The authors study the Newton map $N:\mathbb{C}^2\rightarrow\mathbb{C}^2$ associated to two equations in two unknowns, as a dynamical system. They focus on the first non-trivial case: two simultaneous quadratics, to intersect two conics. In the first two chapters, the authors prove among other things: The Russakovksi-Shiffman measure does not change the points of indeterminancy. The lines joining pairs of roots are invariant, and the Julia set of the restriction of $N$ to such a line has under appropriate circumstances an invariant manifold, which shares features of a stable manifold and a center manifold. The main part of the article concerns the behavior of $N$ at infinity. To compactify $\mathbb{C}^2$ in such a way that $N$ extends to the compactification, the authors must take the projective limit of an infinite sequence of blow-ups. The simultaneous presence of points of indeterminancy and of critical curves forces the authors to define a new kind of blow-up: the Farey blow-up. This construction is studied in its own right in chapter 4, where they show among others that the real oriented blow-up of the Farey blow-up has a topological structure reminiscent of the invariant tori of the KAM theorem. They also show that the cohomology, completed under the intersection inner product, is naturally isomorphic to the classical Sobolev space of functions with square-integrable derivatives. In chapter 5 the authors apply these results to the mapping $N$ in a particular case, which they generalize in chapter 6 to the intersection of any two conics.
Here is a lively history of modern physics, as seen through the lives of thirty men and women from the pantheon of physics. 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 Niels Bohr, 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--each section 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.
Edmond Halley (1656-1742), MA, LLD, FRS, Capt. RN, Savillian Professor of Geometry and Astronomer Royal, stands pre-eminent among Oxford, English, and European scientists. A contemporary of Wren, Pepys, Hooke, Handel, Purcell, and Dryden, he was a schoolboy in London while the Great Fireraged, and was an active participant in the Enlightenment, an age of profound developments in all the arts and sciences. As a younger contemporary of Isaac Newton, he had a crucial part in the Newtonian revolution in the natural sciences. It was Halley who set the question that led Newton to writethe Principia, and who edited, paid for, and reviewed it. In later years he applied the methods of the Principia widely in astronomy and geophysics. Now more widely known for his prediction of the return of "his" comet, Halley discovered the proper motion of stars, made important studies of themoon's motion, and his investigations of the Earth's magnetic field and of tides were unrialled for centuries. His prediction of the transit of Venus led to Cook's voyage to Tahiti. He was far more than an cloistered academic; his exploits as a naval captain led to perilous adventures, and he wasalso a notable servant of the State. Much material about his eventful career has come to light in recent years, making this a timely new account of the life, scientific interests, and continuing influence of this engaging and adventurous scholar. Sir Alan Cook has written a fascinating andilluminating account of Halley's life and science, making this a unique and highly readable biography of one of the key figures of his time.
Do you want easy access to the latest methods in scientific computing? This greatly expanded third edition of Numerical Recipes has it, with wider coverage than ever before, many new, expanded and updated sections, and two completely new chapters. The executable C++ code, now printed in colour for easy reading, adopts an object-oriented style particularly suited to scientific applications. Co-authored by four leading scientists from academia and industry, Numerical Recipes starts with basic mathematics and computer science and proceeds to complete, working routines. The whole book is presented in the informal, easy-to-read style that made earlier editions so popular. Highlights of the new material include: a new chapter on classification and inference, Gaussian mixture models, HMMs, hierarchical clustering, and SVMs; a new chapter on computational geometry, covering KD trees, quad- and octrees, Delaunay triangulation, and algorithms for lines, polygons, triangles, and spheres; interior point methods for linear programming; MCMC; an expanded treatment of ODEs with completely new routines; and many new statistical distributions. For support, or to subscribe to an online version, please visit www.nr.com.
A thorough and highly accessible resource for analysts in a broadrange of social sciences. Optimization: Foundations and Applications presents a series ofapproaches to the challenges faced by analysts who must find thebest way to accomplish particular objectives, usually with theadded complication of constraints on the available choices.Award-winning educator Ronald E. Miller provides detailed coverageof both classical, calculus-based approaches and newer,computer-based iterative methods. Dr. Miller lays a solid foundation for both linear and nonlinearmodels and quickly moves on to discuss applications, includingiterative methods for root-finding and for unconstrainedmaximization, approaches to the inequality constrained linearprogramming problem, and the complexities of inequality constrainedmaximization and minimization in nonlinear problems. Otherimportant features include: More than 200 geometric interpretations of algebraic results,emphasizing the intuitive appeal of mathematics Classic results mixed with modern numerical methods to aidusers of computer programs Extensive appendices containing mathematical details importantfor a thorough understanding of the topic With special emphasis on questions most frequently asked by thoseencountering this material for the first time, Optimization:Foundations and Applications is an extremely useful resource forprofessionals in such areas as mathematics, engineering, economicsand business, regional science, geography, sociology, politicalscience, management and decision sciences, public policy analysis,and numerous other social sciences. An Instructor's Manual presenting detailed solutions to all theproblems in the book is available upon request from the Wileyeditorial department.
Listing of 100 people from around the world and from many different fields of endeavor, whose actions--the author has determined--have had, or will have, the greatest influence on the course of history.
As with Numerical Recipes in C, the FORTRAN edition has been greatly revised to make this edition the most up to date handbook for those working with FORTRAN. Between both editions of Numerical Recipes, over 300,000 copies have been sold.
A Brief Introduction to Fluid Mechanics, 5th Edition is designed to cover the standard topics in a basic fluid mechanics course in a streamlined manner that meets the learning needs of today?s student better than the dense, encyclopedic manner of traditional texts. This approach helps students connect the math and theory to the physical world and practical applications and apply these connections to solving problems. The text lucidly presents basic analysis techniques and addresses practical concerns and applications, such as pipe flow, open-channel flow, flow measurement, and drag and lift. It offers a strong visual approach with photos, illustrations, and videos included in the text, examples and homework problems to emphasize the practical application of fluid mechanics principles
This volume consists of more than twenty articles by Richard H. Popkin on the history of modern philosophy, written between 1980 and 1990, including several not published before this. The topics covered in these studies range over religious and theological influences in modern philosophy, further material in the history of scepticism dealing with Hobbes, Henry More and Pascal, as well as Moritz Schlick, new findings about Spinoza, pre-Adamism, Ralph Cudworth, Isaac Newton's religious views, 18th century racism, and the liberalism of Condorcet.
This is an updated guide for anyone who needs an introduction to personal computer technology, including computer programming, new technologies and shopping for a PC.
There are few books that show how to build programs of any kind. One common theme is compiler building, and there are shelves full of them. There are few others. It's an area, or a void, that needs filling. this book does a great job of showing how to build numerical analysis programs." -David N. Smith, IBM T J Watson Research Center Numerical methods naturally lend themselves to an object-oriented approach. Mathematics builds high- level ideas on top of previously described, simpler ones. Once a property is demonstrated for a given concept, it can be applied to any new concept sharing the same premise as the original one, similar to the ideas of reuse and inheritance in object-oriented (OO) methodology. Few books on numerical methods teach developers much about designing and building good code. Good computing routines are problem-specific. Insight and understanding are what is needed, rather than just recipes and black box routines. Developers need the ability to construct new programs for different applications. Object-Oriented Implementation of Numerical Methods reveals a complete OO design methodology in a clear and systematic way. Each method is presented in a consistent format, beginning with a short explanation and following with a description of the general OO architecture for the algorithm. Next, the code implementations are discussed and presented along with real-world examples that the author, an experienced software engineer, has used in a variety of commercial applications. Features: Reveals the design methodology behind the code, including design patterns where appropriate, rather than just presenting canned solutions. Implements all methods side by side in both Java and Smalltalk. This contrast can significantly enhance your understanding of the nature of OO programming languages. Provides a step-by-step pathway to new object-oriented techniques for programmers familiar with using procedural languages such as C or Fortran for numerical methods. Includes a chapter on data mining, a key application of numerical methods.
Eine Einführung in alle Aspekte der finiten Elemente, jetzt schon in der 4. Auflage! Geboten wird eine ausgewogene Mischung theoretischer und anwendungsorientierter Kapitel mit vielen Beispielen. Schwerpunkte liegen auf Anwendungen aus der Mechanik, dem Wärmetransport, der Elastizität sowie auf disziplinübergreifenden Problemen (Strömungen von Fluiden, Elektromagnetismus). Eine nützliche und zuverlässige Informationsquelle für Studenten und Praktiker!
In the intervening years since this book was published in 1981, the field of optimization has been exceptionally lively. This fertility has involved not only progress in theory, but also faster numerical algorithms and extensions into unexpected or previously unknown areas such as semidefinite programming. Despite these changes, many of the important principles and much of the intuition can be found in this Classics version of Practical Optimization. This book provides model algorithms and pseudocode, useful tools for users who prefer to write their own code as well as for those who want to understand externally provided code. It presents algorithms in a step-by-step format, revealing the overall structure of the underlying procedures and thereby allowing a high-level perspective on the fundamental differences. And it contains a wealth of techniques and strategies that are well suited for optimization in the twenty-first century, and particularly in the now-flourishing fields of data science, big data, and machine learning. Practical Optimization is appropriate for advanced undergraduates, graduate students, and researchers interested in methods for solving optimization problems.
This book explores how and when biology emerged as a science in Germany. Beginning with the debate about organism between Georg Ernst Stahl and Gottfried Leibniz at the start of the eighteenth century, John Zammito traces the development of a new research program, culminating in 1800, in the formulation of developmental morphology. He shows how over the course of the century, naturalists undertook to transform some domains of natural history into a distinct branch of natural philosophy, which attempted not only to describe but to explain the natural world and became, ultimately, the science of biology.
The fast and easy way to ace your statics course Does the study of statics stress you out? Does just the thought of mechanics make you rigid? Thanks to this book, you can find balance in the study of this often-intimidating subject and ace even the most challenging university-level courses. Statics For Dummies gives you easy-to-follow, plain-English explanations for everything you need to grasp the study of statics. You'll get a thorough introduction to this foundational branch of engineering and easy-to-follow coverage of solving problems involving forces on bodies at rest; vector algebra; force systems; equivalent force systems; distributed forces; internal forces; principles of equilibrium; applications to trusses, frames, and beams; and friction. Offers a comprehensible introduction to statics Covers all the major topics you'll encounter in university-level courses Plain-English guidance help you grasp even the most confusing concepts If you're currently enrolled in a statics course and looking for a friendlier way to get a handle on the subject, Statics For Dummies has you covered.
Praise from the Second Edition "...an excellent introduction to optimization theory..." (Journal of Mathematical Psychology, 2002) "A textbook for a one-semester course on optimization theory and methods at the senior undergraduate or beginning graduate level." (SciTech Book News, Vol. 26, No. 2, June 2002) Explore the latest applications of optimization theory and methods Optimization is central to any problem involving decision making in many disciplines, such as engineering, mathematics, statistics, economics, and computer science. Now, more than ever, it is increasingly vital to have a firm grasp of the topic due to the rapid progress in computer technology, including the development and availability of user-friendly software, high-speed and parallel processors, and networks. Fully updated to reflect modern developments in the field, An Introduction to Optimization, Third Edition fills the need for an accessible, yet rigorous, introduction to optimization theory and methods. The book begins with a review of basic definitions and notations and also provides the related fundamental background of linear algebra, geometry, and calculus. With this foundation, the authors explore the essential topics of unconstrained optimization problems, linear programming problems, and nonlinear constrained optimization. An optimization perspective on global search methods is featured and includes discussions on genetic algorithms, particle swarm optimization, and the simulated annealing algorithm. In addition, the book includes an elementary introduction to artificial neural networks, convex optimization, and multi-objective optimization, all of which are of tremendous interest to students, researchers, and practitioners. Additional features of the Third Edition include: New discussions of semidefinite programming and Lagrangian algorithms A new chapter on global search methods A new chapter on multipleobjective optimization New and modified examples and exercises in each chapter as well as an updated bibliography containing new references An updated Instructor's Manual with fully worked-out solutions to the exercises Numerous diagrams and figures found throughout the text complement the written presentation of key concepts, and each chapter is followed by MATLAB exercises and drill problems that reinforce the discussed theory and algorithms. With innovative coverage and a straightforward approach, An Introduction to Optimization, Third Edition is an excellent book for courses in optimization theory and methods at the upper-undergraduate and graduate levels. It also serves as a useful, self-contained reference for researchers and professionals in a wide array of fields.
Apocalyptic millennialism is one of the most powerful strands in evangelical Christianity. It is not a single belief, but across many powerful evangelical groups there is general adhesion to faith in the physical return of Jesus in the Second Coming, the affirmation of a Rapture heavenward of "saved" believers, a millennium of peace under the rule of Jesus and his saints and, eventually, a final judgement and entry into deep eternity. In Discovering the End of Time (2016) Donald Harman Akenson traced the emergence of the primary packaging of modern apocalyptic millennialism back to southern Ireland in the 1820s and '30s. In Exporting the Rapture, he documents for the first time how the complex theological construction that has come to dominate modern evangelical thought was enhulled in an organizational system that made it exportable from the British Isles to North America-- and subsequently around the world. A key figure in this process was John Nelson Darby who was at first a formative influence on evangelical apocalypticism in Ireland; then the volatile central figure in Brethren apocalypticism throughout the British Isles; and also a crusty but ultimately very successful missionary to the United States and Canada. Akenson emphasizes that, as strong a personality as John Nelson Darby was, the real story is that he became a vector for the transmission of a terrifically complex and highly seductive ideological system from the old world to the new. So beguiling, adaptable, and compelling was the new Dispensational system that Darby injected into North-American evangelicalism that it continued to spread logarithmically after his death. By the 1920s, the system had become the doctrinal template of the fundamentalist branch of North-American evangelicalism and the distinguishing characteristic of the bestselling Scofield Bible.
Making Women's Medicine Masculine challenges the common belief that prior to the eighteenth century men were never involved in any aspect of women's healthcare in Europe. Using sources ranging from the writings of the famous twelfth-century female practitioner, Trota of Salerno, all the way to the great tomes of Renaissance male physicians, and covering both medicine and surgery, this study demonstrates that men slowly established more and more authority in diagnosing and prescribing treatments for women's gynaecological conditions (especially infertility) and even certain obstetrical conditions. Even if their 'hands-on' knowledge of women's bodies was limited by contemporary mores, men were able to establish their increasing authority in this and all branches of medicine due to their greater access to literacy and the knowledge contained in books, whether in Latin or the vernacular. As Monica Green shows, while works written in French, Dutch, English, and Italian were sometimes addressed to women, nevertheless even these were often re-appropriated by men, both by practitioners who treated women and by laymen interested to learn about the 'secrets' of generation. While early in the period women were considered to have authoritative knowledge on women's conditions (hence the widespread influence of the alleged authoress 'Trotula'), by the end of the period to be a woman was no longer an automatic qualification for either understanding or treating the conditions that most commonly afflicted the female sex - with implications of women's exclusion from production of knowledge on their own bodies extending to the present day.
This book provides a thorough introduction to Einstein's special theory of relativity, suitable for anyone with a minimum of one year's university physics with calculus. It is divided into fundamental and advanced topics. The first section starts by recalling the Pythagorean rule and its relation to the geometry of space, then covers every aspect of special relativity, including the history. The second section covers the impact of relativity in quantum theory, with an introduction to relativistic quantum mechanics and quantum field theory. It also goes over the group theory of the Lorentz group, a simple introduction to supersymmetry, and ends with cutting-edge topics such as general relativity, the standard model of elementary particles and its extensions, superstring theory, and a survey of important unsolved problems. Each chapter comes with a set of exercises. The book is accompanied by a CD-ROM illustrating, through interactive animation, classic problems in relativity involving motion.
A balanced guide to the essential techniques for solving elliptic partial differential equations Numerical Analysis of Partial Differential Equations provides a comprehensive, self-contained treatment of the quantitative methods used to solve elliptic partial differential equations (PDEs), with a focus on the efficiency as well as the error of the presented methods. The author utilizes coverage of theoretical PDEs, along with the nu merical solution of linear systems and various examples and exercises, to supply readers with an introduction to the essential concepts in the numerical analysis of PDEs. The book presents the three main discretization methods of elliptic PDEs: finite difference, finite elements, and spectral methods. Each topic has its own devoted chapters and is discussed alongside additional key topics, including: The mathematical theory of elliptic PDEs Numerical linear algebra Time-dependent PDEs Multigrid and domain decomposition PDEs posed on infinite domains The book concludes with a discussion of the methods for nonlinear problems, such as Newton's method, and addresses the importance of hands-on work to facilitate learning. Each chapter concludes with a set of exercises, including theoretical and programming problems, that allows readers to test their understanding of the presented theories and techniques. In addition, the book discusses important nonlinear problems in many fields of science and engineering, providing information as to how they can serve as computing projects across various disciplines. Requiring only a preliminary understanding of analysis, Numerical Analysis of Partial Differential Equations is suitable for courses on numerical PDEs at the upper-undergraduate and graduate levels. The book is also appropriate for students majoring in the mathematical sciences and engineering.
The rapid development of high speed digital computers and the increasing desire for numerical answers to applied problems have led to increased demands in the courses dealing with the methods and techniques of numerical analysis. Numerical methods have always been useful but their role in the present-day scientific research has become prominent. For example, they enable one to find the roots of transcendental equations and in solving nonlinear differential equations. Indeed, they give the solution when ordinary analytical methods fail. This well-organized and comprehensive text aims at enhancing and strengthening numerical methods concepts among students using C++ programming, a fast emerging preferred programming language among software developers. The book provides an synthesis of both theory and practice. It focuses on the core areas of numerical analysis including algebraic equations, interpolation, boundary value problem, and matrix eigenvalue problems. The mathematical concepts are supported by a number of solved examples. Extensive self-review exercises and answers are provided at the end of each chapter to help students review and reinforce the key concepts. KEY FEATURES : C++ programs are provided for all numerical methods discussed. More than 400 unsolved problems and 200 solved problems are included to help students test their grasp of the subject. The book is intended for undergraduate and postgraduate students of Mathematics, Engineering and Statistics. Besides, students pursuing BCA and MCA and having Numerical Methods with C++ Programming as a subject in their course will benefit from this book.
Numerical Recipes: The Art of Scientific Computing was first published in 1986 and became an instant classic among scientists, engineers, and social scientists. In this book the original, time-tested programs have been completely reworked into a clear, consistent Pascal style. This represents a significant improvement to the immensely successful programs contained in the first edition, which were originally written in Fortran. The authors make extensive use of pointers, dynamic memory allocation, and other features utilized by this language. The explanatory text accompanying the programs replicates the lucid, and easy-to-read prose found in the original version, and incorporates corrections, improvements, and explanations of special Pascal features. The product of a unique collaboration among four leading scientists in academic research and industry, Numerical Recipes in Pascal fills a long-recognized need for a practical, comprehensive handbook of scientific computing in the Pascal language. The book is designed both for the Pascal programmer who wants exposure to the techniques of scientific computing, and for the working scientist, social scientist, and engineer. The scope of the book ranges from standard areas of numerical analysis (linear algebra, differential equations, roots) through subjects useful to signal processing (Fourier methods, filtering), data analysis (least squares, robust fitting, statistical functions), simulation (random deviates and Monte Carlo), and more. The lively, informal text combined with an underlying degree of mathematical sophistication makes the book useful to a wide range of readers, beginning at the advanced undergraduate level.
In the last hundred years, the philosophy of natural law has suffered a fate that could hardly have been envisaged by the seventeenth and eighteenth century exponents of its universality and eternity: it has become old-fashioned. The positivists and the Marxists were happy to throw eternal moral ity out of the window, confident that some magic temporal harmony would eventually follow Progress in by the front door. Their hopes may not have been fully realized, but they did succeed in discrediting natural law. What is often not appreciated is the extent to which we have adopted the tenets of the philosophy they despised, borh in the field of politics, and in the field of personal and social ethics, which Barbeyrac called "la science des mreurs" and which the positivists re christened "social science". Consequently, though we live in a world whose freedom, such as it is, is largely a result of the popularization of the philosophy of natural law, and whose conscious and unconscious standards, such as they are, are a result of that philosophy as it became combined with Christianity, the doctrine of natural law is itself for gotten. In view of the oblivion into which it has fallen, natural law is a concept which means little to the average reader. All too often, Montesquieu scholars have traded on this oblivion in order to give an exaggerated picture of his originality.
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