Calculus on Normed Vector Spaces

2012
ISBN: 978-1-4614-3893-9
Verlag: Springer

Buch, Englisch, 249 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 406 g

Reihe: Universitext

This book serves as an introduction to calculus on normed vector spaces at a higher undergraduate or beginning graduate level. The prerequisites include basic calculus and linear algebra, as well as a certain mathematical maturity. All the important topology and functional analysis topics are introduced where necessary.

In its attempt to show how calculus on normed vector spaces extends the basic calculus of functions of several variables, this book is one of the few textbooks to bridge the gap between the available elementary texts and high level texts.  The inclusion of many non-trivial applications of the theory and interesting exercises provides motivation for the reader.

Zielgruppe

Graduate

Autoren/Hrsg.

Coleman, Rodney

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Vektoranalysis, Physikalische Felder

Inhaltsverzeichnis

Preface.- 1 Normed Vector Spaces.- 2 Differentiation.- 3 Mean value theorems.- 4 Higher derivatives and differentials.- 5 Taylor theorems and applications.- 6 Hilbert spaces.- 7 Convex functions.- 8 The inverse and implicit mapping theorems.- 9 Vector fields.- 10 The flow of a vector field.- 11 The calculus of variations: an introduction.- Bibliography.- Index

Über Autor(innen)

Coleman, Rodney
Rodney Coleman lives close to Grenoble in France, where he is engaged in teaching and research. His interests include literature, bicycle riding and hiking in the mountains.