Authors:
- A geometric approach to problems in physics, many of which cannot be solved by any other methods
- Text is enriched with good examples and exercises at the end of every chapter
- Fine for a course or seminar directed at grad and adv. undergrad students interested in elliptic and hyperbolic differential equations, differential geometry, calculus of variations, quantum mechanics, and physics
Part of the book series: Applied and Numerical Harmonic Analysis (ANHA)
Buy it now
Buying options
Tax calculation will be finalised at checkout
Other ways to access
This is a preview of subscription content, log in via an institution to check for access.
Table of contents (12 chapters)
-
Front Matter
-
Back Matter
About this book
Differential geometry techniques have very useful and important applications in partial differential equations and quantum mechanics. This work presents a purely geometric treatment of problems in physics involving quantum harmonic oscillators, quartic oscillators, minimal surfaces, and Schrödinger's, Einstein's and Newton's equations.
Geometric Mechanics on Riemannian Manifolds is a fine text for a course or seminar directed at graduate and advanced undergraduate students interested in elliptic and hyperbolic differential equations, differential geometry, calculus of variations, quantum mechanics, and physics. The text is enriched with good examples and exercises at the end of every chapter. It is also an ideal resource for pure and applied mathematicians and theoretical physicists working in these areas.
Reviews
"...This book, which contains some very interesting ideas and results, is primarily oriented towards graduate or advanced undergraduate students in mathematics and theoretical physics with interests in differential geometry, the calculus of variations and the study of PDE's, as well as in classical and quantum mechanics. In addition, for more experienced researchers in these fields, it may be a useful resource, written in a style that makes it easily accessible to a wide audience..." --- Mathematical Reviews
"The differential operators which are treated in the book are among the most important, not only in the theory of partial differential equation, but they appear naturally in geometry, mechanics or theoretical physics (especially quantum mechanics). Thus, the book should be of interest for anyone working in these fields, from advanced undergraduate students to experts. The book is written in a very pedagogical manner and does not assume many prerequisites, therefore it is quite appropriate to be used for special courses or for self-study. I have to mention that all chapters end with a number of well-chosen exercises that will imporve the understanding of the material and, also, that there are a lot of worked examples that will serve the same purpose." ---Mathematics Vol. L, No. 4
"The book is well written and contains a wealth of material. The authors make a concerted effort to simplify proofs taken from many sources [so] researchers will readily fin dthe infromations they seek, while students can develop their skills by filling in details of proofs, as well as by using the problem sets that end each chapter. The book provides the reader with an in-depth introduction to a rich and rapidly developing research area that has already produced remarkable results.
This book contains old and new basic results from a significant part of the modern theory of partial differential equations on Riemannian manifolds. All results are presented in an elementary way. Only a basic knowledge of basic functional analysis, mechanics and analysis is assumed. The book is well written and contains a wealth of material …. To conclude, this book provides the reader with an in-depth introduction to a rich and rapidly developing research area that has already produced remarkable results." ---Zentralblatt MATH
Authors and Affiliations
-
Department of Mathematics, Eastern Michigan University, Ypsilanti, USA
Ovidiu Calin
-
Department of Mathematics, Georgetown University, Wahington, DC, USA
Der-Chen Chang
Bibliographic Information
Book Title: Geometric Mechanics on Riemannian Manifolds
Book Subtitle: Applications to Partial Differential Equations
Authors: Ovidiu Calin, Der-Chen Chang
Series Title: Applied and Numerical Harmonic Analysis
DOI: https://doi.org/10.1007/b138771
Publisher: Birkhäuser Boston, MA
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkhäuser Boston 2005
Hardcover ISBN: 978-0-8176-4354-6Published: 25 October 2004
eBook ISBN: 978-0-8176-4421-5Published: 15 March 2006
Series ISSN: 2296-5009
Series E-ISSN: 2296-5017
Edition Number: 1
Number of Pages: XVI, 278
Number of Illustrations: 26 b/w illustrations
Topics: Fourier Analysis, Differential Geometry, Partial Differential Equations, Mathematical Methods in Physics, Abstract Harmonic Analysis, Applications of Mathematics