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.

    Simmons advocates a careful approach to the subject, covering such topics as the wave equation, Gauss's hypergeometric function, the gamma function and the basic problems of the calculus of variations in an explanatory fashions - ensuring that students fully understand and appreciate the topics.

    This book is built around the idea that students must study the discipline of psychology as a whole, that the sub-disciplines are intricately connected, and that human behavior is best understood by exploring its functioning state in addition to its potential dysfunctions.

    Second, it proposes that the inhabitants of this subterranean biosphere are not plants or animals as we know them, but heat-loving bacteria that survive on a diet consisting solely of hydrocarbons that is, natural gas and petroleum. And third and perhaps most heretically, the book advances the stunning idea that most hydrocarbons on Earth are not the byproduct of biological debris ("fossil fuels"), but were a common constituent of the materials from which the earth itself was formed some 4.5 billion years ago.The implications are astounding. The theory proposes answers to often-asked questions: Is the deep hot biosphere where life originated, and do Mars and other seemingly barren planets contain deep biospheres? Even more provocatively, is it possible that there is an enormous store of hydrocarbons upwelling from deep within the earth that can provide us with abundant supplies of gas and petroleum?However far-fetched these ideas seem, they are supported by a growing body of evidence, and by the indisputable stature and seriousness Gold brings to any scientific debate. In this book we see a brilliant and boldly original thinker, increasingly a rarity in modern science, as he develops potentially revolutionary ideas about how our world works.

    She explains ideas at the cutting-edge of scientific enquiry, making them comprehensible and accessible to the layperson.

    It deals with one powerful obsession that preoccupied Escher: what he called "the regular division of the plane," the puzzlelike interlocking of birds, fish, lizards, and other natural forms in continuous patterns. Schattschneider asks, "How did he do it?" She answers the question by analyzing Escher's notebooks." Visions of Symmetry includes many of Escher's masterworks, as well as hundreds of lesser-known examples of his work. This new edition also features a foreward and an illustrated epilogue that reveals new information about Escher's inspiration and shows how his ideas of symmetry have influenced mathematicians, computer scientists, and contemporary artists.