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Advanced Calculus: An Introduction to Linear Analysis
Leonard F. Richardson,
Department of Mathematics, Louisiana State University, Baton Rouge, LA
ISBN: 978-0-470-23288-0
©2008
388 pages
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Hallmark Features
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Provides a rigorous approach to proofs, fundamental theorems, and the foundations of calculus
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Highlights the connections and interplay between calculus and linear algebra, emphasizing the concepts of a vector space, a linear transformation (including a linear functional), a norm, and a scalar product
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Offers a 'Test Yourself' section at the end of every chapter, which is a sample hour test with solutions to aid the study of readers
- Gradually guides the reader from the study of topology of the real line to the beginning theorems and concepts of graduate analysis, expressed from a modern viewpoint
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Features the system of real numbers as a Cauchy-complete Archimedean ordered field, and the traditional theorems of advanced calculus are presented.
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Employs a multi-part outline approach and provides broad hints to guide students through the more substantial proof exercises. Solutions to most of the non-proof exercises are also provided.
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