Textbook

Advanced Calculus: An Introduction to Linear Analysis

ISBN: 978-0-470-23288-0

Hardcover

416 pages

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Provides a rigorous approach to proofs, fundamental theorems, and the foundations of calculus
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
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
Features the system of real numbers as a Cauchy-complete Archimedean ordered field, and the traditional theorems of advanced calculus are presented.
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.