The presentation stresses analytical methods, concrete examples, and geometric intuition. 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.About the Author:Steven Strogatz is in the Center for Applied Mathematics and the Department of Theoretical and Applied Mathematics at Cornell University. Since receiving his Ph.D. from Harvard university in 1986, Professor Strogatz has been honored with several awards, including the E.M. Baker Award for Excellence, the highest teaching award given by MIT.

    The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. To help students construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. Previous Edition Hb (1994) 0-521-44116-1 Previous Edition Pb (1994) 0-521-44663-5

    This is a new view of mathematics, not the one we learned at school but a comprehensive guide to the patterns that recur through the universe and underlie human affairs. A Beginner's Guide to Constructing, the Universe shows you: Why cans, pizza, and manhole covers are round.Why one and two weren't considered numbers by the ancient Greeks.Why squares show up so often in goddess art and board games.What property makes the spiral the most widespread shape in nature, from embryos and hair curls to hurricanes and galaxies. How the human body shares the design of a bean plant and the solar system. How a snowflake is like Stonehenge, and a beehive like a calendar. How our ten fingers hold the secrets of both a lobster a cathedral, and much more.

    The progressively more difficult puzzles include a double murder.

    . .he believes these ideas to be accessible to the audience he wantsto reach, and he writes so that they are. -- NatureIf you want to encourage anyone's interest in math, get them TheMathematical Universe. * New Scientist

    He was especially careful to present new and unfamiliar puzzles that had not been included in such classic collections as those by Sam Loyd and Henry Dudeney. Later, these puzzles were published in book collections, incorporating reader feedback on alternate solutions or interesting generalizations.The present volume contains a rich selection of 70 of the best of these brain teasers, in some cases including references to new developments related to the puzzle. Now enthusiasts can challenge their solving skills and rattle their egos with such stimulating mind-benders as The Returning Explorer, The Mutilated Chessboard, Scrambled Box Tops, The Fork in the Road, Bronx vs. Brooklyn, Touching Cigarettes, and 64 other problems involving logic and basic math. Solutions are included.

    This book synthesizes these recent advances and makes them accessible to first-year graduate students. James Hamilton provides the first adequate text-book treatments of important innovations such as vector autoregressions, generalized method of moments, the economic and statistical consequences of unit roots, time-varying variances, and nonlinear time series models. In addition, he presents basic tools for analyzing dynamic systems (including linear representations, autocovariance generating functions, spectral analysis, and the Kalman filter) in a way that integrates economic theory with the practical difficulties of analyzing and interpreting real-world data. Time Series Analysis fills an important need for a textbook that integrates economic theory, econometrics, and new results.The book is intended to provide students and researchers with a self-contained survey of time series analysis. It starts from first principles and should be readily accessible to any beginning graduate student, while it is also intended to serve as a reference book for researchers.-- "Journal of Economics"

    This book leads the reader from simple graphs through planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, more. Includes exercises. 1976 edition.

    The book begins with a rapid course on manifolds and differential forms, emphasizing how these provide a proper language for formulating Maxwell's equations on arbitrary spacetimes. The authors then introduce vector bundles, connections and curvature in order to generalize Maxwell theory to the Yang-Mills equations. The relation of gauge theory to the newly discovered knot invariants such as the Jones polynomial is sketched. Riemannian geometry is then introduced in order to describe Einstein's equations of general relativity and show how an attempt to quantize gravity leads to interesting applications of knot theory.

    A sensible and novel solution to the math block that afflicts our society today.

    The most obvious change is the creation of a separate Chapter 7 on convex analysis. Parts of this chapter appeared in elsewhere in the second edition, but much of it is new to the third edition. In particular, there is an expanded discussion of support points of convex sets, and a new section on subgradients of convex functions. There is much more material on the special properties of convex sets and functions in ?nite dimensional spaces. There are improvements and additions in almost every chapter. There is more new material than might seem at ?rst glance, thanks to a change in font that - duced the page count about ?ve percent. We owe a huge debt to Valentina Galvani, Daniela Puzzello, and Francesco Rusticci, who were participants in a graduate seminar at Purdue University and whose suggestions led to many improvements, especially in chapters ?ve through eight. We particularly thank Daniela Puzzello for catching uncountably many errors throughout the second edition, and simplifying the statements of several theorems and proofs. In another graduate seminar at Caltech, many improvements and corrections were suggested by Joel Grus, PJ Healy, Kevin Roust, Maggie Penn, and Bryan Rogers."

    It is of especial interest today as an application of mathematical techniques to problems in social and biological sciences.Generally recognized as the founder of the modern phase of probability theory, Laplace here applies the principles and general results of his theory "to the most important questions of life, which are, in effect, for the most part, problems in probability." Thus, without the use of higher mathematics, he demonstrates the application of probability to games of chance, physics, reliability. of witnesses, astronomy, insurance, democratic government and many other areas.General readers will find it an exhilarating experience to follow Laplace's nontechnical application of mathematical techniques to the appraisal, solution and/or prediction of the outcome of many types of problems. Skilled mathematicians, too, will enjoy and benefit from seeing how one of the immortals of science expressed so many complex ideas in such simple terms.

    For example, guess-and-check is a natural strategy to apply in algebra. Advanced math students often use finite differences to study functions and sequences. And drawing a diagram and using physical representations are commonly employed strategies in many contexts. However, many students never encounter valuable strategies such as matrix logic or unit analysis. And in content-crowded math classes, few students get the concentrated practice or time necessary to fully develop their problem-solving skills. By taking a semester course in problem solving, students can master a multitude of strategies while developing confidence in their problem-solving abilities. Your students will be better prepared to meet the challenges of school and life by taking this course.

    The book includes numerous specific applications, making it beneficial to physicists and engineers. Specific examples and applications show how the theory works, backed by up-to-date techniques, all of which make the text accessible to a wide variety of readers, especially senior undergraduates and graduates in mathematics, physics and engineering. This second edition has been rewritten and updated for clarity throughout, with a major revamping and expansion of the exercises. Internet supplements containing additional material are also available.

    In studying number theory from such a perspective, mathematics majors are spared repetition and provided with new insights, while other students benefit from the consequent simplicity of the proofs for many theorems.Among the topics covered in this accessible, carefully designed introduction are multiplicativity-divisibility, including the fundamental theorem of arithmetic, combinatorial and computational number theory, congruences, arithmetic functions, primitive roots and prime numbers. Later chapters offer lucid treatments of quadratic congruences, additivity (including partition theory) and geometric number theory.Of particular importance in this text is the author's emphasis on the value of numerical examples in number theory and the role of computers in obtaining such examples. Exercises provide opportunities for constructing numerical tables with or without a computer. Students can then derive conjectures from such numerical tables, after which relevant theorems will seem natural and well-motivated..

    The first five chapters deal with abstract measurement and integration. Chapter 6, on differentiation, includes a treatment of changes of variables in Rd.

    It features discussion of punctured convolutional codes; performance analysis of block codes; system implementation issues for the Viterbi Decoder and the various decoders for ReedSolomon and BCH codes; the theory of finite fields; error control for channels with feedback; trellis coded modulation; and historical background and up-to-date applications. This text is intended for use by introductory postgraduate courses in coding for telecommunications engineering, and digital communications.

    Its strengths include a wide range of exercises, both computational and theoretical, plus many nontrivial applications. The first half of the book presents group theory, through the Sylow theorems, with enough material for a semester-long course. The second-half is suitable for a second semester and presents rings, integral domains, Boolean algebras, vector spaces, and fields, concluding with Galois Theory.

    Concentrates on infinite-horizon discrete-time models. Discusses arbitrary state spaces, finite-horizon and continuous-time discrete-state models. Also covers modified policy iteration, multichain models with average reward criterion and sensitive optimality. Features a wealth of figures which illustrate examples and an extensive bibliography.

    The study of knots has led to important applications in DNA research and the synthesis of new molecules, and has had a significant impact on statistical mechanics and quantum field theory. Colin Adams’s The Knot Book is the first book to make cutting-edge research in knot theory accessible to a non-specialist audience. Starting with the simplest knots, Adams guides readers through increasingly more intricate twists and turns of knot theory, exploring problems and theorems mathematicians can now solve, as well as those that remain open. He also explores how knot theory is providing important insights in biology, chemistry, physics, and other fields. The new paperback edition has been updated to include the latest research results, and includes hundreds of illustrations of knots, as well as worked examples, exercises and problems. With a simple piece of string, an elementary mathematical background, and The Knot Book, anyone can start learning about some of the most advanced ideas in contemporary mathematics.

    This adaptation addresses the student's need for more concise and accessible information. Beck has trimmed to book to half its original size, focusing on the functions and topics likely to be encountered by students.

    It is not abstraction for its own sake, but abstraction for the sake of efficiency, power and insight. Algebra emerged from the struggle to solve concrete, physical problems in geometry, and succeeded after 2000 years of failure by other forms of mathematics. It did this by exposing the mathematical structure of geometry, and by providing the tools to analyse it. This is typical of the way algebra is applied; it is the best and purest form of application because it reveals the simplest and most universal mathematical structures. The present book aims to foster a proper appreciation of algebra by showing abstraction at work on concrete problems, the classical problems of construction by straightedge and compass. These problems originated in the time of Euclid, when geometry and number theory were paramount, and were not solved until th the 19 century, with the advent of abstract algebra. As we now know, alge- bra brings about a unification of geometry, number theory and indeed most branches of mathematics. This is not really surprising when one has a historical understanding of the subject, which I also hope to impart.

    Preliminaries 2. Simplest Properties of Functions 3. Basic Elementary Functions 4. Inverse Function. Power, Exponential and Logarithmic Functions 5. Trigonometric and Inverse Trigonometric Functions 6. Computational Problems Chapter II. Limit. Continuity 1. Basic Definitions 2. Infinite Magnitudes. Tests for the Existence of the Limit 3. Continuous Functions 4. Finding Limits. Comparison of Infinitesimals Chapter III. Derivative and Differential. Differential Calculus 1. Derivative. The Rate of Change of a Function 2. Differentiating Functions 3. Differential. Differentiability of a Function 4. The Derivative as the Rate of Change 5. Repeated Differentiation Chapter IV. Investigating Functions and Their Graphs 1. Behavior of a Function 2. Application of the First Derivative 3. Application of the Second Derivative 4. Additional Items. Solving Equations 5. Taylor's Formula and Its Application 6. Curvature 7. Computational Problems Chapter V. The Definite Integral 1. The Definite Integral and Its Simplest Properties 2. Basic Properties of the Definite Integral Chapter VI. Indefinite Integral. Integral Calculus 1. Simplest Integration Rules 2. Basic Methods of Integration 3. Basic Classes of Integrable Functions Chapter VII. Methods for Evaluating Definite Integrals. Improper Integrals 1. Methods for Exact Evaluation of Integrals 2. Approximate Methods 3. Improper Integrals Chapter VIII. Application of Integral Calculus 1. Some Problems in Geometry and statics 2. Some Physics Problems Chapter IX. Series 1. Numerical Series 2. Functional Series 3. Power Series 4. Some Applications of Taylor;s series Chapter X. Functions of Several Variables. Differential Calculus 1. Functions of Several Variables 2. Simplest Properties of Functions 3. Derivatives and Differentials

    In Beginner's Guide to Revelation, Robin Robertson uses his unique skills as a Jungian-oriented therapist to reinterpret this magnificent document as a saga of changing human consciousness. Robertson follows a spiral path around the central issues of our time, drawing from Jung's psychology, neurophysiology, shamanic rituals and modern mathematics. The author reveals how the Book of Revelation express in symbolic language our collective ability to experience within us the spiritual depths of the universe. This exciting new material offers a sensitive journey into the meaning of death, transformation and changing consciousness.

    Sets of observations are represented by matrices, linear combinations are formed from these matrices by multiplying them by coefficient matrices, and useful statistics are found by imposing various criteria of optimization on these combinations. Matrix algebra is the vehicle for these calculations. A second approach is computational. Since many users find that they do not need to know the mathematical basis of the techniques as long as they have a way to transform data into results, the computation can be done by a package of computer programs that somebody else has written. An approach from this perspective emphasizes how the computer packages are used, and is usually coupled with rules that allow one to extract the most important numbers from the output and interpret them. Useful as both approaches are--particularly when combined--they can overlook an important aspect of multivariate analysis. To apply it correctly, one needs a way to conceptualize the multivariate relationships that exist among variables.This book is designed to help the reader develop a way of thinking about multivariate statistics, as well as to understand in a broader and more intuitive sense what the procedures do and how their results are interpreted. Presenting important procedures of multivariate statistical theory geometrically, the author hopes that this emphasis on the geometry will give the reader a coherent picture into which all the multivariate techniques fit.

    The straightforward exposition features many illustrations, and complete proofs for most theorems. With only linear algebra as a prerequisite, it takes the reader quickly from the basics to topics of recent research. The lectures introduce basic facts about polytopes, with an emphasis on methods that yield the results, discuss important examples and elegant constructions, and show the excitement of current work in the field. They will provide interesting and enjoyable reading for researchers as well as students.

    In the past this was necessary, but today's software packages make FE accessible to users who knows nothing to the theory or of how FE works. People are now using FE software packages as black boxes', without knowing the dangers of poor modeling, the need to verify that results are reasonable, or that worthless results can be convincingly displayed. Therefore, it is important to understand the physics of the problem, how elements behave, the assumptions and restrictions of FE implementations, and the need to assess the correctness of computed results.

    Various programming paradigms are explained in a uniform manner, with fully worked out examples that are useful tools in their own right. The floppy disk contains numerous Mathematica notebooks and packages, valuable tools for applying each of the methods discussed.

    This material, formerly unavailable to the Western world, is now accessible in English for the first time.

    It shows what the general picture should look like and provides results that are useful again and again. Despite this, however, there are few, if any introductory texts that present a unified picture of the general abstract theory.A Course in Abstract Harmonic Analysis offers a concise, readable introduction to Fourier analysis on groups and unitary representation theory. After a brief review of the relevant parts of Banach algebra theory and spectral theory, the book proceeds to the basic facts about locally compact groups, Haar measure, and unitary representations, including the Gelfand-Raikov existence theorem. The author devotes two chapters to analysis on Abelian groups and compact groups, then explores induced representations, featuring the imprimitivity theorem and its applications. The book concludes with an informal discussion of some further aspects of the representation theory of non-compact, non-Abelian groups.

    Information-theoretic concepts play a central role in the development of the theory, which provides, in particular, a detailed discussion of the problem of specification of so-called prior ignorance . The work is written from the authors s committed Bayesian perspective, but an overview of non-Bayesian theories is also provided, and each chapter contains a wide-ranging critical re-examination of controversial issues. The level of mathematics used is such that most material is accessible to readers with knowledge of advanced calculus. In particular, no knowledge of abstract measure theory is assumed, and the emphasis throughout is on statistical concepts rather than rigorous mathematics. The book will be an ideal source for all students and researchers in statistics, mathematics, decision analysis, economic and business studies, and all branches of science and engineering, who wish to further their understanding of Bayesian statistics

    

    These articles--both scholarly and sympathetic to the Pythagorean perspective--are proof of the contemporary interest in Pythagoras' philosophy as a living reality and provide a major addition to the field of Pythagorean studies and traditional mathematics. Contents: Introduction by Christopher Bamford"Ancient Temple Architecture" by Robert Lawlor"The Platonic Tradition on the Nature of Proportion" by Keith Critchlow"What is Sacred Architecture? by Keith Critchlow"Twelve Criteria for Sacred Architecture" by Keith Critchlow"Pythagorean Number as Form, Color, and Light" by Robert Lawlor"The Two Lights" by Arthur Zajonc"Apollo: The Pythagorean Definition of God" by Anne Macaulay"Blake, Yeats, and Pythagoras" by Kathleen RaineAbout the AuthorsROBERT LAWLOR is the author of Sacred Geometry; Earth Honoring; and Voices of the First Day. After training as a painter and a sculptor, he became a yoga student of Sri Aurobindo and lived for many years in Pondicherry, India, where he was a founding member of Auroville. In India, he discovered the works of the French Egyptologist and esotericist, R. A. Schwaller de Lubicz, which led him to explore the principles and practices of ancient sacred science.KEITH CRITCHLOW is the author of Order in Space; and Time Stands Still. A painter, Critchlow discovered geometry intuitively. A period of intensive geometric practice and work with Buckminster Fuller led him to recognize that the universal principles of geometry are revealed and confirmed both by the area of design where art and mathematics meet and in the study of nature and ancient and medieval sacred cosmological architecture of temples, cathedrals, and mosques. He has been a senior lecturer at the Architectural Association in London and taught Islamic Art at the Royal College of Art. He has also participated as geometer in various sacred architectural projects, and is a cofounder of Temenos, a journal devoted to the arts and imagination, and Kairos, a society that investigates, studies, and promotes traditional values of art and science.ARTHUR ZAJONC is Professor of Physics at Amherst College, where his research has concerned the nature of light and the experimental foundations of quantum mechanics. He has also taught and written extensively on interdisciplinary aspects of science, the history of science, culture, and spirituality, especially the works of Goethe and Rudolf Steiner. He is the author Catching the Light and The New Physics and Cosmology, featuring dialogues with the Dalai Lama. He has been a visiting scientist at many laboratories and was a Fulbright professor.ANNE MACAULAY lives in Scotland where she has, for many years, studied the origins of the alphabet, the history of the guitar, the figure of Apollo, and other mysteries surrounding Pythagorean thought. She has lectured at Research into Lost Knowledge Organization (RILKO) and was a trustee of the Salisbury Center in Edinburgh.KATHLEEN RAINE was a British poet with an international reputation as a scholar of the imagination. A renowned student of William Blake, a penetrating critic, and a profound autobiographer, she wrote numerous books and articles. Kathleen Raine was a cofounder and the editor of Temenos.

    

    NA

    This book, the proceedings of a workshop held to bring together researchers in knot theory and quantum gravity, features a number of expository and research papers that will aid significantly in closing the gap between the two disciplines. It will serve as a guide for mathematicians and physicists seeking to understand this rapidly developing area of research. The book represents a state-of-the-art study of current research and progress. The editor is the author of Gauge Fields, Knots, and Gravity (World Scientific), a graduate level text on the topic.

    Very well written, '' said one reader of volume 1. The writing is brilliant, positively brilliant.'' A terrific publication, '' said another. This is a wonderful tool for showing people what mathematics is about and what mathematicians can do.'' One reader called it a must for all mathematics department reading and coffee lounges.'' Volume 2 of What's Happening features the same lively writing and all new topics. Here you can read about a new class of solitons, the contributions wavelets are making to solving scientific problems, how mathematics is improving medical imaging, and Andrew Wiles's acclaimed work on Fermat's Last Theorem. What's Happening is great for mathematics undergraduates, graduate students, and mathematics clubs---not to mention mathematics faculty, who will enjoy reading about recent developments in fields other than their own. Highlighting the excitement and wonder of mathematics, What's Happening is in a class by itself.

    Members of these groups came from different traditions, had different perspectives, and rarely gathered in the same place to discuss issues of common interest. Part of the problem was that there was no common ground for the discussions -- given the disparate traditions and perspectives.As one way of addressing this problem, the Sloan Foundation funded two conferences in the mid-1980s, bringing together members of the different communities in a ground clearing effort, designed to establish a base for communication. In those conferences, interdisciplinary teams reviewed major topic areas and put together distillations of what was known about them.*A more recent conference -- upon which this volume is based -- offered a forum in which various people involved in education reform would present their work, and members of the broad communities gathered would comment on it. The focus was primarily on college mathematics, informed by developments in K-12 mathematics. The main issues of the conference were mathematical thinking and problem solving.

    Along with formulating this proposition--xn+yn=zn has no rational solution for n > 2--Fermat, an inventor of analytic geometry, also laid the foundations of differential and integral calculus, established, together with Pascal, the conceptual guidelines of the theory of probability, and created modern number theory. In one of the first full-length investigations of Fermat's life and work, Michael Sean Mahoney provides rare insight into the mathematical genius of a hobbyist who never sought to publish his work, yet who ranked with his contemporaries Pascal and Descartes in shaping the course of modern mathematics.

    Images of Mandelbrot and Julia sets abound in publications both mathematical and not. The mathematics behind the pictures are beautiful in their own right and are the subject of this text. Mathematica programs that illustrate the dynamics are included in an appendix.

    Developed centuries ago, mathematics still speaks to us now. This colorful kit is a collection of pop-ups, pullouts, and interactive graphics that allows everyone -- from those who are nimble with numbers to those who are challenged by them -- to explore the beauty, power, and fun of mathematics. Covering arithmetic, plane geometry, trigonometry, and calculus, it includes graphic representations of the basic numerical functions, fractions, and decimals; a calculator for explaining Cartesian coordinates; 3-D models of the Pythagorean theorem, solid polygons, and trigonometric angles; and games for geometry, probability, and problem solving; plus a complete glossary of terms, punch-out numbers and shapes, and a pair of dice. 9 1/2" x 12".

    Valiant details a promising new computational approach to studying the intricate workings of the human brain. Focusing on the brain's enigmatic ability to access a massive store of accumulated information very quickly during reasoning processes, the author asks how such feats are possible given the extreme constraints imposed by the brain's finite number of neurons, their limited speed of communication, and their restricted interconnectivity. Valiant proposes a neuroidal model that serves as a vehicle to explore these fascinating questions. While embracing the now classic theories of McCulloch and Pitts, the neuroidal model also accommodates state information in the neurons, more flexible timing mechanisms, a variety of assumptions about interconnectivity, and the possibility that different areas perform different functions. Programmable so that a wide range of algorithmic theories can be described and evaluated, the model provides a concrete computational language and a unified framework in which diverse cognitive phenomena--such as memory, learning, and reasoning--can be systematically and concurrently analyzed. Included in this volume is a new preface that highlights some remarkable points of agreement between the neuroidal model and findings in neurobiology made since that model's original publication. Experiments have produced strong evidence for the theory's predictions about the existence of strong synapses in cortex and about the use of precise timing mechanisms within and between neurons. The theory also provides a quantitative explanation of how randomly placed neurons can be harnessed as resources for general purpose learning and memory--and is therefore synergistic with the striking recent discovery of neurogenesis in cortex. Requiring no specialized knowledge, Circuits of the Mind, masterfully offers an exciting new approach to brain science for students and researchers in computer science, neurobiology, neuroscience, artificial intelligence, and cognitive science.

    A comprehensive study aid for the graduate student and beyond.

    Get a firm grip on core concepts and key material, and test your newfound knowledge with review questions.CliffsQuickReview Trigonometry provides you with all you need to know to understand the basic concepts of trigonometry whether you need a supplement to your textbook and classes or an at-a-glance reference. Trigonometry isn't just measuring angles; it has many applications in the real world, such as in navigation, surveying, construction, and many other branches of science, including mathematics and physics. As you work your way through this review, you'll be ready to tackle such concepts asTrigonometric functions, such as sines and cosinesGraphs and trigonometric identitiesVectors, polar coordinates, and complex numbersInverse functions and equationsYou can use CliffsQuickReview Trigonometry in any way that fits your personal style for study and review you decide what works best with your needs. You can read the book from cover to cover or just look for the information you want and put it back on the shelf for later. Here are just a few ways you can search for topics:Use the free Pocket Guide full of essential informationGet a glimpse of what you ll gain from a chapter by reading through the Chapter Check-In at the beginning of each chapterUse the Chapter Checkout at the end of each chapter to gauge your grasp of the important information you need to knowTest your knowledge more completely in the CQR Review and look for additional sources of information in the CQR Resource CenterUse the glossary to find key terms fastWith titles available for all the most popular high school and college courses, CliffsQuickReview guides are a comprehensive resource that can help you get the best possible grades."

    Besides correcting misprints and inaccuracies, the author has added plenty of new material, mostly concrete geometrical material such as Grassmannian varieties, plane cubic curves, the cubic surface, degenerations of quadrics and elliptic curves, the Bertini theorems, and normal surface singularities.

    The author has succeeded in producing a text on nonlinear PDEs that is not only quite readable but also accessible to students from diverse backgrounds." --SIAM ReviewA practical introduction to nonlinear PDEs and their real-world applicationsNow in a Second Edition, this popular book on nonlinear partial differential equations (PDEs) contains expanded coverage on the central topics of applied mathematics in an elementary, highly readable format and is accessible to students and researchers in the field of pure and applied mathematics. This book provides a new focus on the increasing use of mathematical applications in the life sciences, while also addressing key topics such as linear PDEs, first-order nonlinear PDEs, classical and weak solutions, shocks, hyperbolic systems, nonlinear diffusion, and elliptic equations. Unlike comparable books that typically only use formal proofs and theory to demonstrate results, An Introduction to Nonlinear Partial Differential Equations, Second Edition takes a more practical approach to nonlinear PDEs by emphasizing how the results are used, why they are important, and how they are applied to real problems.The intertwining relationship between mathematics and physical phenomena is discovered using detailed examples of applications across various areas such as biology, combustion, traffic flow, heat transfer, fluid mechanics, quantum mechanics, and the chemical reactor theory. New features of the Second Edition also include:Additional intermediate-level exercises that facilitate the development of advanced problem-solving skillsNew applications in the biological sciences, including age-structure, pattern formation, and the propagation of diseasesAn expanded bibliography that facilitates further investigation into specialized topicsWith individual, self-contained chapters and a broad scope of coverage that offers instructors the flexibility to design courses to meet specific objectives, An Introduction to Nonlinear Partial Differential Equations, Second Edition is an ideal text for applied mathematics courses at the upper-undergraduate and graduate levels. It also serves as a valuable resource for researchers and professionals in the fields of mathematics, biology, engineering, and physics who would like to further their knowledge of PDEs.