Functions of Several Variables

Graven, B. D.

ISBN 10: 0412233401 / ISBN 13: 9780412233401

Edité par Springer 1981-12, 1981

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N° de réf. du vendeur 6666-IUK-9780412233401

Détails bibliographiques

• Titre: Functions of Several Variables
• Éditeur: Springer 1981-12
• Date de parution: 1981
• Langue: anglais
• ISBN à 10 chiffres: 0412233401
• ISBN à 13 chiffres: 9780412233401
• Reliure: PF
• État de l'article: New

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Synopsis

This book is aimed at mathematics students, typically in the second year of a university course. The first chapter, however, is suitable for first-year students. Differentiable functions are treated initially from the standpoint of approximating a curved surface locally by a fiat surface. This enables both geometric intuition, and some elementary matrix algebra, to be put to effective use. In Chapter 2, the required theorems - chain rule, inverse and implicit function theorems, etc- are stated, and proved (for n variables), concisely and rigorously. Chapter 3 deals with maxima and minima, including problems with equality and inequality constraints. The chapter includes criteria for discriminating between maxima, minima and saddlepoints for constrained problems; this material is relevant for applications, but most textbooks omit it. In Chapter 4, integration over areas, volumes, curves and surfaces is developed, and both the change-of-variable formula, and the Gauss-Green-Stokes set of theorems are obtained. The integrals are defined with approximative sums (ex- pressed concisely by using step-functions); this preserves some geometrical (and physical) concept of what is happening. Consequent on this, the main ideas of the 'differential form' approach are presented, in a simple form which avoids much of the usual length and complexity. Many examples and exercises are included.