Functions of Two Variables  book cover
2nd Edition

Functions of Two Variables

ISBN 9781584881902
Published June 22, 2000 by Chapman and Hall/CRC
208 Pages 95 B/W Illustrations

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Book Description

Multivariate calculus, as traditionally presented, can overwhelm students who approach it directly from a one-variable calculus background. There is another way-a highly engaging way that does not neglect readers' own intuition, experience, and excitement. One that presents the fundamentals of the subject in a two-variable context and was set forth in the popular first edition of Functions of Two Variables.

The second edition goes even further toward a treatment that is at once gentle but rigorous, atypical yet logical, and ultimately an ideal introduction to a subject important to careers both within and outside of mathematics. The author's style remains informal and his approach problem-oriented. He takes care to motivate concepts prior to their introduction and to justify them afterwards, to explain the use and abuse of notation and the scope of the techniques developed.

Functions of Two Variables, Second Edition includes a new section on tangent lines, more emphasis on the chain rule, a rearrangement of several chapters, refined examples, and more exercises. It maintains a balance between intuition, explanation, methodology, and justification, enhanced by diagrams, heuristic comments, examples, exercises, and proofs.

Table of Contents

Functions from R2 to R
Partial Derivatives
Critical Points
Maxima and Minima
Saddle Points
Sufficiently Regular Functions
Linear Approximation
Tangent Lines
Method and Examples of Lagrange Multipliers
Theory and Examples of Lagrange Multipliers
Tangent Planes
The Chain Rule
Directed Curves
Quadratic Approximation
Vector Valued Differentiation
Complex Analysis
Line Integrals
The Fundamental Theorem of Calculus
Double Integrals
Coordinate Systems
Green's Theorem

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"The whole text is nicely written, and can be strongly recommended as an excellent and comprehensive source, suitable for self-study or classroom use at the undergraduate level. For students demanding motivation, its study will be a rewarding experience."
-European Mathematical Society Newsletter, December 2002