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Differentiable Manifolds : A First Course. Lawrence Conlon. This book is based on the full year Ph. 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.
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.
Flows and Foliation. Covectors and 1Forms. Multilinear Algebra Integration and Cohomology. Forms and Foliations. Riemannian Geometry. Appendix A Vector Fields on Spheres. Ordinary Differential Equations. Local Theory. Global Theory.
Lie Groups Sards Theorem.
Differentiable Manifolds : A First Course. Lawrence Conlon. This book is based on the full year Ph. 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.
Differentiable Manifolds : A First Course
It seems that you're in Germany. We have a dedicated site for Germany. The basics of differentiable manifolds, global calculus, differential geometry, and related topics constitute a core of information essential for the first or second year graduate student preparing for advanced courses and seminars in differential topology and geometry. Differentiable Manifolds is a text designed to cover this material in a careful and sufficiently detailed manner, presupposing only a good foundation in general topology, calculus, and modern algebra. This second edition contains a significant amount of new material, which, in addition to classroom use, will make it a useful reference text. Topics that can be omitted safely in a first course are clearly marked, making this edition easier to use for such a course, as well as for private study by non-specialists wishing to survey the field.
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