Differentiable Manifolds
A First Course
Lawrence Conlon(Author)
Birkhauser Boston Inc (Publisher)
Published on 1. February 1994
Book
Hardback
XIII, 395 pages
978-0-8176-3626-5 (ISBN)
Article exhausted; check for reprint
Description
This book is based on the full year Ph.D. qualifying course on differentiable manifolds, global calculus, differential geometry, and related topics, given by the author at Washington University several times over a twenty year period. It is addressed primarily to second year graduate students and well prepared first year students. Presupposed is a good grounding in general topology and modern algebra, especially linear algebra and the analogous theory of modules over a commutative, unitary ring. Although billed as a "first course" , the book is not intended to be an overly sketchy introduction. Mastery of this material should prepare the student for advanced topics courses and seminars in differen tial topology and geometry. There are certain basic themes of which the reader should be aware. The first concerns the role of differentiation as a process of linear approximation of non linear problems. The well understood methods of linear algebra are then applied to the resulting linear problem and, where possible, the results are reinterpreted in terms of the original nonlinear problem. The process of solving differential equations (i. e., integration) is the reverse of differentiation. It reassembles an infinite array of linear approximations, result ing from differentiation, into the original nonlinear data. This is the principal tool for the reinterpretation of the linear algebra results referred to above.
More details
Series
Edition
1st ed. 1993. Corr. 2nd printing
Language
English
Place of publication
MA
United States
Target group
College/higher education
Professional and scholarly
Illustrations
2 s/w Abbildungen
23 illustrations
Dimensions
Height: 241 mm
Width: 167 mm
Weight
830 gr
ISBN-13
978-0-8176-3626-5 (9780817636265)
DOI
10.1007/978-1-4757-2284-0
Schweitzer Classification
Other editions
New editions

Lawrence Conlon
Differentiable Manifolds
Book
04/2001
2nd Edition
Birkhauser Boston Inc
€72.76
Article exhausted; check different version
Content
1. Topological Manifolds.- 2. Local Theory.- 3. Global Theory.- 4. Flows and Foliation.- 5. Lie Groups.- 6. Covectors and 1-Forms.- 7. Multilinear Algebra.- 8. Integration and Cohomology.- 9. Forms and Foliations.- 10. Riemannian Geometry.- Appendix A. Vector Fields on Spheres.- Appendix B. Inverse Function Theorem.- Appendix C. Ordinary Differential Equations.- C.1. Existence and uniqueness of solutions.- C.2. A digression concerning Banach spaces.- C.3. Smooth dependence on initial conditions.- C.4. The Linear Case.- Appendix D. Sard's Theorem.- Appendix E. de Rham-?ech Theorem.- E.1. ?ech cohomology.- E.2. The de Rham-?ech complex.