This top-selling, theorem-proof text presents a careful treatment of the principal topics of linear algebra, and illustrates the power of the subject through a variety of applications. It emphasizes the symbiotic relationship between linear transformations and matrices, but states theorems in the more general infinite-dimensional case where appropriate.

    But ask what it means, and the result will be a brawl. For a century, most physicists have followed Niels Bohr's Copenhagen interpretation and dismissed questions about the reality underlying quantum physics as meaningless. A mishmash of solipsism and poor reasoning, Copenhagen endured, as Bohr's students vigorously protected his legacy, and the physics community favored practical experiments over philosophical arguments. As a result, questioning the status quo long meant professional ruin. And yet, from the 1920s to today, physicists like John Bell, David Bohm, and Hugh Everett persisted in seeking the true meaning of quantum mechanics. What Is Real? is the gripping story of this battle of ideas and of the courageous scientists who dared to stand up for truth.

    Drawing on a wealth of expertise to explain just what a fascinating field quantum physics is, Rae points out that it is not simply a maze of technical jargon and philosophical ideas, but a reality which affects our daily lives.

    By replacing equations with diagrams, the book allows non-specialist readers to fully understand the concepts in relativity without the slow, painful progress so often associated with a complicated scientific subject. It allows readers not only to know how relativity works, but also to intuitively understand it.

    Indeed, such equations are crucial to mathematical physics. Although simplifications can be made that reduce these equations to ordinary differential equations, nevertheless the complete description of physical systems resides in the general area of partial differential equations.This highly useful text shows the reader how to formulate a partial differential equation from the physical problem (constructing the mathematical model) and how to solve the equation (along with initial and boundary conditions). Written for advanced undergraduate and graduate students, as well as professionals working in the applied sciences, this clearly written book offers realistic, practical coverage of diffusion-type problems, hyperbolic-type problems, elliptic-type problems, and numerical and approximate methods. Each chapter contains a selection of relevant problems (answers are provided) and suggestions for further reading.

    It explores the critical concepts while also examining why they are relevant. The core content is presented within the framework of predicting products, proposing mechanisms, and solving synthesis problems. Readers will fine-tune the key skills involved in solving those types of problems with the help of interactive, step-by-step instructions and problems.

    Clear Science Teaching to Set the Stage for an Awe-Inspiring Course Created for a lay audience and readily accessible, in this course science always takes precedence over drama. The lectures are certainly entertaining, often funny, even awe-inspiring at times, as befits the subject matter. Even though you will be entertained, you will be learning good science. Clear introductions to essential principles of physics support these lectures, including density, quantum theory, gravity, and the General Theory of Relativity. Professor Neil deGrasse Tyson also includes forays into disciplines such as chemistry and biology as needed to explain events in astronomy. For example, Dr. Tyson begins one lecture at a point 13 billion years ago, when all space, matter, and energy in the known universe were contained in a volume less than one-trillionth the size of a pinpoint-about the size of a single atom. By the time he finishes, the cosmos has been stretched, the planets and our Earth formed, and 70 percent of existing Earth species have been wiped out by a gigantic asteroidclearing the way for the evolution of humanity. Along the way he has touched on Einstein's famous equation, E=mc2; on the four forces that were once unified in the early cosmos in a way physicists are still trying to explain; and on the chemical enrichment of the universe by exploding supernovae, which give the universe its necessary supply of heavier elements including oxygen, nitrogen, iron and, most important, carbon. Carbon, we learn, is a "sticky" atom, capable of making more kinds of molecules than all other elements combined. It's the ideal element with which to experiment in the building of life forms and is, of course, the element responsible for the remarkable diversity of life, including us. As Dr. Tyson notes, we are made of stardust, just as the planets are. And he has created a course that explains exactly how that came to be, beginning with a grounding in the basic "machinery" of matter, forces, and energy that has been discovered on Earth and which also reveals itself throughout the universe. The Stark and Violent Beauty of the Universe With this basic foundation in place, explanations of cosmic events fall logically into place, and the realities of the universe-including its eventual demise-are revealed in stark and often violent beauty. You learn: how Saturn's rings were formed, and why they will eventually be lost why low-density conditions are necessary to produce the drama of the northern and southern auroras why even the most jagged and wild of the Earth's mountain ranges are, from a cosmic standpoint, really part of a perfectly smooth sphere how black holes are formed and the extraordinary way in which they can wreak havoc in the universe how asteroids moving through space represent threats of extraordinary consequence to Earth, no matter how long those threats may take to be realized why the seemingly infinite panorama of celestial bodies revealed by the Hubble Space Telescope's famous "Deep Field" so intrigued astronomers how astronomers actually look for new planets, why the odds seem overwhelmingly in favor of some kind of life out there, whether we ever make contact or not. Most important, none of these ideas are presented as isolated "space factoids" that serve no purpose but to entertain. They are there to illustrate and reinforce the key principles of physics and astrophysics that are continually being presented in this course. But the inclusion of real science doesn't prevent Dr. Tyson from having some fun, either. When it's time to show how a black hole might remove one from the universe, he leads you right up to the "event horizon" and slips you in-feet first. Since the event horizon represents the point within which nothing, not even light, can escape, you might think this is a bad idea. And you would be right. But as you plummet toward the "singularity" at the heart of the black hole, you will learn firsthand about the interesting effects of gravity truly unleashed, including what physicists refer to, with a straight face, as "spaghettification." (Actually, Professor Tyson recommends that you be sucked in to a large black hole rather than a small one. You'll still be spaghettified, but it won't happen as quickly.) But make no mistake: Dr. Tyson does not consider the cosmos a laughing matter, this kind of whimsical touch notwithstanding. In spite of his training, he remains, admittedly, still in awe of his subject. And he has created a course that might well produce the same feeling in you.

    Designed for the junior- level astrophysics course, each topic is approached in the context of the major unresolved questions in astrophysics. The core chapters have been designed for a course in stellar structure and evolution, while the extended chapters provide additional coverage of the solar system, galactic structure, dynamics, evolution, and cosmology. * Two versions of this text are available: An Introduction to Modern Stellar Astrophysics, (Chapters 1-17), and An Introduction to Modern Astrophysics, (Chapters 1-28). * Computer programs included with the text allow students to explore the physics of stars and galaxies. * In designing a curriculum, instructors can combine core and extended chapters with the optional advanced sections so as to meet their individual goals. * Up-to-date coverage of current astrophysical discoveries are included. * This text emphasizes computational physics, including computer problems and on-line programs. * This text also includes a selection of over 500 problems. For additional information and computer codes to be used

    Climate changes are cyclical and are driven by the Earth's position in the galaxy, the sun, wobbles in the Earth's orbit, ocean currents, and plate tectonics. In previous times, atmospheric carbon dioxide was far higher than at present but did not drive climate change. No runaway greenhouse effect or acid oceans occurred during times of excessively high carbon dioxide. During past glaciations, carbon dioxide was higher than it is today. The non-scientific popular political view is that humans change climate. Do we have reason for concern about possible human-induced climate change? This book's 504 pages and over 2,300 references to peer-reviewed scientific literature and other authoritative sources engagingly synthesize what we know about the sun, earth, ice, water, and air. Importantly, in a parallel to his 1994 book challenging "creation science," Telling Lies for God, Ian Plimer describes Al Gore's book and movie An Inconvenient Truth as long on scientific "misrepresentations." "Trying to deal with these misrepresentations is somewhat like trying to argue with creationists," he writes, "who misquote, concoct evidence, quote out of context, ignore contrary evidence, and create evidence ex nihilo."

    William H. Cropper vividly portrays the life and accomplishments of such giants as Galileo and Isaac Newton, Marie Curie and Ernest Rutherford, Albert Einstein and NielsBohr, right up to contemporary figures such as Richard Feynman, Murray Gell-Mann, and Stephen Hawking. We meet scientists--all geniuses--who could be gregarious, aloof, unpretentious, friendly, dogged, imperious, generous to colleagues or contentious rivals. As Cropper captures their personalities, he also offers vivid portraits of their great moments of discovery, their bitter feuds, their relations with family and friends, their religious beliefs and education. In addition, Cropper has grouped these biographies by discipline--mechanics, thermodynamics, particle physics, and others--eachsection beginning with a historical overview. Thus in the section on quantum mechanics, readers can see how the work of Max Planck influenced Niels Bohr, and how Bohr in turn influenced Werner Heisenberg.Our understanding of the physical world has increased dramatically in the last four centuries. With Great Physicists, readers can retrace the footsteps of the men and women who led the way.

    Topics covered include matrix multiplication, row reduction, matrix inverse, orthogonality and computation. The self-teaching book is loaded with examples and graphics and provides a wide array of probing problems, accompanying solutions, and a glossary. Chapter 1: Introduction to Vectors; Chapter 2: Solving Linear Equations; Chapter 3: Vector Spaces and Subspaces; Chapter 4: Orthogonality; Chapter 5: Determinants; Chapter 6: Eigenvalues and Eigenvectors; Chapter 7: Linear Transformations; Chapter 8: Applications; Chapter 9: Numerical Linear Algebra; Chapter 10: Complex Vectors and Matrices; Solutions to Selected Exercises; Final Exam. Matrix Factorizations. Conceptual Questions for Review. Glossary: A Dictionary for Linear Algebra Index Teaching Codes Linear Algebra in a Nutshell.

    However, while physicists celebrated these momentous discoveries—which presaged the era of big science and nuclear bombs—Europe was moving inexorably toward totalitarianism and war. In April of that year, about forty of the world’s leading physicists—including Werner Heisenberg, Lise Meitner, and Paul Dirac—came to Niels Bohr’s Copenhagen Institute for their annual informal meeting about the frontiers of physics. Physicist Gino Segrè brings to life this historic gathering, which ended with a humorous skit based on Goethe’s Faust—a skit that eerily foreshadowed events that would soon unfold. Little did the scientists know the Faustian bargains they would face in the near future. Capturing the interplay between the great scientists as well as the discoveries they discussed and debated, Segrè evokes the moment when physics—and the world—was about to lose its innocence.

    Meet a man who can pull two railroad passenger cars with his teeth and a real-life human cannon ball. Come face to face with a dead rattlesnake that still bites. And unlock the secrets of a magician's bodiless head. Welcome to this updated edition of The Flying Circus of Physics, where death-defying stunts, high-flying acrobatics, strange curiosities, and mind-bending illusions bring to life the fascinating feats of physics in the world around us. In 1977, Wiley published the first edition of Jearl Walker's The Flying Circus of Physics, which has sold over 100,000 copies and become a cult classic in the physics community. The Flying Circus is a compendium of interesting real world phenomena that can be explained using basic laws of physics. This new edition represents a thorough updating and modernization of the book. The new edition gives us the opportunity to highlight Jearl's creativity, his communication skills, and his ability to make physics interesting.Jearl Walker, Ph.D., professor of physics at Cleveland State University and the man who frequently walked on hot coals and lay on beds of nails all in the name of science, is the first recipient of the Outstanding Teaching Award from Cleveland State's College of Science. The College's Faculty Affairs Committee selected Dr. Walker as the first honoree based on his impressive contributions to science teaching over the last 30 years. In fact, the award in future years will be named the Jearl Walker Outstanding Teaching Award in recognition of his many achievements.Jearl Walker received his B.S. in physics from MIT in 1967 and his Ph.D. in physics from the University of Maryland in 1973. His popular book, The Flying Circus of Physics, has been translated into at least 10 languages and is still being sold worldwide. For 16 years he toured his fun-filled Flying Circus lecture throughout the U.S. and Canada, introducing countless teachers to such physics phenomena as molecular adhesion by hanging spoons from his face and Leidenfrost's phenomenon by dipping his wet hand in molten lead without getting hurt.These lectures led to his national PBS television show, Kinetic Karnival, which ran for several years and won him a local Emmy Award. During his 13 years as a columnist with Scientific American magazine, Dr. Walker wrote 152 articles for The Amateur Scientist section, which were translated into at least 9 languages worldwide. His topics ranged from the physics of judo to the physics of bearnaise sauce and lemon meringue pie. In 1990, he took over the textbook Fundamentals of Physics from David Halliday and Robert Resnick and has now published the seventh edition of the book. He has appeared countless times on television and radio and in newspapers and magazines.

    What happened during those years and what has happened since to refine the understanding of this phenomenon is the fascinating story told here.We move from a coffee shop in Zurich, where Einstein and Max von Laue discuss the madness of quantum theory, to a bar in Brazil, as David Bohm and Richard Feynman chat over cervejas. We travel to the campuses of American universities—from J. Robert Oppenheimer’s Berkeley to the Princeton of Einstein and Bohm to Bell’s Stanford sabbatical—and we visit centers of European physics: Copenhagen, home to Bohr’s famous institute, and Munich, where Werner Heisenberg and Wolfgang Pauli picnic on cheese and heady discussions of electron orbits.Drawing on the papers, letters, and memoirs of the twentieth century’s greatest physicists, Louisa Gilder both humanizes and dramatizes the story by employing their own words in imagined face-to-face dialogues. Here are Bohr and Einstein clashing, and Heisenberg and Pauli deciding which mysteries to pursue. We see Schrödinger and Louis de Broglie pave the way for Bell, whose work is here given a long-overdue revisiting. And with his characteristic matter-of-fact eloquence, Richard Feynman challenges his contemporaries to make something of this entanglement.

    It has an algebra and trigonometry prerequisite, but calculus is preferred.