A Course in Modern Analysis and its Applications [Hardcover]

An advanced 2003 undergraduate text on mathematical analysis designed for pure or applied mathematicians, covering theory as well as applications.Designed for one-semester courses at the senior undergraduate level, this book will appeal to mathematics majors, 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.Nominal divisions of pure and applied mathematics have been merged, leaving enough for students of either inclination to have a feeling for further developments. Applications have been included from such fields as differential and integral equations, systems of linear algebraic equations, approximation theory, numerical analysis and quantum mechanics.Designed for one-semester courses at the senior undergraduate level, this book will appeal to mathematics majors, 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.Nominal divisions of pure and applied mathematics have been merged, leaving enough for students of either inclination to have a feeling for further developments. Applications have been included from such fields as differential and integral equations, systems of linear algebraic equations, approximation theory, numerical analysis and quantum mechanics.Designed for one-semester courses at the senior undergraduate level, this book is written for mathematics students and teachers, as well as others needing to learn mathematical analysis for engineering, physics, biology or finance. Nominal divisions between pure and applied mathematics have been merged to provide easier access. Applications are included from differential and integral equations, systems of linear algebraic equations, approximation theory, numerical analysis and quantum mechanics.Preface; 1. Prelude to modern analysis; 2. Metric spaces; 3. The fixed point theorem and its applications; lÁ