The problems to be treated belong mainly to the classical matherhatical literature, as shown by their connection with the names of Laplace, Fourier, Green, Gauss, Riemann, and William Thomson. In order to show that these methods are adequate to deal with actual problems, we treat the propagation of radio waves in some detail in Chapter VI.
The Second Edition maintained the accessibility of the first, while providing an introduction to the use of computers and expanding discussion on certain topics. Further emphasis was placed on topological properties, properties of geodesics, singularities of vector fields, and the theorems of Bonnet and Hadamard.
This revision of the Second Edition provides a thorough update of commands for the symbolic computation programs Mathematica or Maple, as well as additional computer exercises. As with the Second Edition, this material supplements the content but no computer skill is necessary to take full advantage of this comprehensive text.Over 36,000 copies sold worldwideAccessible, practical yet rigorous approach to a complex topic--also suitable for self-studyExtensive update of appendices on Mathematica and Maple software packagesThorough streamlining of second edition's numbering systemFuller information on solutions to odd-numbered problemsAdditional exercises and hints guide students in using the latest computer modeling tools
The treatment begins with a chapter on curves, followed by explorations of regular surfaces, the geometry of the Gauss map, the intrinsic geometry of surfaces, and global differential geometry. Suitable for advanced undergraduates and graduate students of mathematics, this text's prerequisites include an undergraduate course in linear algebra and some familiarity with the calculus of several variables. For this second edition, the author has corrected, revised, and updated the entire volume.
The text begins with a substantial chapter offering background on the mathematics needed for the rest of the book. Subsequent chapters emphasize physical interpretations of geometric properties such as curvature, geodesics, isometries, totally geodesic submanifolds, and topological structure. Further investigations cover relativistic concepts such as causality, Petrov types, optical scalars, and the Goldberg-Sachs theorem. Four helpful appendixes supplement the text.
How did his mind work? What made him a genius? Isaacson’s biography shows how his scientific imagination sprang from the rebellious nature of his personality. His fascinating story is a testament to the connection between creativity and freedom.
Based on newly released personal letters of Einstein, this book explores how an imaginative, impertinent patent clerk—a struggling father in a difficult marriage who couldn’t get a teaching job or a doctorate—became the mind reader of the creator of the cosmos, the locksmith of the mysteries of the atom, and the universe. His success came from questioning conventional wisdom and marveling at mysteries that struck others as mundane. This led him to embrace a morality and politics based on respect for free minds, free spirits, and free individuals.
These traits are just as vital for this new century of globalization, in which our success will depend on our creativity, as they were for the beginning of the last century, when Einstein helped usher in the modern age.
The authors outline how their positions have further diverged on a number of key issues, including the spatial geometry of the universe, inflationary versus cyclic theories of the cosmos, and the black-hole information-loss paradox. Though much progress has been made, Hawking and Penrose stress that physicists still have further to go in their quest for a quantum theory of gravity.
The text includes a wide range of techniques and applications, and will serve as an amenable introduction and useful reference to the modern theory of interpolation of operators.
In this collection of his seven most important essays on physics, Einstein guides his reader step-by-step through the many layers of scientific theory that formed a starting point for his discoveries. By both supporting and refuting the theories and scientific efforts of his predecessors, Einstein reveals in a clear voice the origins and meaning of such significant topics as physics and reality, the fundamentals of theoretical physics, the common language of science, the laws of science and of ethics, and an elementary derivation of the equivalence of mass and energy.
This remarkable collection allows the general reader to understand not only the significance of Einstein’s masterpiece, but also the brilliant mind behind it.
This authorized ebook features a new introduction by Neil Berger and an illustrated biography of Albert Einstein, which includes rare photos and never-before-seen documents from the Albert Einstein Archives at the Hebrew University of Jerusalem.
This book comprises 10 chapters and begins with some background material as an introduction. The following chapters then discuss elementary representation theory; real reductive groups; the basic theory of (g, K)-modules; the asymptotic behavior of matrix coefficients; The Langlands Classification; a construction of the fundamental series; cusp forms on G; character theory; and unitary representations and (g, K)-cohomology.
This book will be of interest to mathematicians and statisticians.
Ever since Albert Einstein's general theory of relativity burst upon the world in 1915 some of the most brilliant minds of our century have sought to decipher the mysteries bequeathed by that theory, a legacy so unthinkable in some respects that even Einstein himself rejected them.
Which of these bizarre phenomena, if any, can really exist in our universe? Black holes, down which anything can fall but from which nothing can return; wormholes, short spacewarps connecting regions of the cosmos; singularities, where space and time are so violently warped that time ceases to exist and space becomes a kind of foam; gravitational waves, which carry symphonic accounts of collisions of black holes billions of years ago; and time machines, for traveling backward and forward in time.
Kip Thorne, along with fellow theorists Stephen Hawking and Roger Penrose, a cadre of Russians, and earlier scientists such as Oppenheimer, Wheeler and Chandrasekhar, has been in the thick of the quest to secure answers. In this masterfully written and brilliantly informed work of scientific history and explanation, Dr. Thorne, a Nobel Prize-winning physicist and the Feynman Professor of Theoretical Physics Emeritus at Caltech, leads his readers through an elegant, always human, tapestry of interlocking themes, coming finally to a uniquely informed answer to the great question: what principles control our universe and why do physicists think they know the things they think they know? Stephen Hawking's A Brief History of Time has been one of the greatest best-sellers in publishing history. Anyone who struggled with that book will find here a more slowly paced but equally mind-stretching experience, with the added fascination of a rich historical and human component.
Winner of the Phi Beta Kappa Award in Science.
What does E=mc2 actually mean? Dr. Brian Cox and Professor Jeff Forshaw go on a journey to the frontier of twenty-first century science to unpack Einstein's famous equation. Explaining and simplifying notions of energy, mass, and light-while exploding commonly held misconceptions-they demonstrate how the structure of nature itself is contained within this equation. Along the way, we visit the site of one of the largest scientific experiments ever conducted: the now-famous Large Hadron Collider, a gigantic particle accelerator capable of re-creating conditions that existed fractions of a second after the Big Bang.A collaboration between one of the youngest professors in the United Kingdom and a distinguished popular physicist, Why Does E=mc2? is one of the most exciting and accessible explanations of the theory of relativity.
This practical, friendly guide focuses on critical conceptstaught in a typical geometry course, from the properties oftriangles, parallelograms, circles, and cylinders, to the skillsand strategies you need to write geometry proofs. GeometryEssentials For Dummies is perfect for cramming or doing homework,or as a reference for parents helping kids study for exams.
Get down to the basics — get a handle on the basics ofgeometry, from lines, segments, and angles, to vertices, altitudes,and diagonals
Conquer proofs with confidence — follow easy-to-graspinstructions for understanding the components of a formal geometryproof
Take triangles in strides — learn how to take in atriangle's sides, analyze its angles, work through an SAS proof,and apply the Pythagorean Theorem
Polish up on polygons — get the lowdown on quadrilateralsand other polygons: their angles, areas, properties, perimeters,and much more
Open the book and find:
Plain-English explanations of geometry terms
Tips for tackling geometry proofs
The seven members of the quadrilateral family
Straight talk on circles
Essential triangle formulas
The lowdown on 3-D: spheres, cylinders, prisms, and pyramids
Ten things to use as reasons in geometry proofs
Core concepts about the geometry of shapes and geometryproofs
Critical theorems, postulates, and definitions
The principles and formulas you need to know
Mr. Gardner offers lucid explanations of not only the special and general theories of relativity, but of the Michelson-Morley experiment, gravity and spacetime, Mach's principle, the twin paradox, models of the universe, and other topics. A new Postscript, examining the latest developments in the field, and specially written for this edition, is also included.
The clarity of the text is especially enhanced by the brilliant graphics of Anthony Ravielli, making this "by far the best layman's account of this difficult subject." — Christian Science Monitor.
This second edition of Adam's 'classic' reference text contains many additions and much modernizing and refining of material. The basic premise of the book remains unchanged: Sobolev Spaces is intended to provide a solid foundation in these spaces for graduate students and researchers alike.Self-contained and accessible for readers in other disciplinesWritten at elementary level making it accessible to graduate students
In Three Roads to Quantum Gravity, Lee Smolin provides an accessible overview of the attempts to build a final "theory of everything." He explains in simple terms what scientists are talking about when they say the world is made from exotic entities such as loops, strings, and black holes and tells the fascinating stories behind these discoveries: the rivalries, epiphanies, and intrigues he witnessed firsthand.
"Provocative, original, and unsettling." --New York Review of Books
"An excellent writer, a creative thinker."--Nature
Infinite Words explores all aspects of the theory, including Automata, Semigroups, Topology, Games, Logic, Bi-infinite Words, Infinite Trees and Finite Words. The book also looks at the early pioneering work of Büchi, McNaughton and Schützenberger.
Serves as both an introduction to the field and as a reference book.
Contains numerous exercises desgined to aid students and readers.
Self-contained chapters provide helpful guidance for lectures.
This revised and enlarged third edition reflects the latest developements in the field and convey a greater experience with results previously formulated. For example, the theory of skew-orthogoanl and bi-orthogonal polynomials, parallel to that of the widely known and used orthogonal polynomials, is explained here for the first time.Presentation of many new results in one place for the first timeFirst time coverage of skew-orthogonal and bi-orthogonal polynomials and their use in the evaluation of some multiple integralsFredholm determinants and Painlevé equationsThe three Gaussian ensembles (unitary, orthogonal, and symplectic); their n-point correlations, spacing probabilitiesFredholm determinants and inverse scattering theoryProbability densities of random determinants