文档介绍：An Introduction to
Multivariable Mathematics
Copyright © 2008 by Morgan & Claypool
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in
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An Introduction to Multivariable Mathematics
Leon Simon
ISBN: 9781598298017 paperback
ISBN: 9781598298024 ebook
DOI
A Publication in the Morgan & Claypool Publishers series
SYNTHESIS LECTURES ON MATHEMATICS AND STATISTICS
Lecture #3
Series Editor: Steven G. Krantz, Washington University, St. Louis
Series ISSN
Synthesis Lectures on Mathematics and Statistics
ISSN pending.
An Introduction to
Multivariable Mathematics
Leon Simon
Stanford University
SYNTHESIS LECTURES ON MATHEMATICS AND STATISTICS #3
M
&C Morgan& cLaypool publishers
ABSTRACT
The text is designed for use in a 40 lecture introductory course covering linear algebra, multivariable
differential calculus, and an introduction to real analysis.
The core material of the book is arranged to allow for the main introductory material on linear
algebra, including basic vector space theory in Euclidean space and the initial theory of matrices and
linear systems, to be covered in the first 10 or 11 lectures, followed by a similar number of lectures
on basic multivariable analysis, including first theorems on differentiable functions on domains in
Euclidean space and a brief introduction to submanifolds. The book then concludes with further
essential linear algebra, including the theory of determinants, eigenvalues, and the spectral theorem
for real symmetric matrices, and further multivariable analysis, including the contraction mapping
principle and the inverse and implicit function theorems. There is also an appendix which provides
a 9 lecture introduction to rea