About this product

Product Identifiers

PublisherMorgan & Claypool Publishers

ISBN-101598298011

ISBN-139781598298017

eBay Product ID (ePID)70215757

Product Key Features

Number of Pages132 Pages

Publication NameIntroduction to Multivariable Mathematics

LanguageEnglish

SubjectAlgebra / Linear, General, Mathematical Analysis

Publication Year2008

TypeTextbook

AuthorLeon Simon

Subject AreaMathematics, Technology & Engineering

SeriesSynthesis Lectures on Mathematics and Statistics Ser.

FormatTrade Paperback

Dimensions

Item Length9.3 in

Item Width7.4 in

Additional Product Features

Intended AudienceScholarly & Professional

TitleLeadingAn

Table Of ContentLinear Algebra Analysis in R More Linear Algebra More Analysis in R Appendix: Introductory Lectures on Real Analysis

SynopsisThe text is designed for use in a forty-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 ten or eleven 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 nine-lecture introduction to real analysis. There are various ways in which the additional material in the appendix could be integrated into a course--for example in the Stanford Mathematics honors program, run as a four-lecture per week program in the Autumn Quarter each year, the first six lectures of the nine-lecture appendix are presented at the rate of one lecture per week in weeks two through seven of the quarter, with the remaining three lectures per week during those weeks being devoted to the main chapters of the text. It is hoped that the text would be suitable for a quarter or semester course for students who have scored well in the BC Calculus advanced placement examination (or equivalent), particularly those who are considering a possible major in mathematics. The author has attempted to make the presentation rigorous and complete, with the clarity and simplicity needed to make it accessible to an appropriately large group of students., The core material of this text 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 ten or eleven 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.