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This book stresses the similarities between apparently quite different areas of physics, tying together similar phenomena wherever they may appear in mechanics, acoustics, optics, electricity, heat, or theoretical physics. Intended as an aid to learning and understanding for undergraduate students, it will undoubtedly be useful to their teachers and will appeal to older physicists.

HARDCOVER Very Good - Crisp, clean, unread book with some shelfwear/edgewear, may have a remainder mark - NICE Standard-sized.

The aim of this book is to provide a systematic and practical account of methods of integration of ordinary and partial differential equations based on invariance under continuous (Lie) groups of trans­ formations. The goal of these methods is the expression of a solution in terms of quadrature in the case of ordinary differential equations of first order and a reduction in order for higher order equations. For partial differential equations at least a reduction in the number of independent variables is sought and in favorable cases a reduction to ordinary differential equations with special solutions or quadrature. In the last century, approximately one hundred years ago, Sophus Lie tried to construct a general integration theory, in the above sense, for ordinary differential equations. Following Abel's approach for algebraic equations he studied the invariance of ordinary differential equations under transformations. In particular, Lie introduced the study of continuous groups of transformations of ordinary differential equations, based on the infinitesimal properties of the group. In a sense the theory was completely successful. It was shown how for a first-order differential equation the knowledge of a group leads immediately to quadrature, and for a higher order equation (or system) to a reduction in order. In another sense this theory is somewhat disappointing in that for a first-order differ­ ential equation essentially no systematic way can be given for finding the groups or showing that they do not exist for a first-order differential equation.

The aim of this book is to provide a systematic and practical account of methods of integration of ordinary and partial differential equations based on invariance under continuous (Lie) groups of trans­ formations. The goal of these methods is the expression of a solution in terms of quadrature in the case of ordinary differential equations of first order and a reduction in order for higher order equations. For partial differential equations at least a reduction in the number of independent variables is sought and in favorable cases a reduction to ordinary differential equations with special solutions or quadrature. In the last century, approximately one hundred years ago, Sophus Lie tried to construct a general integration theory, in the above sense, for ordinary differential equations. Following Abel's approach for algebraic equations he studied the invariance of ordinary differential equations under transformations. In particular, Lie introduced the study of continuous groups of transformations of ordinary differential equations, based on the infinitesimal properties of the group. In a sense the theory was completely successful. It was shown how for a first-order differential equation the knowledge of a group leads immediately to quadrature, and for a higher order equation (or system) to a reduction in order. In another sense this theory is somewhat disappointing in that for a first-order differ­ ential equation essentially no systematic way can be given for finding the groups or showing that they do not exist for a first-order differential equation.

Paperback: 542 pages Publisher: American Bible Society (December 31, 2007) Language: English ISBN-10: 8884983746 ISBN-13: 978-8884983749 Product Dimensions: 1.3 x 6.4 x 9.1 inches Shipping Weight: 2 pounds

Middle Grades Mathematics Project Reproducible worksheets, teacher instruction models, review problems, a unit test, and complete answers are included. This National Science Foundation-funded teacher resource helps develop problem-solving and critical-thinking skills. Interest Level: 5-8

Similarity and analogy are fundamental in human cognition. They are crucial for recognition and classification, and have been associated with scientific discovery and creativity. Any adequate understanding of similarity and analogy requires the integration of theory and data from diverse domains. This interdisciplinary volume explores current development in research and theory from psychological, computational, and educational perspectives, and considers their implications for learning and instruction. The distinguished contributors examine the psychological processes involved in reasoning by similarity and analogy, the computational problems encountered in simulating analogical processing in problem solving, and the conditions promoting the application of analogical reasoning in everyday situations.

In the 1950s, John Reber convinced many Californians that the best way to solve the state's water shortage problem was to dam up the San Francisco Bay. Against massive political pressure, Reber's opponents persuaded lawmakers that doing so would lead to disaster. They did this not by empirical measurement alone, but also through the construction of a model. Simulation and Similarity explains why this was a good strategy while simultaneously providing an account of modeling and idealization in modern scientific practice. Michael Weisberg focuses on concrete, mathematical, and computational models in his consideration of the nature of models, the practice of modeling, and nature of the relationship between models and real-world phenomena. In addition to a careful analysis of physical, computational, and mathematical models, Simulation and Similarity offers a novel account of the model/world relationship. Breaking with the dominant tradition, which favors the analysis of this relation through logical notions such as isomorphism, Weisberg instead presents a similarity-based account called weighted feature matching. This account is developed with an eye to understanding how modeling is actually practiced. Consequently, it takes into account the ways in which scientists' theoretical goals shape both the applications and the analyses of their models.

Nonlinearity plays a major role in the understanding of most physical, chemical, biological, and engineering sciences. Nonlinear problems fascinate scientists and engineers, but often elude exact treatment. However elusive they may be, the solutions do exist-if only one perseveres in seeking them out.Self-Similarity and Beyond presents a myriad of approaches to finding exact solutions for a diversity of nonlinear problems. These include group-theoretic methods, the direct method of Clarkson and Kruskal, traveling waves, hodograph methods, balancing arguments, embedding special solutions into a more general class, and the infinite series approach.The author's approach is entirely constructive. Numerical solutions either motivate the analysis or confirm it, therefore they are treated alongside the analysis whenever possible. Many examples drawn from real physical situations-primarily fluid mechanics and nonlinear diffusion-illustrate and emphasize the central points presented.Accessible to a broad base of readers, Self-Similarity and Beyond illuminates a variety of productive methods for meeting the challenges of nonlinearity. Researchers and graduate students in nonlinearity, partial differential equations, and fluid mechanics, along with mathematical physicists and numerical analysts, will re-discover the importance of exact solutions and find valuable additions to their mathematical toolkits.

Finally back in print, Any Similarity... is a collection of Drew and Josh Alan Friedman's earliest comic strips and illustrations, featuring Drew's most obsessively stippled black-and-white panels and his most hilarious wise-guy takes on the stars and demi-stars and never-quite-stars of that swamp we like to call showbiz. Drew is the kind of pop-culture aficionado whose Three Stooges worship is focused not on Moe, Larry or Curly but on Shemp (whose unmistakable mug graces the new cover of this edition), and whose teasing adoration can often be mistaken for mockery or contempt. Who but a worshipful fan would lavish quite so many dots on the loving delineation of these greats' every pimple and wrinkle?

Finally back in print, Any Similarity... is a collection of Drew and Josh Alan Friedman's earliest comic strips and illustrations, featuring Drew's most obsessively stippled black-and-white panels and his most hilarious wise-guy takes on the stars and demi-stars and never-quite-stars of that swamp we like to call showbiz. Drew is the kind of pop-culture aficionado whose Three Stooges worship is focused not on Moe, Larry or Curly but on Shemp (whose unmistakable mug graces the new cover of this edition), and whose teasing adoration can often be mistaken for mockery or contempt. Who but a worshipful fan would lavish quite so many dots on the loving delineation of these greats' every pimple and wrinkle?

Nonlinearity plays a major role in the understanding of most physical, chemical, biological, and engineering sciences. Nonlinear problems fascinate scientists and engineers, but often elude exact treatment. However elusive they may be, the solutions do exist-if only one perseveres in seeking them out.Self-Similarity and Beyond presents a myriad of approaches to finding exact solutions for a diversity of nonlinear problems. These include group-theoretic methods, the direct method of Clarkson and Kruskal, traveling waves, hodograph methods, balancing arguments, embedding special solutions into a more general class, and the infinite series approach.The author's approach is entirely constructive. Numerical solutions either motivate the analysis or confirm it, therefore they are treated alongside the analysis whenever possible. Many examples drawn from real physical situations-primarily fluid mechanics and nonlinear diffusion-illustrate and emphasize the central points presented.Accessible to a broad base of readers, Self-Similarity and Beyond illuminates a variety of productive methods for meeting the challenges of nonlinearity. Researchers and graduate students in nonlinearity, partial differential equations, and fluid mechanics, along with mathematical physicists and numerical analysts, will re-discover the importance of exact solutions and find valuable additions to their mathematical toolkits.

Clustering and tree models are being widely used in the social and biological sciences to analyze similarity relations. This volume describes how matrices of similarities or associations among entities can be modelled using trees, and explains some of the issues that arise in performing such analyses and interpreting the results correctly. James E Corter distinguishes ultrametric trees from additive trees and discusses how specific aspects of each type of tree can be interpreted through the use of applications as examples. He concludes with a discussion of when tree models might be preferable to spatial geometric models.

This book explores the importance of cross-linguistic similarity in foreign language learning. While linguists have primarily focussed upon differences between languages, learners strive to make use of any similarities to prior linguistic knowledge they can perceive. The role of positive transfer is emphasized as well as the essential differences between comprehension and production. In comprehension of related languages, cross-linguistic similarities are easily perceived while in comprehension of distant languages they are merely assumed. Production may be based on previous perception of similarities, but frequently similarities are here merely assumed. Initially, effective learning is based on quick establishment of cross-linguistic one-to-one relations between individual items. As learning progresses, the learner learns to modify such oversimplified relations. The book describes the ways in which transfer affects different areas of language, taking account of the differences between learning a language perceived to be similar and a language where few or no cross-linguistic similarities can be established.

Scaling (power-type) laws reveal the fundamental property of the phenomena--self similarity. Self-similar (scaling) phenomena repeat themselves in time and/or space. The property of self-similarity simplifies substantially the mathematical modeling of phenomena and its analysis--experimental, analytical and computational. The book begins from a non-traditional exposition of dimensional analysis, physical similarity theory and general theory of scaling phenomena. Classical examples of scaling phenomena are presented. It is demonstrated that scaling comes on a stage when the influence of fine details of initial and/or boundary conditions disappeared but the system is still far from ultimate equilibrium state (intermediate asymptotics). It is explained why the dimensional analysis as a rule is insufficient for establishing self-similarity and constructing scaling variables. Important examples of scaling phenomena for which the dimensional analysis is insufficient (self-similarities of the second kind) are presented and discussed. A close connection of intermediate asymptotics and self-similarities of the second kind with a fundamental concept of theoretical physics, the renormalization group, is explained and discussed. Numerous examples from various fields--from theoretical biology to fracture mechanics, turbulence, flame propagation, flow in porous strata, atmospheric and oceanic phenomena are presented for which the ideas of scaling, intermediate asymptotics, self-similarity and renormalization group were of decisive value in modeling.

In the 1950s, John Reber convinced many Californians that the best way to solve the state's water shortage problem was to dam up the San Francisco Bay. Against massive political pressure, Reber's opponents persuaded lawmakers that doing so would lead to disaster. They did this not by empirical measurement alone, but also through the construction of a model. Simulation and Similarity explains why this was a good strategy while simultaneously providing an account of modeling and idealization in modern scientific practice. Michael Weisberg focuses on concrete, mathematical, and computational models in his consideration of the nature of models, the practice of modeling, and nature of the relationship between models and real-world phenomena. In addition to a careful analysis of physical, computational, and mathematical models, Simulation and Similarity offers a novel account of the model/world relationship. Breaking with the dominant tradition, which favors the analysis of this relation through logical notions such as isomorphism, Weisberg instead presents a similarity-based account called weighted feature matching. This account is developed with an eye to understanding how modeling is actually practiced. Consequently, it takes into account the ways in which scientists' theoretical goals shape both the applications and the analyses of their models.

Finally back in print, this collection of Drew Friedman's earliest comic strips and illustrations features his most obsessively stippled black-and-white panels and his most hilarious wise-guy takes on the stars and demi-stars and never-quite-stars of that swamp we like to call showbiz.

Unread book in perfect condition.

In this book, Dr. Jerald Dirks explores the similarities and contrasts among Judaism, Christianity, and Islam. Using the analogy of a tree, he notes that each of the three Abrahamic faiths claims to be the one, true, vertical extension of a trunk of primary revelation, with the other two religions being seen as lateral branches that deviate from the true verticality of the original trunk. Working within the framework of this metaphor, Dr. Dirks focuses on a series of topics, including his own journey from Christianity to Islam, the extensive common ground that is to be found among the three faiths, the basic differences that separate Islam and Christianity, the issue of religious pluralism in a global world, Islamophobia in the Christian West, and the role of women in the scriptures and foundational texts of the three religions. Along the way, he exposes and corrects numerous myths about the faiths, myths that are too often accepted as common knowledge. Dr. Dirks concludes by calling for a reconciliation among the faiths that embraces and celebrates the commonalities to be found among them and that honestly and respectfully acknowledges their differences. About the author -- Dr. Jerald F. Dirks holds B.A. and M. Divinity from Harvard University and doctorate in Psychology from the University of Denver. He is a former ordained minister (deacon) in the United Methodist Church and is author of The Cross & The Crescent and Abraham - The Friend of God. He published over sixty articles in the field of clinical psychology and over one hundred and fifty articles on Arabian horses. He has traveled extensively in the Middle East and interacted widely with the Muslim communities in the United States.

Finally, the truth...about Jesus and Muhammad This provocative book presents a factual analysis of the two most influential men of all time-Jesus, the founder of Christianity, with 2 billion adherents, and Muhammad, the founder of Islam, with 1.3 billion followers. Dr. Mark A. Gabriel allows you to walk side by side with Jesus and Muhammad from their births to their deaths. You will discover that both were prophesied over as children, endorsed by their cousins, rejected by their hometowns, and assisted by twelve disciples. With an understanding of their biographies, you are prepared to compare their teachings, including: ·How they described themselves ·How they responded to challenges from Jews ·The healings and miracles they performed ·Guidelines for acceptable prayer ·When to fight an enemy ·What they taught about women Dr. Gabriel's balanced historical comparison will shatter false images and give you new insight into the influence of Jesus and Muhammad in the world today.