Item description for Fundamental Concepts in Modern Analysis by Vagn Lundsgaard Hansen...
Many advanced mathematical disciplines, such as dynamical systems, calculus of variations, differential geometry and the theory of Lie groups, have a common foundation in general topology and calculus in normed vector spaces. In this book, mathematically inclined engineering students are offered an opportunity to go into some depth with fundamental notions from mathematical analysis that are not only important from a mathematical point of view but also occur frequently in the more theoretical parts of the engineering sciences. The book should also appeal to university students in mathematics and in the physical sciences.
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Studio: World Scientific Publishing Company
Est. Packaging Dimensions: Length: 8.5" Width: 6.3" Height: 0.79" Weight: 1.06 lbs.
Publisher World Scientific Publishing Company
ISBN 9810238940 ISBN13 9789810238940
Availability 0 units.
More About Vagn Lundsgaard Hansen
Vagn Lundsgaard Hansen has an academic affiliation as follows - Technical University of Denmark, Lyngby.
Reviews - What do customers think about Fundamental Concepts in Modern Analysis?
A very nice overview and foundation for nonlinear analysis Jun 1, 2000
My collaborator Gary Sandine, and I are using this text as the basis for an introduction to nonlinear analysis that we are teaching at Los Alamos National Laboratory. The course is being attended by technical staff members and graduate students. I like the book because it has all the right topics, assumes little in the way of prerequisites, and is small in size.
We are not simply presenting the book in the course. We are creating our own notes, adding various variations, as well as giving a large amount of intuitive background and connection to how two mathematicians think about those subjects in their daily practice. This said, we find the book to be very good for self study or as a backbone for a course.
A note of "correction": His definition of sequentially compact is not the standard one (see page 40) but this is a minor "flaw" ... one should compare with George Simmons "An Introduction to Topology and Modern Analysis", which makes a good supplement to a course taught or studied out of Hansen's book.
All in all, I would pick this book again for such an introductory course and I would recommend it very strongly to anyone wanting to begin the study of nonlinear analysis. Mastery of the subjects covered gives the student a big start on any follow up courses such as "Applied Functional Analysis" or "Differentiable Manifolds and Riemannian Geometry" or "Differential Topology and Singularities of Mappings" (which in fact are planned for the next couple of years). For someone not taking follow up courses, the book should make the ideas in papers using the tools of nonlinear analysis fairly accessible especially with a little explanation by an expert. I give the book 5 stars because of the choice of topics, the clarity and the (short) length.