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An Introduction to Multivariable Analysis from Vector to Manifold Piotr Mikusinski

An Introduction to Multivariable Analysis from Vector to Manifold By Piotr Mikusinski

An Introduction to Multivariable Analysis from Vector to Manifold by Piotr Mikusinski

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Summary

Multivariable analysis is of interest to pure and applied mathematicians, physicists, electrical, mechanical and systems engineers, mathematical economists, biologists, and statisticians. Systematic exposition, with numerous examples and exercises from the computational to the theoretical, makes difficult ideas as concrete as possible.

An Introduction to Multivariable Analysis from Vector to Manifold Summary

An Introduction to Multivariable Analysis from Vector to Manifold by Piotr Mikusinski

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.

An Introduction to Multivariable Analysis from Vector to Manifold Reviews

"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 descriptionon the book's back cover]is absolutely true, but omits any statement attesting to the high quality of the writing andthe 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

Table of Contents

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 Taylors 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 Birds-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 Fubinis 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 StokesTheorem for Chains.- 7.5 StokesTheorem for Oriented Manifolds.- 7.6 Applications.- 7.7 Manifolds and Differential Forms: An Intrinsic Point of View.- References.

Additional information

NPB9780817642341
9780817642341
081764234X
An Introduction to Multivariable Analysis from Vector to Manifold by Piotr Mikusinski
Piotr Mikusinski
New
Hardback
Birkhauser Boston Inc
2001-11-26
295
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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Customer Reviews - An Introduction to Multivariable Analysis from Vector to Manifold