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Functions of Several Variables

Author: Wendell Fleming
Publisher: New York, NY : Springer New York, 1977.
Series: Undergraduate texts in mathematics.
Edition/Format:   eBook : Document : English : 2nd editionView all editions and formats
Summary:
This new edition of FUNCTIONS OF SEVERAL VARIABLES is an extensive revision. Like the first edition it presents a thorough introduction to differential and integral calculus, including the integration of differential forms on manifolds. A new chapter on elementary topology makes the book more complete as an advanced calculus text; sections have been added introducing physical applications in thermodynamics, fluid  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Wendell Fleming
ISBN: 9781468494617 1468494619
OCLC Number: 853262309
Description: 1 online resource (428 pages 96 illustrations).
Contents: 1 Euclidean spaces --
1.1 The real number system --
1.2 Euclidean En --
1.3 Elementary geometry of En --
1.4 Basic topological notions in En --
*1.5 Convex sets --
2 Elementary topology of En --
2.1 Functions --
2.2 Limits and continuity of transformations --
2.3 Sequences in En --
2.4 Bolzano-Weierstrass theorem --
2.5 Relative neighborhoods, continuous transformations --
2.6 Topological spaces --
2.7 Connectedness --
2.8 Compactness --
2.9 Metric spaces --
2.10 Spaces of continuous functions --
*2.11 Noneuclidean norms on En --
3 Differentiation of real-valued functions --
3.1 Directional and partial derivatives --
3.2 Linear functions --
**3.3 Difierentiable functions --
3.4 Functions of class C(q) --
3.5 Relative extrema --
*3.6 Convex and concave functions --
4 Vector-valued functions of several variables --
4.1 Linear transformations --
4.2 Affine transformations --
4.3 Differentiable transformations --
4.4 Composition --
4.5 The inverse function theorem --
4.6 The implicit function theorem --
4.7 Manifolds --
4.8 The multiplier rule --
5 Integration --
5.1 Intervals --
5.2 Measure --
5.3 Integrals over En --
5.4 Integrals over bounded sets --
5.5 Iterated integrals --
5.6 Integrals of continuous functions --
5.7 Change of measure under affine transformations --
5.8 Transformation of integrals --
5.9 Coordinate systems in En --
5.10 Measurable sets and functions; further properties --
5.11 Integrals: general definition, convergence theorems --
5.12 Differentiation under the integral sign --
5.13 Lp-spaces --
6 Curves and line integrals --
6.1 Derivatives --
6.2 Curves in En --
6.3 Differential 1-forms --
6.4 Line integrals --
*6.5 Gradient method --
*6.6 Integrating factors; thermal systems --
7 Exterior algebra and differential calculus --
7.1 Covectors and differential forms of degree 2 --
7.2 Alternating multilinear functions --
7.3 Multicovectors --
7.4 Differential forms --
7.5 Multivectors --
7.6 Induced linear transformations --
7.7 Transformation law for differential forms --
7.8 The adjoint and codifferential --
*7.9 Special results for n = 3 --
*7.10 Integrating factors (continued) --
8 Integration on manifolds --
8.1 Regular transformations --
8.2 Coordinate systems on manifolds --
8.3 Measure and integration on manifolds --
8.4 The divergence theorem --
*8.5 Fluid flow --
8.6 Orientations --
8.7 Integrals of r-forms --
8.8 Stokes's formula --
8.9 Regular transformations on submanifolds --
8.10 Closed and exact differential forms --
8.11 Motion of a particle --
8.12 Motion of several particles --
Axioms for a vector space --
Mean value theorem; Taylor's theorem --
Review of Riemann integration --
Monotone functions --
References --
Answers to problems.
Series Title: Undergraduate texts in mathematics.
Responsibility: by Wendell Fleming.

Abstract:

This new edition, like the first, presents a thorough introduction to differential and integral calculus, including the integration of differential forms on manifolds.  Read more...

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