous. I'll be recommending this book highly."

--Tom Igoe, author of Physical Computing and Making Things Talk

Want to learn the fundamentals of electronics in a fun, hands-on way? With Make: Electronics, you'll start working on real projects as soon as you crack open the book. Explore all of the key components and essential principles through a series of fascinating experiments. You'll build the circuits first, then learn the theory behind them!

Build working devices, from simple to complex You'll start with the basics and then move on to more complicated projects. Go from switching circuits to integrated circuits, and from simple alarms to programmable microcontrollers. Step-by-step instructions and more than 500 full-color photographs and illustrations will help you use -- and understand -- electronics concepts and techniques.

Discover by breaking things: experiment with components and learn from failure Set up a tricked-out project space: make a work area at home, equipped with the tools and parts you'll need Learn about key electronic components and their functions within a circuit Create an intrusion alarm, holiday lights, wearable electronic jewelry, audio processors, a reflex tester, and a combination lock Build an autonomous robot cart that can sense its environment and avoid obstacles Get clear, easy-to-understand explanations of what you're doing and whyThe normal physical laws like, transport theory, electrodynamics, equation of motions, elasticity, viscosity, and several others of are based on ‘ordinary’ calculus. In this book these physical laws are generalized in fractional calculus contexts; taking, heterogeneity effect in transport background, the space having traps or islands, irregular distribution of charges, non-ideal spring with mass connected to a pointless-mass ball, material behaving with viscous as well as elastic properties, system relaxation with and without memory, physics of random delay in computer network; and several others; mapping the reality of nature closely. The concept of fractional and complex order differentiation and integration are elaborated mathematically, physically and geometrically with examples. The practical utility of local fractional differentiation for enhancing the character of singularity at phase transition or characterizing the irregularity measure of response function is deliberated. Practical results of viscoelastic experiments, fractional order controls experiments, design of fractional controller and practical circuit synthesis for fractional order elements are elaborated in this book. The book also maps theory of classical integer order differential equations to fractional calculus contexts, and deals in details with conflicting and demanding initialization issues, required in classical techniques. The book presents a modern approach to solve the ‘solvable’ system of fractional and other differential equations, linear, non-linear; without perturbation or transformations, but by applying physical principle of action-and-opposite-reaction, giving ‘approximately exact’ series solutions.

Historically, Sir Isaac Newton and Gottfried Wihelm Leibniz independently discovered calculus in the middle of the 17th century. In recognition to this remarkable discovery, J.von Neumann remarked, “...the calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more equivocally than anything else the inception of modern mathematical analysis which is logical development, still constitute the greatest technical advance in exact thinking.”

This XXI century has thus started to ‘think-exactly’ for advancement in science & technology by growing application of fractional calculus, and this century has started speaking the language which nature understands the best.

- 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 analysis of tensors is to investigate those relations which remain valid when we change from one coordinate system to another. This book on Tensors requires only a knowledge of elementary calculus, differential equations and classical mechanics as pre-requisites. It provides the readers with all the information about the tensors along with the derivation of all the tensorial relations/equations in a simple manner. The book also deals in detail with topics of importance to the study of special and general relativity and the geometry of differentiable manifolds with a crystal clear exposition. The concepts dealt within the book are well supported by a number of solved examples. A carefully selected set of unsolved problems is also given at the end of each chapter, and the answers and hints for the solution of these problems are given at the end of the book. The applications of tensors to the fields of differential geometry, relativity, cosmology and electromagnetism is another attraction of the present book.

This book is intended to serve as text for postgraduate students of mathematics, physics and engineering. It is ideally suited for both students and teachers who are engaged in research in General Theory of Relativity and Differential Geometry.

Finite Element Modeling and Simulation with ANSYS Workbench combines finite element theory with real-world practice. Providing an introduction to finite element modeling and analysis for those with no prior experience, and written by authors with a combined experience of 30 years teaching the subject, this text presents FEM formulations integrated with relevant hands-on applications using ANSYS Workbench for finite element analysis (FEA). Incorporating the basic theories of FEA and the use of ANSYS Workbench in the modeling and simulation of engineering problems, the book also establishes the FEM method as a powerful numerical tool in engineering design and analysis.

Include FEA in Your Design and Analysis of Structures Using ANSYS Workbench

The authors reveal the basic concepts in FEA using simple mechanics problems as examples, and provide a clear understanding of FEA principles, element behaviors, and solution procedures. They emphasize correct usage of FEA software, and techniques in FEA modeling and simulation. The material in the book discusses one-dimensional bar and beam elements, two-dimensional plane stress and plane strain elements, plate and shell elements, and three-dimensional solid elements in the analyses of structural stresses, vibrations and dynamics, thermal responses, fluid flows, optimizations, and failures. Contained in 12 chapters, the text introduces ANSYS Workbench through detailed examples and hands-on case studies, and includes homework problems and projects using ANSYS Workbench software that are provided at the end of each chapter.

Covers solid mechanics and thermal/fluid FEA Contains ANSYS Workbench geometry input files for examples and case studies Includes two chapters devoted to modeling and solution techniques, design optimization, fatigue, and buckling failure analysis Provides modeling tips in case studies to provide readers an immediate opportunity to apply the skills they learn in a problem-solving contextFinite Element Modeling and Simulation with ANSYS Workbench benefits upper-level undergraduate students in all engineering disciplines, as well as researchers and practicing engineers who use the finite element method to analyze structures.

Helping you overcome these hurdles, Hydraulic Power System Analysis demonstrates modern computer-aided analytical techniques used to model nonlinear, dynamic fluid power systems. Following an overview of fluid power, the authors examine various relevant fluid properties, energy calculations, and steady state and dynamic analysis along with a review of automatic control theory. Turning to modeling, the next few chapters address valves and motors and then apply dynamic modeling to examples relating to pumps, hydrostatic transmissions, and valves. The book includes a unique chapter showing how to combine flow resistance equations with the differential equations governing dynamic system performance. The final chapter translates electrical circuit theory concepts to noise attenuation in fluid power systems.

Illustrated with many equations, practical computer modeling examples, and exercises, Hydraulic Power System Analysis provides a much-needed modernization of dynamic modeling for fluid power systems using powerful computational tools.

Chapter 1 of this book deals with the extraordinary physico-chemical properties of the water molecule while Chapter 2 provides insight on theories regarding the origin of water on Earth. In the third chapter, the author focuses on the chemical composition of the main water reservoirs of our planet. Chapters 4 and 5 discuss water’s relationship with plate tectonics and life, respectively. The sixth and final chapter uses stable isotope tracking to look into the water cycle and past climates.

Contents

1. Water: A Molecule Endowed with Extraordinary Physicochemical Properties.

2. Theories about the Origin of Water on Earth.

3. The Main Water Reservoirs on Earth and their Chemical Composition.

4. Water and Plate Tectonics.

5. Water and Life.

6. Stable Isotope Tracking: Water Cycles and Climates of the Past.

The presence of water on Earth is discussed on the basis of the various theories about its origin such as a massive degassing of the primitive parent bodies that built our planet as well as a late addition from comets that collided with its surface. The extraordinary physico-chemical properties of the water molecule combined with its abundance and distribution over the Earth’s surface have contributed to regulating the global climate and favoring the evolution of species for more than 4 billion years. The early emergence of life in the deep ocean and its further diversification were closely linked to the global water cycle whose dynamics result from the energy balance between solar radiation and the internal heat flux of the Earth.

The approach begins with sets and functions and advances to Lebesgue measure, including considerations of measurable sets, sets of measure zero, and Borel sets and nonmeasurable sets. A two-part exploration of the integral covers measurable functions, convergence theorems, convergence in mean, Fourier theory, and other topics. A chapter on calculus examines change of variables, differentiation of integrals, and integration of derivatives and by parts. The text concludes with a consideration of more general measures, including absolute continuity and convolution products.

Totally redesigned to meet today's mechanical design challenges, this classic handbook provides a practical overview of the complex principles and data associated with the design and control of dynamic mechanical systems.

New Chapters on continuous control systems, digital control systems, and optical systems Covers power transmission and control subsystems