Advanced Calculus (Revised Edition)

基本信息

Format Paperback | 596 pages

Dimensions 165.1 x 246.38 x 33.02mm | 997.9g

Publication date 12 Mar 2014

Publisher World Scientific Publishing Co Pte Ltd

Language English

Edition Revised

Edition Statement Revised

ISBN10 9814583936

ISBN13 9789814583930

页面参数仅供参考，具体以实物为准

书籍简介

《高等微积分(修订版)》是哈佛大学的高等微积分教材，内容涵盖了从基本的向量空间概念到经典力学基本定理。包括多元微积分、外微分、微分形式的积分等。《高等微积分(修订版)》的特点是作者从拓扑一几何的观点来写微积分。用更现代的方式讲线性代数，把线性代数与微积分紧密地结合起来，这顺应了当代数学“拓扑几何与分析结合”的发展潮流。

An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades.This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis.The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra.

The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives.In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.

目录

Introduction; Vector Spaces; Finite-Dimensional Vector Spaces; The Differential Calculus; Compactness and Completeness; Scalar Product Spaces; Differential Equations; Multilinear Functionals; Integration; Differentiable Manifolds; The Integral Calculus on Manifolds; Exterior Calculus; Potential Theory in En; Classical Mechanics.

作者简介

Lynn Harold Loomis (April 1915 – June 1994) was an American mathematician working on analysis. Together with Hassler Whitney, he discovered the Loomis–Whitney inequality.

Loomis received his PhD in 1942 from Harvard University under Salomon Bochner with thesis Some Studies on Simply-Connected Riemann Surfaces: I. The Problem of Imbedding II. Mapping on the Boundary for Two Classes of Surfaces. After completing his PhD, Loomis was a professor at Radcliffe College and from 1949 at Harvard. From 1956, he was a member of the American Academy of Arts and Sciences.