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020 _a9783031023941
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024 7 _a10.1007/978-3-031-02394-1
_2doi
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_2bicssc
072 7 _aMAT000000
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082 0 4 _a510
_223
100 1 _aSimon, Leon.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_981175
245 1 3 _aAn Introduction to Multivariable Mathematics
_h[electronic resource] /
_cby Leon Simon.
250 _a1st ed. 2008.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2008.
300 _aVIII, 132 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSynthesis Lectures on Mathematics & Statistics,
_x1938-1751
505 0 _aLinear Algebra -- Analysis in R -- More Linear Algebra -- More Analysis in R -- Appendix: Introductory Lectures on Real Analysis.
520 _aThe 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 toreal 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. Table of Contents: Linear Algebra / Analysis in R / More Linear Algebra / More Analysis in R / Appendix: Introductory Lectures on Real Analysis.
650 0 _aMathematics.
_911584
650 0 _aStatistics .
_931616
650 0 _aEngineering mathematics.
_93254
650 1 4 _aMathematics.
_911584
650 2 4 _aStatistics.
_914134
650 2 4 _aEngineering Mathematics.
_93254
710 2 _aSpringerLink (Online service)
_981176
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031012662
776 0 8 _iPrinted edition:
_z9783031035227
830 0 _aSynthesis Lectures on Mathematics & Statistics,
_x1938-1751
_981177
856 4 0 _uhttps://doi.org/10.1007/978-3-031-02394-1
912 _aZDB-2-SXSC
942 _cEBK
999 _c85121
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