Serge Lang: Calculus of Several Variables

Cover: 9780387964058 | Calculus of Several Variables | Serge Lang | Buch | Englisch | 1996

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Beschreibung

The present course on calculus of several variables is meant as a text, either for one semester following A First Course in Calculus, or for a year if the calculus sequence is so structured. For a one-semester course, no matter what, one should cover the first four chapters, up to the law of conservation of energy, which provides a beautiful application of the chain rule in a physical context, and ties up the mathematics of this course with standard material from courses on physics. Then there are roughly two possibilities: One is to cover Chapters V and VI on maxima and minima, quadratic forms, critical points, and Taylor's formula. One can then finish with Chapter IX on double integration to round off the one-term course. The other is to go into curve integrals, double integration, and Green's theorem, that is Chapters VII, VIII, IX, and X, §1. This forms a coherent whole.

Zusammenfassung

This is a new, revised edition of this widely known text. All of the basic topics in calculus of several variables are covered. The presentation is self-contained, assuming only a knowledge of basic calculus in one variable. Many completely worked-out problems have been included.

Inhaltsverzeichnis

One Basic Material.- I Vectors.- II Differentiation of Vectors.- III Functions of Several Variables.- IV The Chain Rule and the Gradient.- Two Maxima, Minima, and Taylor's Formula.- V Maximum and Minimum.- VI Higher Derivatives.- Three Curve Integrals and Double Integrals.- VII Potential Functions.- VIII Curve Integrals.- IX Double Integrals.- X Green's Theorem.- Four Triple and Surface Integrals.- XI Triple Integrals.- XII Surface Integrals.- Five Mappings, Inverse Mappings, and Change of Variables Formula..- XIII Matrices.- XIV Linear Mappings.- XV Determinants.- XVI Applications to Functions of Several Variables.- XVII The Change of Variables Formula.- Appendix Fourier Series.- §1. General Scalar Products.- §2. Computation of Fourier Series.- Answers to Exercises.

Erscheinungsjahr:	1987
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Reihe:	Undergraduate Texts in Mathematics
Inhalt:	xii 619 S. 298 s/w Zeichng.
ISBN-13:	9780387964058
ISBN-10:	0387964053
Sprache:	Englisch
Herstellernummer:	10349032
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Lang, Serge
Auflage:	3rd ed. 1987
Hersteller:	Springer New York Springer US, New York, N.Y. Undergraduate Texts in Mathematics
Maße:	241 x 160 x 40 mm
Von/Mit:	Serge Lang
Erscheinungsdatum:	17.02.1987
Gewicht:	1,109 kg

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