Author: Kishore Marathe
Publisher: Springer Science & Business Media
View: 2384As many readers will know, the 20th century was a time when the fields of mathematics and the sciences were seen as two separate entities. Caused by the rapid growth of the physical sciences and an increasing abstraction in mathematical research, each party, physicists and mathematicians alike, suffered a misconception; not only of the opposition’s theoretical underpinning, but of how the two subjects could be intertwined and effectively utilized. One sub-discipline that played a part in the union of the two subjects is Theoretical Physics. Breaking it down further came the fundamental theories, Relativity and Quantum theory, and later on Yang-Mills theory. Other areas to emerge in this area are those derived from the works of Donaldson, Chern-Simons, Floer-Fukaya, and Seiberg-Witten. Aimed at a wide audience, Physical Topics in Mathematics demonstrates how various physical theories have played a crucial role in the developments of Mathematics and in particular, Geometric Topology. Issues are studied in great detail, and the book steadfastly covers the background of both Mathematics and Theoretical Physics in an effort to bring the reader to a deeper understanding of their interaction. Whilst the world of Theoretical Physics and Mathematics is boundless; it is not the intention of this book to cover its enormity. Instead, it seeks to lead the reader through the world of Physical Mathematics; leaving them with a choice of which realm they wish to visit next.
Author: P.G. Harper,D. L. Weaire
Publisher: CUP Archive
View: 7758Directed primarily at college and university undergraduates, this book covers at basic level the essential applications of mathematics to the physical sciences. It contains all the usual topics covered in a first-year course such as vectors, matrices, differential equations, basic mathematical functions and their analysis, and power series. There is a strong emphasis on qualitative understanding (such as curve sketching) and practical methods of solution. The latter take due account of the impact of computers on the subject. The principles of mathematical expression are illustrated by copious examples taken from a wide range of topics in physics and chemistry. Each of the short chapters concludes with a summary and a large number of problems.
Author: CTI Reviews
Publisher: Cram101 Textbook Reviews
View: 5926Facts101 is your complete guide to Physical Mathematics. In this book, you will learn topics such as as those in your book plus much more. With key features such as key terms, people and places, Facts101 gives you all the information you need to prepare for your next exam. Our practice tests are specific to the textbook and we have designed tools to make the most of your limited study time.
Author: Yvonne Choquet-Bruhat,Cécile DeWitt-Morette,Margaret Dillard Bleick
Publisher: Gulf Professional Publishing
View: 2930This reference book, which has found wide use as a text, provides an answer to the needs of graduate physical mathematics students and their teachers. The present edition is a thorough revision of the first, including a new chapter entitled ``Connections on Principle Fibre Bundles'' which includes sections on holonomy, characteristic classes, invariant curvature integrals and problems on the geometry of gauge fields, monopoles, instantons, spin structure and spin connections. Many paragraphs have been rewritten, and examples and exercises added to ease the study of several chapters. The index includes over 130 entries.
Volume I: Physical, Mathematical, and Numerical Principles
Author: Gerhard Beutler
Publisher: Springer Science & Business Media
View: 5560G. Beutler's Methods of Celestial Mechanics is a coherent textbook for students as well as an excellent reference for practitioners. The first volume gives a thorough treatment of celestial mechanics and presents all the necessary mathematical details that a professional would need. The reader will appreciate the well-written chapters on numerical solution techniques for ordinary differential equations, as well as that on orbit determination. In the second volume applications to the rotation of earth and moon, to artificial earth satellites and to the planetary system are presented. The author addresses all aspects that are of importance in high-tech applications, such as the detailed gravitational fields of all planets and the earth, the oblateness of the earth, the radiation pressure and the atmospheric drag. The concluding part of this monumental treatise explains and details state-of-the-art professional and thoroughly-tested software for celestial mechanics.
How Mathematical Rules Can be Positively Bent
Author: Alberto A. Martinez
Publisher: Princeton University Press
View: 6348A student in class asks the math teacher: "Shouldn't minus times minus make minus?" Teachers soon convince most students that it does not. Yet the innocent question brings with it a germ of mathematical creativity. What happens if we encourage that thought, odd and ungrounded though it may seem? Few books in the field of mathematics encourage such creative thinking. Fewer still are engagingly written and fun to read. This book succeeds on both counts. Alberto Martinez shows us how many of the mathematical concepts that we take for granted were once considered contrived, imaginary, absurd, or just plain wrong. Even today, he writes, not all parts of math correspond to things, relations, or operations that we can actually observe or carry out in everyday life. Negative Math ponders such issues by exploring controversies in the history of numbers, especially the so-called negative and "impossible" numbers. It uses history, puzzles, and lively debates to demonstrate how it is still possible to devise new artificial systems of mathematical rules. In fact, the book contends, departures from traditional rules can even be the basis for new applications. For example, by using an algebra in which minus times minus makes minus, mathematicians can describe curves or trajectories that are not represented by traditional coordinate geometry. Clear and accessible, Negative Math expects from its readers only a passing acquaintance with basic high school algebra. It will prove pleasurable reading not only for those who enjoy popular math, but also for historians, philosophers, and educators. Key Features: Uses history, puzzles, and lively debates to devise new mathematical systems Shows how departures from rules can underlie new practical applications Clear and accessible Requires a background only in basic high school algebra
The Bar-Hillel Colloquium: Studies in History, Philosophy, and Sociology of Science
Author: Edna Ullmann-Margalit
Publisher: Springer Science & Business Media
View: 4103The volume before us is the fourth in the series of proceedings of what used to be the Israel Colloquium for the History, Philosophy and Sociology of Science. This Colloquium has in the meantime been renamed. It now bears the name of Yehoshua Bar-Hillel (1915-1975). Bar-Hillel was an eminent philosopher of science, language, and cognition, as well as a fearless fighter for enlightenment and a passionate teacher who had a durable influence on Israeli philosophical life. The essays collected in this volume have of course this much in common, that they are all in, of, and pertaining to science. They also share the property of having all been delivered before live, and often lively, audiences in Jerusalem and in Tel Aviv, in the years 1984-1986. As is customary in the volumes of this series, the essays and commentaries presented here are intended to strike a rather special balance between the disciplines to which the Colloquium is dedicated. The historical and sociological vantage point is addressed in Kramnick's and Mali's treatment of Priestley, in Vickers' and Feldhay's studies of the Renaissance occult, and in Warnke's and Barasch's work on the imagination. From a philosophical angle several concepts, all material to the methodology of science, are taken up: rule following, by Smart and Margalit; analysis, by Ackerman; explanation, by Taylor; and the role of mathematics in physics, by Levy-Leblond and Pitowsky.
Author: Robert G. Mortimer
View: 7368Mathematics for Physical Chemistry, Third Edition, is the ideal text for students and physical chemists who want to sharpen their mathematics skills. It can help prepare the reader for an undergraduate course, serve as a supplementary text for use during a course, or serve as a reference for graduate students and practicing chemists. The text concentrates on applications instead of theory, and, although the emphasis is on physical chemistry, it can also be useful in general chemistry courses. The Third Edition includes new exercises in each chapter that provide practice in a technique immediately after discussion or example and encourage self-study. The first ten chapters are constructed around a sequence of mathematical topics, with a gradual progression into more advanced material. The final chapter discusses mathematical topics needed in the analysis of experimental data. * Numerous examples and problems interspersed throughout the presentations * Each extensive chapter contains a preview, objectives, and summary * Includes topics not found in similar books, such as a review of general algebra and an introduction to group theory * Provides chemistry specific instruction without the distraction of abstract concepts or theoretical issues in pure mathematics
Mathematically Modeling the Most Everyday of Physical Phenomena
Author: Martin H. Krieger
Publisher: University of Chicago Press
View: 5691In this insightful work, Martin H. Krieger shows what physicists are really doing when they employ mathematical models as research tools. He argues that the technical details of these complex calculations serve not only as a means to an end, but also reveal key aspects of the physical properties they model. Krieger's lucid discussions will help readers to appreciate the larger physical issues behind the mathematical detail of modern physics and gain deeper insights into how theoretical physicists work. Constitutions of Matter is a rare, behind-the-scenes glimpse into the world of modern physics. "[Krieger] provides students of physics and applied mathematics with a view of the physical forest behind the mathematical trees, historians and philosophers of science with insights into how theoretical physicists go about their work, and technically advanced general readers with a glimpse into the discipline."—Scitech Book News
Author: Oliver Heaviside
Publisher: American Mathematical Soc.
View: 5934Oliver Heaviside is probably best known to the majority of mathematicians for the Heaviside function in the theory of distribution. However, his main research activity concerned the theory of electricity and magnetism, the area in which he worked for most of his life. Results of this work are presented in his fundamental three-volume ""Electromagnetic Theory"". The book brings together many of Heaviside's published and unpublished notes and short articles written between 1891 and 1912. One of Heaviside's main achievements was the recasting of Maxwell's theory of electromagnetism into the form currently used by everyone. He is also known for the invention of operational calculus and for major contributions to solving theoretical and practical problems of cable and radio communication.All this is collected in three volumes of ""Electromagnetic Theory"". However, there is even more. For example, Chapter V in Volume II discusses the age of Earth, and several sections in Volume III talk about the teaching of mathematics in school. In addition to Heaviside's writings, two detailed surveys of Heaviside's work, by Sir Edmund Whittaker and by B. A. Behrend, are included in Volume I, and a long account of Heaviside's unpublished notes (which he presumably planned to publish as Volume IV of ""Electromagnetic Theory"") is included in Volume III.
Author: Herbert S Wilf
Publisher: Courier Corporation
View: 7326Topics include vector spaces and matrices; orthogonal functions; polynomial equations; asymptotic expansions; ordinary differential equations; conformal mapping; and extremum problems. Includes exercises and solutions. 1962 edition.
Science, Life and Turbulent Times 1868-1951
Author: Michael Eckert
Publisher: Springer Science & Business Media
View: 9047The subject of the book is a biography of the theoretical physicist Arnold Sommerfeld (1868-1951). Although Sommerfeld is famous as a quantum theorist for the elaboration of the semi-classical atomic theory (Bohr-Sommerfeld model, Sommerfeld's fine-structure constant), his role in the history of modern physics is not confined to atoms and quanta. Sommerfeld left his mark in the history of mathematics, fluid mechanics, a number of physical subdisciplines and, in particular, as founder of a most productive "school" (Peter Debye, Wolfgang Pauli, Werner Heisenberg, Linus Pauling and Hans Bethe were his pupils, to name only the Nobel laureates among them). This biography is to a large extent based on primary source material (correspondence, diaries, unpublished manuscripts). It should be of particular interest to students who are keen to know more about the historical roots of modern science. Sommerfeld lived through turbulent times of German history (Wilhelmian Empire, Weimar Republic, Nazi period). His life, therefore, illustrates how science and scientists perform in changing social environments. From this perspective, the biography should also attract readers with a general interest in the history of science and technology.