Functions of several variables (eBook)

B. Craven (Autor)

eBook Download: PDF

2012
Springer Netherlands (Verlag)
978-94-010-9347-7 (ISBN)

Infos

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.

Produkt-Details

• Erscheint lt. Verlag: 6.12.2012
• Sprache: englisch
• Themenwelt: Kinder- / Jugendbuch ► Spielen / Lernen ► Lernen / Lernspiele
• Themenwelt: Schulbuch / Wörterbuch
• Themenwelt: Sonstiges ► Geschenkbücher
• Themenwelt: Naturwissenschaften
• Themenwelt: Sozialwissenschaften
• ISBN-10: 94-010-9347-4 / 9401093474
• ISBN-13: 978-94-010-9347-7 / 9789401093477