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.

    Essentially, you make an initial guess, and then get more data to improve it. Bayes Theorem, or Bayes Rule, has a ton of real world applications, from estimating your risk of a heart attack to making recommendations on Netflix But It Isn't That Complicated This book is a short introduction to Bayes Theorem. It is only 15 pages long, and is intended to show you how Bayes Theorem works as quickly as possible. The examples are intentionally kept simple to focus solely on Bayes Theorem without requiring that the reader know complicated probability distributions. If you want to learn the basics of Bayes Theorem as quickly as possible, with some easy to duplicate examples, this is a good book for you.

    The remaining lectures build on that idea, examining the possibility of building a relativistic quantum theory on curved surfaces or flat surfaces.

    These singularities are places where space-time begins or ends, and the presently known laws of physics break down. They will occur inside black holes, and in the past are what might be construed as the beginning of the universe. To show how these predictions arise, the authors discuss the General Theory of Relativity in the large. Starting with a precise formulation of the theory and an account of the necessary background of differential geometry, the significance of space-time curvature is discussed and the global properties of a number of exact solutions of Einstein's field equations are examined. The theory of the causal structure of a general space-time is developed, and is used to study black holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions. A discussion of the Cauchy problem for General Relativity is also included in this 1973 book.

    

    

    The exposition is simple and leads to the most complete direct means of solving problems in mechanics. The final sections on adiabatic invariants have been revised and augmented. In addition a short biography of L D Landau has been inserted.

    Pure Mathematics 1 corresponds to unit P1. It covers quadratics, functions, coordinate geometry, circular measure, trigonometry, vectors, series, differentiation and integration.

    This book provides a practical guidebook for those seeking to understand and defeat the Alinsky tactics used by the Obama Administration, Occupy Wall Street, and other far-Left organizations.

    This work includes differential forms and the elegant forms of Maxwell's equations, and a chapter on probability and statistics. It also illustrates and proves mathematical relations.

    His talents are vividly revealed in this exciting and penetrating explanation of how the central laws of physical science evolved — from Pythagoras' discovery of frequency ratios in the 6th century B.C. to today's research on elementary particles.Unlike many books on physics which focus entirely on fact and theory with little or no historic detail, the present work incorporates fascinating personal and biographical data about the great physicists of past and present. Thus Dr. Gamow discusses on an equal basis the trail of Galileo and the basic laws of mechanics which he discovered, or gives his personal recollections about Niels Bohr along with detailed discussion of Bohr's atomic model. You'll also find revealing glimpses of Newton, Huygens, Heisenberg, Pauli, Einstein, and many other immortals of science.Each chapter is centered around a single great figure, or at most two, with other physicists of the era and their contributions forming a background. Major topics include the dawn of physics, the Dark Ages and the Renaissance, Newtonian physics, heat as energy, electricity, the relativistic revolution, quantum theory, and the atomic nucleus and elementary particles.As Dr. Gamow points out in the Preface, the aim of this book is to give the reader the feeling of what physics is, and what kind of people physicists are. This delightfully informal approach, combined with the book's clear, easy-to-follow explanations, will especially appeal to young readers but will stimulate and entertain science enthusiasts of all ages. 1961 edition."The whole thing is a tour de force covering all the important landmarks." — Guardian

    But then a series of meetings of "natural philosophers" in Oxford and London saw the beginning of a new method of thinking based on proof and experiment. At the heart of this renaissance were the founding fathers of modern western science: The Royal Society. John Gribbin's gripping, colorful account of this unparalleled time of discovery explores the birth of the Society and brings its prime movers to life. Gribbin shows how the triumph of the scientific revolution changed the world--and still continues to change it 350 years later. The Fellowship reveals that all that ensued was ultimately not the work of any single isolated genius, but of a Fellowship of brave and inquisitive men in search of the truth.

    

    This process of “self-organization” reveals itself in the inanimate worlds of crystals and seashells, but as Len Fisher shows, it is also evident in living organisms, from fish to ants to human beings. The coordinated movements of fish in shoals, for example, arise from the simple rule: “Follow the fish in front.” Traffic flow arises from simple rules: “Keep your distance” and “Keep to the right.”Now, in his new book, Fisher shows how we can manage our complex social lives in an ever more chaotic world. His investigation encompasses topics ranging from “swarm intelligence” to the science of parties and the best ways to start a fad. Finally, Fisher sheds light on the beauty and utility of complexity theory. An entertaining journey into the science of everyday life, The Perfect Swarm will delight anyone who wants to understand the complex situations in which we so often find ourselves.

    Extraterrestrials ... Our genetic destiny ... The roots of language and learning ... Quantum physics and the shape of the universe ... Artificial intelligence .. In a masterful "trial by reason," author John L. Casti presents all sides of the most important and vital scientific debates raging in the world today -- scrutinizing six perplexing "great questions" in the most engaging, astonishing and accessible amalgam of science and literature since "A Brief History of Time.