This completely revised edition provides a tour of the mathematical knowledge and techniques needed by students across the physical sciences. There are new chapters on probability and statistics and on inverse problems. It serves as a stand-alone text or as a source of exercises and examples to complement other textbooks.

An engagingly-written account of mathematical tools and ideas, this book provides a graduate-level introduction to the mathematics used in research in physics. The first half of the book focuses on the traditional mathematical methods of physics – differential and integral equations, Fourier series and the calculus of variations. The second half contains an introduction to more advanced subjects, including differential geometry, topology and complex variables. The authors' exposition avoids excess rigor whilst explaining subtle but important points often glossed over in more elementary texts. The topics are illustrated at every stage by carefully chosen examples, exercises and problems drawn from realistic physics settings. These make it useful both as a textbook in advanced courses and for self-study. Password-protected solutions to the exercises are available to instructors at www.cambridge.org/9780521854030.

Provides a comprehensive tour of the mathematical methods needed by physical science students.

Market_Desc: · Physicists and Engineers· Students in Physics and Engineering Special Features: · Covers everything from Linear Algebra, Calculus, Analysis, Probability and Statistics, to ODE, PDE, Transforms and more· Emphasizes intuition and computational abilities· Expands the material on DE and multiple integrals· Focuses on the applied side, exploring material that is relevant to physics and engineering· Explains each concept in clear, easy-to-understand steps About The Book: The book provides a comprehensive introduction to the areas of mathematical physics. It combines all the essential math concepts into one compact, clearly written reference. This book helps readers gain a solid foundation in the many areas of mathematical methods in order to achieve a basic competence in advanced physics, chemistry, and engineering.

A delightful tour of the greatest ideas of math, showing how math intersects with philosophy, science, art, business, current events, and everyday life, by an acclaimed science communicator and regular contributor to the "New York Times."

From science fiction death rays to supermarket scanners, lasers have become deeply embedded in our daily lives and our culture. But in recent decades the standard laser beam has evolved into an array of more specialized light beams with a variety of strange and counterintuitive properties. Some of them have the ability to reconstruct themselves after disruption by an obstacle, while others can bend in complicated shapes or rotate like a corkscrew. These unusual optical effects open new and exciting possibilities for science and technology. For example, they make possible microscopic tractor beams that pull objects toward the source of the light, and they allow the trapping and manipulation of individual molecules to construct specially-tailored nanostructures for engineering or medical use. It has even been found that beams of light can produce lines of darkness that can be tied in knots. This book is an introductory survey of these specialized light beams and their scientific applications, at a level suitable for undergraduates with a basic knowledge of optics and quantum mechanics. It provides a unified treatment of the subject, collecting together in textbook form for the first time many topics currently found only in the original research literature.