杭州电子科技大学图书馆书目检索系统

Online Public Access Catalogue

题名/责任者:

Multivariable calculus / Rolland Trapp.

版本说明:

First edition.

出版发行项:

Oxford, United Kingdom ; New York, NY, United States of America : Oxford University Press, 2019.

ISBN:

9780198835172

ISBN:

9780198835189

载体形态项:

x, 468 pages : color illustrations ; 25 cm

个人责任者:

Trapp, Rolland J., author.

论题主题:

Calculus.

中图法分类号:

O172

书目附注:

Includes bibliographical references (page 465) and index.

摘要附注:

"Multivariable Calculus is a basic introduction to the subject that is intended for a one-semester, second-year undergraduate course. It begins by familiarizing the reader with three-dimensions, introducing several coordinate systems, and describing surfaces three ways: parametrically, as level surfaces and as graphs of functions. Vectors and vector products are the topic of the second chapter and are presented as tools for analyzing geometric and physical applications. A chapter on differentiation follows in which partial differentiation is defined and investigated. The multivariable chain rule motivates directional derivatives, as well as orthogonality between gradients and level sets. Applications to optimization questions round out the discussion of differentiation. Multiple integration is defined in chapter four as a limit of Riemann sums. Three-dimensional intuition from chapter one facilitates the set up and evaluation of multiple integrals in Cartesian, polar, cylindrical and spherical coordinates. Curve and surface integrals provide yet another generalization to single-variable integration. Chapter five is an introduction to vector analysis. The physical notions of work and flux motivate integrals of vector fields along curves and across surfaces, respectively. Derivatives of vector fields are defined and used in the main theorems of vector analysis-Green's, Stokes', and the Divergence Theorem. Curvilinear formulas for the gradient, divergence, Laplacian, and curl are seen to follow from these theorems"--

豆瓣简介：