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# ðŸ“™ Analysis in Vector Spaces - A Course in Advanced Calculus by Mustafa A. Akcoglu, Paul F.A. Bartha, Dzung Minh Ha â€” epub download

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A rigorous introduction to calculus in vector spacesThe 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 functionsReal numbersVector functionsNormed vector spacesFirst- and higher-order derivativesDiffeomorphisms and manifoldsMultiple integralsIntegration on manifoldsStokes' theoremBasic point set topologyNumerous 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 and graduate levels. It also serves as a valuable reference for further study in any discipline that requires a firm understanding of mathematical techniques and concepts.

## About book:

## About file:

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- Author:
**Mustafa A. Akcoglu, Paul F.A. Bartha, Dzung Minh Ha** - Year:
**2009** - Publisher:
**Wiley** - Language:
**English** - ISBN:
**0470148241,9780470148242**

- File size:
**13 124 543** - Format:
**pdf**

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Designed for a one-semester advanced calculus course, Advanced Calculus explores the theory of calculus and highlights the connections between calculus and real analysis -- providing a mathematically sophisticated introduction to functional analytical con...

Based on courses taught to advanced undergraduate students, this book offers a broad introduction to the methods of numerical linear algebra and optimization. The prerequisites are familiarity with the basic properties of matrices, finite-dimensional vect...

Features an introduction to advanced calculus and highlights its inherent concepts from linear algebraAdvanced Calculus reflects the unifying role of linear algebra in an effort to smooth readers' transition to advanced mathematics. The book fosters the d...

This book serves as an introduction to calculus on normed vector spaces at a higher undergraduate or beginning graduate level. The prerequisites include basic calculus and linear algebra, as well as a certain mathematical maturity. All the important topol...

Problems in Real Analysis: Advanced Calculus on the Real Axis features a comprehensive collection of challenging problems in mathematical analysis that aim to promote creative, non-standard techniques for solving problems. This self-contained text offers ...

Problems in Real Analysis: Advanced Calculus on the Real Axis features a comprehensive collection of challenging problems in mathematical analysis that aim to promote creative, non-standard techniques for solving problems. This self-contained text offers ...

Ordinary differential equations play a central role in science and have been extended to evolution equations in Banach spaces. For many applications, however, it is difficult to specify a suitable normed vector space. Shapes without a priori restrictions,...

Problems in Real Analysis: Advanced Calculus on the Real Axis features a comprehensive collection of challenging problems in mathematical analysis that aim to promote creative, non-standard techniques for solving problems. This self-contained text offers ...

This best-selling guide--which has sold more than 340,000 copies since its first publication--has been thoroughly updated throughout to correspons to current advanced calculus courses. A complete and comprehensive review of the subject, this updated editi...

Compiled by the Editors of Popular Mechanics Magazine. The instructions, pictures and plans were prepared for ease of understanding. Offers something for every lover of boats....

Both a fascinating challenge and a great training tool, these tricky tactical problems are not only fun to solve, but great for advanced beginners, intermediate, and expert players to use as tools to improve their game.Â Tactics are presented in order of ...