Multivariate Calculus and Geometry / by Seán Dineen.

Format:

Book

Author/Creator:

Dineen, Seán, Author.

Series:

Springer Undergraduate Mathematics Series, 1615-2085

Language:

English

Subjects (All):

Mathematics.

Mathematics, general.

Local Subjects:

Mathematics, general.

Physical Description:

1 online resource (XIV, 257 p. 103 illus.)

Edition:

3rd ed. 2014.

Place of Publication:

London : Springer London : Imprint: Springer, 2014.

Language Note:

English

Summary:

Multivariate calculus can be understood best by combining geometric insight, intuitive arguments, detailed explanations and mathematical reasoning. This textbook has successfully followed this programme. It additionally provides a solid description of the basic concepts, via familiar examples, which are then tested in technically demanding situations. In this new edition the introductory chapter and two of the chapters on the geometry of surfaces have been revised. Some exercises have been replaced and others provided with expanded solutions. Familiarity with partial derivatives and a course in linear algebra are essential prerequisites for readers of this book. Multivariate Calculus and Geometry is aimed primarily at higher level undergraduates in the mathematical sciences. The inclusion of many practical examples involving problems of several variables will appeal to mathematics, science and engineering students.

Contents:

Introduction to Differentiable Functions

Level Sets and Tangent Spaces

Lagrange Multipliers

Maxima and Minima on Open Sets

Curves in Rn

Line Integrals

The Frenet–Serret Equations

Geometry of Curves in R3

Double Integration

Parametrized Surfaces in R3

Surface Area

Surface Integrals

Stokes’ Theorem

Triple Integrals

The Divergence Theorem

Geometry of Surfaces in R3

Gaussian Curvature

Geodesic Curvature.

Notes:

Includes index.

Description based on publisher supplied metadata and other sources.

ISBN:

1-4471-6419-9

OCLC:

891136625