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Short description/annotation
Advanced undergraduate text on mathematical analysis designed for pure or applied mathematicians, covering theory as well as applications.
Main description
Designed for one-semester courses at the senior undergraduate level, this book will appeal to mathematics undergraduates, to mathematics teachers, and to others who need to learn some mathematical analysis for use in other areas such as engineering, physics, biology or finance. Topics such as completeness and compactness are approached initially through convergence of sequences in metric space, and the emphasis remains on this approach. However, the alternative topological approach is described in a separate chapter. This gives the book more flexibility, making it especially useful as an introduction to more advanced areas such as functional analysis. Nominal divisions of pure and applied mathematics have been merged, leaving enough for students of either inclination to have a feeling for what further developments might look like. Applications have been included from such fields as differential and integral equations, systems of linear algebraic equations, approximation theory, numerical analysis and quantum mechanics.
Table of contents:
Preface; 1. Prelude to modern analysis; 2. Metric spaces; 3. The fixed point theorem and its applications; 4. Compactness; 5. Topological spaces; 6. Nomed vector spaces; 7. Mappings on normed spaces; 8. Inner product spaces; 9. Hilbert spaces; References; Index.
Advanced undergraduate text on mathematical analysis designed for pure or applied mathematicians, covering theory as well as applications.
Main description
Designed for one-semester courses at the senior undergraduate level, this book will appeal to mathematics undergraduates, to mathematics teachers, and to others who need to learn some mathematical analysis for use in other areas such as engineering, physics, biology or finance. Topics such as completeness and compactness are approached initially through convergence of sequences in metric space, and the emphasis remains on this approach. However, the alternative topological approach is described in a separate chapter. This gives the book more flexibility, making it especially useful as an introduction to more advanced areas such as functional analysis. Nominal divisions of pure and applied mathematics have been merged, leaving enough for students of either inclination to have a feeling for what further developments might look like. Applications have been included from such fields as differential and integral equations, systems of linear algebraic equations, approximation theory, numerical analysis and quantum mechanics.
Table of contents:
Preface; 1. Prelude to modern analysis; 2. Metric spaces; 3. The fixed point theorem and its applications; 4. Compactness; 5. Topological spaces; 6. Nomed vector spaces; 7. Mappings on normed spaces; 8. Inner product spaces; 9. Hilbert spaces; References; Index.