Functions of Several Variables (Undergraduate Texts in Mathematics) - gebunden oder broschiert

EAN (ISBN-13): 9780387902067
ISBN (ISBN-10): 0387902066
Gebundene Ausgabe
Taschenbuch
Erscheinungsjahr: 2007
Herausgeber: Springer
428 Seiten
Gewicht: 0,801 kg
Sprache: eng/Englisch

Buch in der Datenbank seit 2007-05-26T16:39:32+02:00 (Berlin)
Detailseite zuletzt geändert am 2024-03-05T13:56:27+01:00 (Berlin)
ISBN/EAN: 9780387902067

ISBN - alternative Schreibweisen:
0-387-90206-6, 978-0-387-90206-7
Alternative Schreibweisen und verwandte Suchbegriffe:
Autor des Buches: wendell fleming, helms, lebesgue
Titel des Buches: functions several variables, mathematics

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Daten vom Verlag:

Autor/in: Wendell Fleming
Titel: Undergraduate Texts in Mathematics; Functions of Several Variables
Verlag: Springer; Springer US
412 Seiten
Erscheinungsjahr: 1977-03-08
New York; NY; US
Sprache: Englisch
64,15 € (DE)
65,95 € (AT)
93,68 CHF (CH)
Available
XII, 412 p.

BB; Hardcover, Softcover / Mathematik/Sonstiges; Optimierung; Verstehen; Algebra; Differentialform; Differentialrechnung; Functions; Integralrechnung; Manifold; Topology; Variable; calculus; function; geometry; theorem; Calculus of Variations and Optimization; Analysis; Mathematische Analysis, allgemein; BC

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 multilinearfunctions.- 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.