Functions of Two Variables / Edition 2

by Sean Dineen

Overview

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.

Product Details

ISBN-13:	9781138417762
Publisher:	Taylor & Francis
Publication date:	07/27/2017
Edition description:	2nd ed.
Pages:	208
Product dimensions:	6.12(w) x 9.19(h) x (d)

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. Curvature. Quadratic Approximation. Vector Valued Differentiation. Complex Analysis. Line Integrals. The Fundamental Theorem of Calculus. Double Integrals. Coordinate Systems. Green's Theorem. Solutions. Index.

Editorial Reviews

Offers a gentle but rigorous treatment of fundamentals of multivariate calculus in a two-variable context, featuring an informal writing style and a problem-oriented approach. Material maintains a balance between intuition, explanation, methodology, and justification, enhanced by heuristic comments, examples, exercises, and proofs. This edition includes a new section on tangent lines, greater emphasis on the chain rule, a rearrangement of several chapters, refined examples, and more exercises. Dineen teaches mathematics at the University College Dublin. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Booknews

"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

From the Publisher