Picture 1 of 1
Stock photo
Picture 1 of 1
Stock photo
Symmetry in Mechanics : A Gentle, Modern Introduction by Stephanie Frank Singer (2001, Trade Paperback)
ZUBER (277349)
98.2% positive feedback
Price:
US $59.95
ApproximatelyC $83.74
+ $14.81 shipping
Returns:
30 days return. Buyer pays for return shipping. If you use an eBay shipping label, it will be deducted from your refund amount.
Condition:
- Buy It NowSYMMETRY IN MECHANICS: A GENTLE, MODERN INTRODUCTION By Stephanie Frank Singer
Oops! Looks like we're having trouble connecting to our server.
Refresh your browser window to try again.
About this product
Product Identifiers
PublisherBirkhäuser Boston
ISBN-100817641459
ISBN-139780817641450
eBay Product ID (ePID)1863768
Product Key Features
Number of PagesXii, 193 Pages
Publication NameSymmetry in Mechanics : a Gentle, Modern Introduction
LanguageEnglish
SubjectGroup Theory, Geometry / Differential, Mechanics / General, Topology, Applied
Publication Year2001
TypeTextbook
Subject AreaMathematics, Science
AuthorStephanie Frank Singer
FormatTrade Paperback
Dimensions
Item Height0.2 in
Item Weight16 Oz
Item Length9.3 in
Item Width6.1 in
Additional Product Features
Intended AudienceScholarly & Professional
LCCN00-049398
Dewey Edition21
Reviews"Symmetry in Mechanics is directed to students at the undergraduate level and beyond, and offers a lovely presentation of the subject . . . The first chapter presents a standard derivation of the equations for two-body planetary motion. Kepler's laws are then obtained and the rule of conservation laws is emphasized. . . . Singer uses this example from classical physics throughout the book as a vehicle for explaining the concepts of differential geometry and for illustrating their use. These ideas and techniques will allow the reader to understand advanced texts and research literature in which considerably more difficult problems are treated and solved by identical or related methods. The book contains 122 student exercises, many of which are solved in an appendix. The solutions, especially, are valuable for showing how a mathematician approaches and solves specific problems. Using this presentation, the book removes some of the language barriers that divide the worlds of mathematics and physics." --Physics Today "This is a very interesting book. Those educated in traditional mechanics will acquire [from reading it] knowledge of modern mathematics hidden beyond traditional concepts in the realm of celestial mechanics, [and] . . . pure mathematicians will understand how their discipline enters into practical problems. The author shows how fundamental concepts of symplectic geometry implicitly occur in mechanics . . . the mathematical presentation is ingenious and subtle. There are a lot of exercises for the reader and the solutions of most of them are given in a separate chapter. I can highly recommend this book to undergraduate and PhD students . . . it is ideally suited for teaching a course on the subject." --Mathematical Reviews
Number of Volumes1 vol.
IllustratedYes
Dewey Decimal531
Table Of Content0 Preliminaries.- 1 The Two-Body Problem.- 2 Phase Spaces are Symplectic Manifolds.- 3 Differential Geometry.- 4 Total Energy Functions are Hamiltonian Functions.- 5 Symmetries are Lie Group Actions.- 6 Infinitesimal Symmetries are Lie Algebras.- 7 Conserved Quantities are Momentum Maps.- 8 Reduction and The Two-Body Problem.- Recommended Reading.- Solutions.- References.
Synopsis[see attached for complete text] Recent years have seen the appearance of several books bridging the gap between mathematics and physics; most are aimed at the graduate level and above. {\it Symmetry in Mechanics: A Gentle, Modern Introduction} is geared towards a broad audience, requiring only competency in multivariable calculus, linear algebra, and introductory physics. This work was written with two goals in mind: to chip away at the language barrier between physicists and mathematicians and to link the abstract constructions of symplectic to concrete, explicitly calculated examples. The context is a careful exposition of the two-body problem, namely, the derivation of Kepler's laws of planetary motion from Newton's laws of gravitation. Key features of this work include:· straightforward and elementary presentation of the derivation of Kepler's laws in the language of vector calculus,· short historical introduction to the subject,· gentle introduction to symplectic manifolds, Hamiltonian flows, Lie group actions, Lie algebras, momentum maps, and symplectic reduction with many examples, exercises, and solutions,· cyclical treatment of material---book ends with the derivation it started with, in the language of symplectic and differential geometry. For the student, mathematician or physicist who has noticed that symmetry yields simplification and wants to know why, this book will be a rewarding experience. The book is an excellent resource for self-study or classroom use at the undergraduate level, requiring only competency in multivariable calculus, linear algebra and introductory physics., [see attached for complete text] Recent years have seen the appearance of several books bridging the gap between mathematics and physics; most are aimed at the graduate level and above. {\it Symmetry in Mechanics: A Gentle, Modern Introduction} is geared towards a broad audience, requiring only competency in multivariable calculus, linear algebra, and introductory physics. This work was written with two goals in mind: to chip away at the language barrier between physicists and mathematicians and to link the abstract constructions of symplectic to concrete, explicitly calculated examples. The context is a careful exposition of the two-body problem, namely, the derivation of Kepler's laws of planetary motion from Newton's laws of gravitation. Key features of this work include: - straightforward and elementary presentation of the derivation of Kepler's laws in the language of vector calculus, - short historical introduction to the subject, - gentle introduction to symplectic manifolds, Hamiltonian flows, Lie group actions, Lie algebras, momentum maps, and symplectic reduction with many examples, exercises, and solutions, - cyclical treatment of material---book ends with the derivation it started with, in the language of symplectic and differential geometry. For the student, mathematician or physicist who has noticed that symmetry yields simplification and wants to know why, this book will be a rewarding experience. The book is an excellent resource for self-study or classroom use at the undergraduate level, requiring only competency in multivariable calculus, linear algebra and introductory physics., "And what is the use," thought Alice, "of a book without pictures or conversations in it?" -Lewis Carroll This book is written for modem undergraduate students - not the ideal stu dents that mathematics professors wish for (and who occasionally grace our campuses), but the students like many the author has taught: talented but ap preciating review and reinforcement of past course work; willing to work hard, but demanding context and motivation for the mathematics they are learning. To suit this audience, the author eschews density of topics and efficiency of presentation in favor of a gentler tone, a coherent story, digressions on mathe maticians, physicists and their notations, simple examples worked out in detail, and reinforcement of the basics. Dense and efficient texts play a crucial role in the education of budding (and budded) mathematicians and physicists. This book does not presume to improve on the classics in that genre. Rather, it aims to provide those classics with a large new generation of appreciative readers. This text introduces some basic constructs of modern symplectic geometry in the context of an old celestial mechanics problem, the two-body problem. We present the derivation of Kepler's laws of planetary motion from Newton's laws of gravitation, first in the style of an undergraduate physics course, and x Preface then again in the language of symplectic geometry. No previous exposure to symplectic geometry is required: we introduce and illustrate all necessary con structs., "And what is the use," thought Alice, "of a book without pictures or conversations in it?" -Lewis Carroll This book is written for modem undergraduate students - not the ideal stu- dents that mathematics professors wish for (and who occasionally grace our campuses), but the students like many the author has taught: talented but ap- preciating review and reinforcement of past course work; willing to work hard, but demanding context and motivation for the mathematics they are learning. To suit this audience, the author eschews density of topics and efficiency of presentation in favor of a gentler tone, a coherent story, digressions on mathe- maticians, physicists and their notations, simple examples worked out in detail, and reinforcement of the basics. Dense and efficient texts play a crucial role in the education of budding (and budded) mathematicians and physicists. This book does not presume to improve on the classics in that genre. Rather, it aims to provide those classics with a large new generation of appreciative readers. This text introduces some basic constructs of modern symplectic geometry in the context of an old celestial mechanics problem, the two-body problem. We present the derivation of Kepler's laws of planetary motion from Newton's laws of gravitation, first in the style of an undergraduate physics course, and x Preface then again in the language of symplectic geometry. No previous exposure to symplectic geometry is required: we introduce and illustrate all necessary con- structs.
LC Classification NumberQA252.3
