Buch, Englisch, 151 Seiten, Format (B × H): 183 mm x 259 mm, Gewicht: 522 g
Buch, Englisch, 151 Seiten, Format (B × H): 183 mm x 259 mm, Gewicht: 522 g
ISBN: 978-0-8218-3670-5
Verlag: American Mathematical Society
This book is written by award-winning author, Frank Morgan. It offers a simple and sophisticated point of view, reflecting Morgan's insightful teaching, lecturing, and writing style. Intended for undergraduates studying real analysis, this book builds the theory behind calculus directly from the basic concepts of real numbers, limits, and open and closed sets in $\mathbf{R n$. It gives the three characterizations of continuity: via epsilon-delta, sequences, and open sets. It gives the three characterizations of compactness: as "closed and bounded," via sequences, and via open covers. Topics include Fourier series, the Gamma function, metric spaces, and Ascoli's Theorem. This concise text not only provides efficient proofs, but also shows students how to derive them. The excellent exercises are accompanied at the back of the book by select solutions. Ideally suited as an undergraduate textbook, this complete book on real analysis will fit comfortably into one semester. Frank Morgan received the first national Haimo teaching award from the Mathematical Association of America. He has also garnered top teaching awards from Rice University (Houston, TX) and MIT (Cambridge, MA).
Contents
- Infinity
- Sequences
- Functions and limits
- Continuous functions
- Composition of functions
- Subsequences
- Compactness
- Existence of maximum
- Uniform continuity
- Connected sets and the intermediate value theorem
- The Cantor set and fractals
- The Riemann integral
- The fundamental theorem of calculus
- Sequences of functions
- The Lebesgue theory
- Infinite series $sum {n=1}sigma a n$
- Absolute convergence
- Power series
- Fourier series
- Strings and springs
- Convergence of Fourier series
- The exponential function
- Volumes of $n$-balls and the gamma function
- Analysis on metric spaces
- Compactness in metric spaces
- Ascoli's theorem
- Partial solutions to exercises
- Greek letters
- Index
Zielgruppe
Undergraduate students interested in analysis.
