There are deep connections between stars and atoms, between the cosmos and the microworld. Just six numbers, imprinted in the "big bang," determine the essential features of our entire physical world. Moreover, cosmic evolution is astonishingly sensitive to the values of these numbers. If any one of them were "untuned," there could be no stars and no life. This realization offers a radically new perspective on our universe, our place in it, and the nature of physical laws.

    Even the simplest system of cause and effect can be subject to chaos, denying us accurate predictions of its behaviour, and sometimes giving rise to astonishing structures of large-scale order. Our growing understanding of Chaos Theory is having fascinating applications in the real world - from technology to global warming, politics, human behaviour, and even gambling on the stock market. Leonard Smith shows that we all have an intuitive understanding of chaotic systems. He uses accessible maths and physics (replacing complex equations with simple examples like pendulums, railway lines, and tossing coins) to explain the theory, and points to numerous examples in philosophy and literature (Edgar Allen Poe, Chang-Tzu, Arthur Conan Doyle) that illuminate the problems. The beauty of fractal patterns and their relation to chaos, as well as the history of chaos, and its uses in the real world and implications for the philosophy of science are all discussed in this Very Short Introduction.

    Book is unique in its emphasis on the frequency approach and its use in the solution of problems. Contents include: Fundamentals and Algorithms; Polynomial Approximation — Classical Theory; Fourier Approximation — Modern Theory; and Exponential Approximation.

    His aim is to present calculus as the first real encounter with mathematics: it is the place to learn how logical reasoning combined with fundamental concepts can be developed into a rigorous mathematical theory rather than a bunch of tools and techniques learned by rote. Since analysis is a subject students traditionally find difficult to grasp, Spivak provides leisurely explanations, a profusion of examples, a wide range of exercises and plenty of illustrations in an easy-going approach that enlightens difficult concepts and rewards effort. Calculus will continue to be regarded as a modern classic, ideal for honours students and mathematics majors, who seek an alternative to doorstop textbooks on calculus, and the more formidable introductions to real analysis.

    Since its publication in 1908, it has been a classic work to which successive generations of budding mathematicians have turned at the beginning of their undergraduate courses. In its pages, Hardy combines the enthusiasm of a missionary with the rigor of a purist in his exposition of the fundamental ideas of the differential and integral calculus, of the properties of infinite series and of other topics involving the notion of limit.

    This edition contains NEW tables on Properties of Ionic Liquids, Solubilities of Hydrocarbons in Sea Water, Solubility of Organic Compounds in Superheated Water, and Nutritive Value of Foods. It also updates many tables including Critical Constants, Heats of Vaporization, Aqueous Solubility of Organic Compounds, Vapor Pressure of Mercury, Scientific Abbreviations and Symbols, and Bond Dissociation Energies. The 88th Edition also presents a new Foreword written by Dr. Harold Kroto, a 1996 Nobel Laureate in Chemistry.

    As well as lucid descriptions of all the topics and many worked examples, it contains over 800 exercises. New stand-alone chapters give a systematic account of the 'special functions' of physical science, cover an extended range of practical applications of complex variables, and give an introduction to quantum operators. Further tabulations, of relevance in statistics and numerical integration, have been added. In this edition, half of the exercises are provided with hints and answers and, in a separate manual available to both students and their teachers, complete worked solutions. The remaining exercises have no hints, answers or worked solutions and can be used for unaided homework; full solutions are available to instructors on a password-protected web site, www.cambridge.org/9780521679718.

    In this guide for students, each equation is the subject of an entire chapter, with detailed, plain-language explanations of the physical meaning of each symbol in the equation, for both the integral and differential forms. The final chapter shows how Maxwell's equations may be combined to produce the wave equation, the basis for the electromagnetic theory of light. This book is a wonderful resource for undergraduate and graduate courses in electromagnetism and electromagnetics. A website hosted by the author at www.cambridge.org/9780521701471 contains interactive solutions to every problem in the text as well as audio podcasts to walk students through each chapter.

    Now William Dunham gives them the attention they deserve.Dunham places each theorem within its historical context and explores the very human and often turbulent life of the creator — from Archimedes, the absentminded theoretician whose absorption in his work often precluded eating or bathing, to Gerolamo Cardano, the sixteenth-century mathematician whose accomplishments flourished despite a bizarre array of misadventures, to the paranoid genius of modern times, Georg Cantor. He also provides step-by-step proofs for the theorems, each easily accessible to readers with no more than a knowledge of high school mathematics.A rare combination of the historical, biographical, and mathematical, Journey Through Genius is a fascinating introduction to a neglected field of human creativity.

    Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics.Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics? Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts.Brought up to date with a new chapter by Ian Stewart, What is Mathematics? Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved.Formal mathematics is like spelling and grammar - a matter of the correct application of local rules. Meaningful mathematics is like journalism - it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature - it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature - it opens a window onto the world of mathematics for anyone interested to view.

    

    Just about everyone has at least heard of Albert Einstein's formulation of 1905, which came into the world as something of an afterthought. But far fewer can explain his insightful linkage of energy to mass. David Bodanis offers an easily grasped gloss on the equation. Mass, he writes, "is simply the ultimate type of condensed or concentrated energy," whereas energy "is what billows out as an alternate form of mass under the right circumstances." Just what those circumstances are occupies much of Bodanis's book, which pays homage to Einstein and, just as important, to predecessors such as Maxwell, Faraday, and Lavoisier, who are not as well known as Einstein today. Balancing writerly energy and scholarly weight, Bodanis offers a primer in modern physics and cosmology, explaining that the universe today is an expression of mass that will, in some vastly distant future, one day slide back to the energy side of the equation, replacing the "dominion of matter" with "a great stillness"--a vision that is at once lovely and profoundly frightening. Without sliding into easy psychobiography, Bodanis explores other circumstances as well; namely, Einstein's background and character, which combined with a sterling intelligence to afford him an idiosyncratic view of the way things work--a view that would change the world. --Gregory McNamee

    Intuition and computational abilities are stressed. Original material on DE and multiple integrals has been expanded.

    Language is informal, examples are vivid and lively, and the perspectivie is fresh. Based on lectures delivered to engineering students, this work will also be valued by scientists, engineers, technicians, businessmen, anyone facing energy challenges of the future.

    This supplement will cater to the requirements of students by covering all important topics of Laplace transformation, Matrices, Numerical Methods. Further enhanced is its usability by inclusion of chapter end questions in sync with student needs. Table of contents: 1. Basic Concepts 2. An Introduction to Modeling and Qualitative Methods 3. Classification of First-Order Differential Equations 4. Separable First-Order Differential Equations 5. Exact First-order Differential Equations 6. Linear First-Order Differential Equations 7. Applications of First-Order Differential Equations 8. Linear Differential Equations: Theory of Solutions 9. Second-Order Linear Homogeneous Differential Equations with Constant Coefficients 10. nth-Order Linear Homogeneous Differential Equations with Constant Coefficients 11. The Method of Undetermined Coefficients 12. Variation of Parameters 13. Initial-Value Problems for Linear Differential Equations 14. Applications of Second-Order Linear Differential Equations 15. Matrices 16. eAt 17. Reduction of Linear Differential Equations to a System of First-Order Equations 18. Existence and Uniqueness of Solutions 19. Graphical and Numerical Methods for Solving First-Order Differential Equations 20. Further Numerical Methods for Solving First-Order Differential Equations 21. Numerical Methods for Solving Second-Order Differential Equations Via Systems 22. The Laplace Transform 23. Inverse Laplace Transforms 24. Convolutions and the Unit Step Function 25. Solutions of Linear Differential Equations with Constant Coefficients by Laplace Transforms 26. Solutions of Linear?Systems by Laplace Transforms 27. Solutions of Linear Differential Equations with Constant Coefficients by Matrix Methods 28. Power Series Solutions of Linear Differential Equations with Variable Coefficients 29. Special Functions 30. Series Solutions N