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Multivariable Analysis

  • G. Baley Price

Table of contents

  1. Front Matter
    Pages i-xiv
  2. G. Baley Price
    Pages 237-262
  3. G. Baley Price
    Pages 407-442
  4. G. Baley Price
    Pages 443-493
  5. G. Baley Price
    Pages 494-495
  6. Back Matter
    Pages 573-655

About this book

Introduction

This book contains an introduction to the theory of functions, with emphasis on functions of several variables. The central topics are the differentiation and integration of such functions. Although many of the topics are familiar, the treatment is new; the book developed from a new approach to the theory of differentiation. Iff is a function of two real variables x and y, its deriva­ tives at a point Po can be approximated and found as follows. Let PI' P2 be two points near Po such that Po, PI, P2 are not on a straight line. The linear function of x and y whose values at Po, PI' P2 are equal to those off at these points approximates f near Po; determinants can be used to find an explicit representation of this linear function (think of the equation of the plane through three points in three-dimensional space). The (partial) derivatives of this linear function are approximations to the derivatives of f at Po ; each of these (partial) derivatives of the linear function is the ratio of two determinants. The derivatives off at Po are defined to be the limits of these ratios as PI and P2 approach Po (subject to an important regularity condition). This simple example is only the beginning, but it hints at a m theory of differentiation for functions which map sets in IRn into IR which is both general and powerful, and which reduces to the standard theory of differentiation in the one-dimensional case.

Keywords

Analysis Differentialrechnung Funktionentheorie Integralrechnung calculus

Authors and affiliations

  • G. Baley Price
    • 1
  1. 1.Department of MathematicsUniversity of KansasLawrenceUSA

Bibliographic information