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Functions of a Real Variable [Hardcover]

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Item description for Functions of a Real Variable by Nicolas Bourbaki...

This book is an English translation of the last French edition of Bourbaki's Fonctions d'une Variable Relle.

The first chapter is devoted to derivatives, Taylor expansions, the finite increments theorem, convex functions. In the second chapter, primitives and integrals (on arbitrary intervals) are studied, as well as their dependence with respect to parameters. Classical functions (exponential, logarithmic, circular and inverse circular) are investigated in the third chapter. The fourth chapter gives a thorough treatment of differential equations (existence and unicity properties of solutions, approximate solutions, dependence on parameters) and of systems of linear differential equations. The local study of functions (comparison relations, asymptotic expansions) is treated in chapter V, with an appendix on Hardy fields. The theory of generalized Taylor expansions and the Euler-MacLaurin formula are presented in the sixth chapter, and applied in the last one to the study of the Gamma function on the real line as well as on the complex plane.

Although the topics of the book are mainly of an advanced undergraduate level, they are presented in the generality needed for more advanced purposes: functions allowed to take values in topological vector spaces, asymptotic expansions are treated on a filtered set equipped with a comparison scale, theorems on the dependence on parameters of differential equations are directly applicable to the study of flows of vector fields on differential manifolds, etc.

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Item Specifications...

Pages   338
Est. Packaging Dimensions:   Length: 0.75" Width: 6.5" Height: 9.5"
Weight:   1.4 lbs.
Binding  Hardcover
Release Date   Nov 5, 2003
Publisher   Springer
ISBN  3540653406  
ISBN13  9783540653400  

Availability  0 units.

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1Books > Subjects > Professional & Technical > Professional Science > Mathematics > Applied > Statistics
2Books > Subjects > Professional & Technical > Professional Science > Mathematics > Geometry & Topology > General Geometry
3Books > Subjects > Professional & Technical > Professional Science > Mathematics > Transformations
4Books > Subjects > Reference
5Books > Subjects > Science > General
6Books > Subjects > Science > Mathematics > Applied > Probability & Statistics
7Books > Subjects > Science > Mathematics > General
8Books > Subjects > Science > Mathematics > Geometry & Topology > General Geometry
9Books > Subjects > Science > Mathematics > Mathematical Analysis
10Books > Subjects > Science > Mathematics > Reference
11Books > Subjects > Science > Mathematics > Transformations

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