# An Introduction to Multivariable Analysis: From Vector to Manifold

## Mikusinski, Piotr; Taylor, Michael D.

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Multivariable analysis is of interest to pure and applied mathematicians, physicists, electrical, mechanical and systems engineers, mathematical economists, biologists, and statisticians. This book takes the student and researcher on a journey through the core topics of the subject. Systematic exposition, with numerous examples and exercises from the computational to the theoretical, makes difficult ideas as concrete as possible. Good bibliography and index.

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Book Description:

"This is a self-contained textbook devoted to multivariable analysis based on nonstandard geometrical methods. The book can be used either as a supplement to a course on single variable analysis or as a semester-long course introducing students to manifolds and differential forms."   ?Mathematical Reviews

"The authors strongly motivate the abstract notions by a lot of intuitive examples and pictures. The exercises at the end of each section range from computational to theoretical. The book is highly recommended for undergraduate or graduate courses in multivariable analysis for students in mathematics, physics, engineering, and economics."   ?Studia Universitatis Babes-Bolyai, Series Mathematica

"All this [the description on the book's back cover] is absolutely true, but omits any statement attesting to the high quality of the writing and the high level of mathematical scholarship. So, go and order a copy of this attractively produced, and nicely composed, scholarly tome. If you're not teaching this sort of mathematics, this book will inspire you to do so."   ?MAA Reviews

Contenuti:

1 Vectors and Volumes.- 1.1 Vector Spaces.- 1.2 Some Geometric Machinery for RN.- 1.3 Transformations and Linear Transformations.- 1.4 A Little Matrix Algebra.- 1.5 Oriented Volume and Determinants.- 1.6 Properties of Determinants.- 1.7 Linear Independence, Linear Subspaces, and Bases.- 1.8 Orthogonal Transformations.- 1.9 K-dimensional Volume of Parallelepipeds in RN.- 2 Metric Spaces.- 2.1 Metric Spaces.- 2.2 Open and Closed Sets.- 2.3 Convergence.- 2.4 Continuous Mappings.- 2.5 Compact Sets.- 2.6 Complete Spaces.- 2.7 Normed Spaces.- 3 Differentiation.- 3.1 Rates of Change and Derivatives as Linear Transformations.- 3.2 Some Elementary Properties of Differentiation.- 3.3 Taylor’s Theorem, the Mean Value Theorem, and Related Results.- 3.4 Norm Properties.- 3.5 The Inverse Function Theorem.- 3.6 Some Consequences of the Inverse Function Theorem.- 3.7 Lagrange Multipliers.- 4 The Lebesgue Integral.- 4.1 A Bird’s-Eye View of the Lebesgue Integral.- 4.2 Integrable Functions.- 4.3 Absolutely Integrable Functions.- 4.4 Series of Integrable Functions.- 4.5 Convergence Almost Everywhere.- 4.6 Convergence in Norm.- 4.7 Important Convergence Theorems.- 4.8 Integrals Over a Set.- 4.9 Fubini’s Theorem.- 5 Integrals on Manifolds.- 5.1 Introduction.- 5.2 The Change of Variables Formula.- 5.3 Manifolds.- 5.4 Integrals of Real-valued Functions over Manifolds.- 5.5 Volumes in RN.- 6 K-Vectors and Wedge Products.- 6.1 K-Vectors in RN and the Wedge Product.- 6.2 Properties of A.- 6.3 Wedge Product and a Characterization of Simple K-Vectors.- 6.4 The Dot Product and the Star Operator.- 7 Vector Analysis on Manifolds.- 7.1 Oriented Manifolds and Differential Forms.- 7.2 Induced Orientation, the Differential Operator, and Stokes’ Theorem; What We Can Learn from Simple Cubes.- 7.3 Integrals and Pullbacks.- 7.4 Stokes’Theorem for Chains.- 7.5 Stokes’Theorem for Oriented Manifolds.- 7.6 Applications.- 7.7 Manifolds and Differential Forms: An Intrinsic Point of View.- References.

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## 1.An Introduction to Multivariable Analysis from Vector to Manifold

Editore: BirkhÇÏuser (2001)
ISBN 10: 081764234X ISBN 13: 9780817642341
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Descrizione libro BirkhÇÏuser, 2001. Hardback. Condizione libro: NEW. 9780817642341 Hardback, This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Codice libro della libreria HTANDREE0285749

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## 2.An Introduction to Multivariable Analysis

Editore: Birkhauser Boston (2001)
ISBN 10: 081764234X ISBN 13: 9780817642341
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## 3.An Introduction to Multivariable Analysis from Vector to Manifold

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## 4.An Introduction to Multivariable Analysis from Vector to Manifold

Editore: BirkhÃ¤user (2016)
ISBN 10: 081764234X ISBN 13: 9780817642341
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Descrizione libro BirkhÃ¤user, 2016. Paperback. Condizione libro: New. PRINT ON DEMAND Book; New; Publication Year 2016; Not Signed; Fast Shipping from the UK. No. book. Codice libro della libreria ria9780817642341_lsuk

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## 5.An Introduction to Multivariable Analysis: from Vector to Manifold

Editore: Birkhauser 2001-12-01 (2001)
ISBN 10: 081764234X ISBN 13: 9780817642341
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Descrizione libro Birkhauser 2001-12-01, 2001. Condizione libro: New. Brand new book, sourced directly from publisher. Dispatch time is 24-48 hours from our warehouse. Book will be sent in robust, secure packaging to ensure it reaches you securely. Codice libro della libreria NU-ING-00857477

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## 6.An Introduction to Multivariable Analysis from Vector to Manifold

Editore: Birkhäuser (2001)
ISBN 10: 081764234X ISBN 13: 9780817642341
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Descrizione libro Birkh&auml;user, 2001. Hardcover. Condizione libro: New. book. Codice libro della libreria 081764234X

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## 7.An Introduction to Multivariable Analysis: From Vector to Manifold (Hardback)

Editore: Birkhauser Boston, Germany (2001)
ISBN 10: 081764234X ISBN 13: 9780817642341
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Descrizione libro Birkhauser Boston, Germany, 2001. Hardback. Condizione libro: New. 2002 ed.. 236 x 157 mm. Language: English . Brand New Book ***** Print on Demand *****.Multivariable analysis is of interest to pure and applied mathematicians, physicists, electrical, mechanical and systems engineers, mathematical economists, biologists, and statisticians. This book takes the student and researcher on a journey through the core topics of the subject. Systematic exposition, with numerous examples and exercises from the computational to the theoretical, makes difficult ideas as concrete as possible. Good bibliography and index. Codice libro della libreria APC9780817642341

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## 8.An Introduction to Multivariable Analysis: From Vector to Manifold (Hardback)

Editore: Birkhauser Boston, Germany (2001)
ISBN 10: 081764234X ISBN 13: 9780817642341
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Descrizione libro Birkhauser Boston, Germany, 2001. Hardback. Condizione libro: New. 2002 ed.. 236 x 157 mm. Language: English . Brand New Book ***** Print on Demand *****. Multivariable analysis is of interest to pure and applied mathematicians, physicists, electrical, mechanical and systems engineers, mathematical economists, biologists, and statisticians. This book takes the student and researcher on a journey through the core topics of the subject. Systematic exposition, with numerous examples and exercises from the computational to the theoretical, makes difficult ideas as concrete as possible. Good bibliography and index. Codice libro della libreria APC9780817642341

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## 9.An Introduction to Multivariable Analysis

Editore: Birkhäuser (2001)
ISBN 10: 081764234X ISBN 13: 9780817642341
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Descrizione libro Birkhäuser, 2001. Hardcover. Condizione libro: New. 2002. Codice libro della libreria DADAX081764234X

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## 10.An Introduction to Multivariable Analysis from Vector to Manifold

Editore: Birkhäuser Nov 2001 (2001)
ISBN 10: 081764234X ISBN 13: 9780817642341
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Descrizione libro Birkhäuser Nov 2001, 2001. Buch. Condizione libro: Neu. 235x155x22 mm. This item is printed on demand - Print on Demand Titel. Neuware - Multivariable analysis is of interest to pure and applied mathematicians, physicists, electrical, mechanical and systems engineers, mathematical economists, biologists, and statisticians. This book takes the student and researcher on a journey through the core topics of the subject. Systematic exposition, with numerous examples and exercises from the computational to the theoretical, makes difficult ideas as concrete as possible. Good bibliography and index. The subject of multivariable analysis is of interest to pure and applied mathematicians, physicists, electrical, mechanical and systems engineers, mathematical economists, biologists, and statisticians. This introductory text provides students and researchers in the above fields with various ways of handling some of the useful but difficult concepts encountered in dealing with the machinery of multivariable analysis and differential forms on manifolds. The approach here is to make such concepts as concrete as possible. Highlights and key features: systematic exposition, supported by numerous examples and exercises from the computational to the theoretical brief development of linear algebra in Rn review of the elements of metric space theory treatment of standard multivariable material: differentials as linear transformations, the inverse and implicit function theorems, Taylor's theorem, the change of variables for multiple integrals (the most complex proof in the book) Lebesgue integration introduced in concrete way rather than via measure theory latar chapters move beyond Rn to manifolds and analysis on manifolds, covering the wedge product, differential forms, and the generalized Stokes' theorem bibliography and comprehensive index Core topics in multivariable analysis that are basic for senior undergraduates and graduate studies in differential geometry and for analysis in N dimensions and on manifolds are covered. Aside from mathematical maturity, prerequisites are a one-semester undergraduate course in advanced calculus or analysis, and linear algebra. Additionally, researchers working in the areas of dynamical systems, control theory and optimization, general relativity and electromagnetic phenomena may use the book as a self-study resource. 295 pp. Englisch. Codice libro della libreria 9780817642341

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