Mathematical Physics

A Student's Guide to Maxwell's Equations

Gauss's law for electric fields, Gauss's law for magnetic fields, Faraday's law, and the Ampere-Maxwell law are four of the most influential equations in science. 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.

Maxwell's equations are four of the most influential equations in science. In this book, each equation is the subject of an entire chapter, making it a wonderful resource for undergraduate and graduate courses in electromagnetism and electromagnetics. Audio podcasts and solutions to the problems are available at www.cambridge.org/9780521701471.

The Complete Idiot's Guide to String Theory (Complete Idiot's Guide to)

Everything is connectedÂ…

We’re living in the midst of a scientific revolution that’s captured the general public’s attention and imagination. The aim of this new revolution is to develop a “theory of everything”—a set of laws of physics that will explain all that can be explained, ranging from the tiniest subatomic particle to the universe as a whole. Here, readers will learn the ideas behind the theories, and their effects upon our world, our civilization, and ourselves.

The Road to Reality: A Complete Guide to the Laws of the Universe

If Albert Einstein were alive, he would have a copy of The Road to Reality on his bookshelf. So would Isaac Newton. This may be the most complete mathematical explanation of the universe yet published, and Roger Penrose richly deserves the accolades he will receive for it. That said, let us be perfectly clear: this is not an easy book to read. The number of people in the world who can understand everything in it could probably take a taxi together to Penrose's next lecture. Still, math-friendly readers looking for a substantial and possibly even thrillingly difficult intellectual experience should pick up a copy (carefully--it's over a thousand pages long and weighs nearly 4 pounds) and start at the beginning, where Penrose sets out his purpose: to describe "the search for the underlying principles that govern the behavior of our universe." Beginning with the deceptively simple geometry of Pythagoras and the Greeks, Penrose guides readers through the fundamentals--the incontrovertible bricks that hold up the fanciful mathematical structures of later chapters. From such theoretical delights as complex-number calculus, Riemann surfaces, and Clifford bundles, the tour takes us quickly on to the nature of spacetime. The bulk of the book is then devoted to quantum physics, cosmological theories (including Penrose's favored ideas about string theory and universal inflation), and what we know about how the universe is held together. For physicists, mathematicians, and advanced students, The Road to Reality is an essential field guide to the universe. For enthusiastic amateurs, the book is a project to tackle a bit at a time, one with unimaginable intellectual rewards. --Therese Littleton

Roger Penrose, one of the most accomplished scientists of our time, presents the only comprehensive and comprehensible account of the physics of the universe. From the very first attempts by the Greeks to grapple with the complexities of our known world to the latest application of infinity in physics, The Road to Reality carefully explores the movement of the smallest atomic particles and reaches into the vastness of intergalactic space. Here, Penrose examines the mathematical foundations of the physical universe, exposing the underlying beauty of physics and giving us one the most important works in modern science writing.

Principles of Quantum Mechanics

Reviews from the First Edition:

"An excellent text … The postulates of quantum mechanics and the mathematical underpinnings are discussed in a clear, succinct manner." (American Scientist)

"No matter how gently one introduces students to the concept of Dirac’s bras and kets, many are turned off. Shankar attacks the problem head-on in the first chapter, and in a very informal style suggests that there is nothing to be frightened of." (Physics Bulletin)

Reviews of the Second Edition:

"This massive text of 700 and odd pages has indeed an excellent get-up, is very verbal and expressive, and has extensively worked out calculational details---all just right for a first course. The style is conversational, more like a corridor talk or lecture notes, though arranged as a text. … It would be particularly useful to beginning students and those in allied areas like quantum chemistry." (Mathematical Reviews)

R. Shankar has introduced major additions and updated key presentations in this second edition of Principles of Quantum Mechanics. New features of this innovative text include an entirely rewritten mathematical introduction, a discussion of Time-reversal invariance, and extensive coverage of a variety of path integrals and their applications. Additional highlights include:

- Clear, accessible treatment of underlying mathematics

- A review of Newtonian, Lagrangian, and Hamiltonian mechanics

- Student understanding of quantum theory is enhanced by separate treatment of mathematical theorems and physical postulates

- Unsurpassed coverage of path integrals and their relevance in contemporary physics

The requisite text for advanced undergraduate- and graduate-level students, Principles of Quantum Mechanics, Second Edition is fully referenced and is supported by many exercises and solutions. The book’s self-contained chapters also make it suitable for independent study as well as for courses in applied disciplines.

Mathematical Methods in the Physical Sciences

Now in its third edition, Mathematical Concepts in the Physical Sciences provides a comprehensive introduction to the areas of mathematical physics. It combines all the essential math concepts into one compact, clearly written reference.

Data Reduction and Error Analysis for the Physical Sciences

The purpose of this book is to provide an introduction to the concepts of statistical analysis of data for students at the undergraduate and graduate level, and to provide tools for data reduction and error analysis commonly required in the physical sciences. The presentation is developed from a practical point of view, including enough derivation to justify the results, but emphasizing methods of handling data more than theory. The text provides a variety of numerical and graphical techniques. Computer programs that support these techniques will be available on an accompanying website in both Fortran and C++.

The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century

Science is inextricably linked with mathematics. Statistician David Salsburg examines the development of ever-more-powerful statistical methods for determining scientific truth in The Lady Tasting Tea, a series of historical and biographical sketches that illuminate without alienating the mathematically timid. Salsburg, who has worked in academia and industry and has met many of the major players he writes about, shares his subjects' enthusiasm for problem solving and deep thinking. His sense of excitement drives the prose, but never at the expense of the reader; if anything, the author has taken pains to eliminate esoterica and ephemera from his stories. This might frustrate a few number-head readers, but the abundant notes and references should keep them happy in the library for weeks after reading the book.

Ultimately, the various tales herein are unified in a single theme: the conversion of science from observational natural history into rigorously defined statistical models of data collection and analysis. This process, usually only implicit in studies of scientific methods and history, is especially important now that we seem to be reaching the point of diminishing returns and are looking for new paradigms of scientific investigation. The Lady Tasting Tea will appeal to a broad audience of scientifically literate readers, reminding them of the humanity underlying the work. --Rob Lightner

An Introduction To Black Holes, Information And The String Theory Revolution: The Holographic Universe

Over the last decade the physics of black holes has been revolutionized by developments that grew out of Jacob Bekenstein s realization that black holes have entropy. Stephen Hawking raised profound issues concerning the loss of information in black hole evaporation and the consistency of quantum mechanics in a world with gravity. For two decades these questions puzzled theoretical physicists and eventually led to a revolution in the way we think about space, time, matter and information. This revolution has culminated in a remarkable principle called The Holographic Principle , which is now a major focus of attention in gravitational research, quantum field theory and elementary particle physics. Leonard Susskind, one of the co-inventors of the Holographic Principle as well as one of the founders of String theory, develops and explains these concepts.

Physics: Algebra/Trig (with CD-ROM)

In Hecht's groundbreaking book, you'll find real-life applications, an unparalleled art and photography program, a presentation that anticipates students' questions, and an approach that emphasizes contemporary physics while interweaving historical perspectives. Hecht's coverage of classical physics is clear and insightful. He shows students how 21st-century physics illuminates the classical topics of each chapter, adding excitement to the subject matter. Over 1,300 illustrations make it possible for students to visualize a diversity of physical phenomena. Many of these are multi-frame, sequential drawings allowing students to comprehend the temporal unfolding of complex events. A selection of sketch art teaches students how to create problem-solving diagrams. This new edition of the text was designed to aggressively address the issue of problem solving for students (guided by contemporary physics education research). To this end Hecht has provided not only his approach to the five-step problem-solving framework but also a wide range of new problems and solutions specifically designed to build student capability and confidence.

Calculus of Variations