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A. Author: Jerrold E. Marsden/Anthony Tromba Hardcover (545 pages) Publisher: Macmillan Higher Education, December 2011
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Author: Jerrold E. Marsden/Anthony Tromba Hardcover (545 pages) Publisher: Macmillan Higher Education, December 2011
Analysis in Vector Spaces: A Course in Advanced Calculus
The concepts and theorems of advanced calculus combined with related computational methods are essential to understanding nearly all areas of quantitative science. Analysis in Vector Spaces presents the central results of this classic subject through rigorous arguments, discussions, and examples. The book aims to cultivate not only knowledge of the major theoretical results, but also the geometric intuition needed for both mathematical problem-solving and modeling in the formal sciences. The authors begin with an outline of key concepts, terminology, and notation and also provide a basic introduction to set theory, the properties of real numbers, and a review of linear algebra. An elegant approach to eigenvector problems and the spectral theorem sets the stage for later results on volume and integration. Subsequent chapters present the major results of differential and integral calculus of several variables as well as the theory of manifolds. Additional topical coverage includes: Sets and functions Real numbers Vector functions Normed vector spaces First- and higher-order derivatives Diffeomorphisms and manifolds Multiple integrals Integration on manifolds Stokes' theorem Basic point set topology Numerous examples and exercises are provided in each chapter to reinforce new concepts and to illustrate how results can be applied to additional problems. Furthermore, proofs and examples are presented in a clear style that emphasizes the underlying intuitive ideas. Counterexamples are provided throughout the book to warn against possible mistakes, and extensive appendices outline the construction of real numbers, include a fundamental result about dimension, and present general results about determinants. Assuming only a fundamental understanding of linear algebra and single variable calculus, Analysis in Vector Spaces is an excellent book for a second course in analysis for mathematics, physics, computer science, and engineering majors at the undergraduate a
Vector Calculus in Regional Development Analysis: Comparative Regional Analysis Using the Example of Poland
This work seeks to propose a methodological basis for regional development analysis based on vector calculus. Existing taxonomic methods are developed further in order to assess regions and micro-regions with regard to their socio-economic and environmental development. In addition to its methodological contribution, this book thus contributes to a framework of comparative assessment of regions and an analysis of underlying factors for regional development and investment decisions. In order to simplify the practical implementation of the presented concepts, the author proposes an IT application with the ability to examine spatial relations among groups of variables. The empirical research presented in this context relates to data from Polish counties as a case study.
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Vector Calculus in Regional Development Analysis
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