eBook - ePub

Advanced Calculus

Name: Advanced Calculus
ISBN: 9789814583954

Lynn Harold Loomis,

Shlomo Sternberg,

596 pages
English
ePUB (mobile friendly)
Available on iOS & Android

eBook - ePub

Advanced Calculus

Lynn Harold Loomis,

Shlomo Sternberg,

About this book

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.

Contents:

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 E n
Classical Mechanics

Readership: Undergraduates in mathematics.

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Yes, you can access Advanced Calculus by Lynn Harold Loomis, Shlomo Sternberg in PDF and/or ePUB format, as well as other popular books in Mathematics & Calculus. We have over one million books available in our catalogue for you to explore.