Advanced Calculus highlights the connections between calculus and linear algebra and provides a mathematically sophisticated introduction to functional analytic concepts. The book stresses that proofs must be written down, scrutinized step-by-step and rewritten whenever there is doubt. Unlike the competition, this book approaches the rigorous foundations of calculus in a manner that reorients thinking in the directions taken by modern analysis. INDICE: Preface. Acknowledgments. Introduction. PART I. ADVANCED CALCULUS IN ONE VARIABLE. 1. Real Numbers and Limits of Sequences. 2. Continuous Functions. 3. Rieman Integral. 4. The Derivative. 5. Infinite Series. PART II. ADVANCED TOPICS IN ONE VARIABLE. 6. Fourier Series. 7. The Riemann-Stieltjes Integral. PART III. ADVANCED CALCULUS IN SEVERAL VARIABLES. 8. Euclidean Space. 9. Continuous Functions on Euclidean Space. 10. The Derivative in Euclidean Space.11. Riemann Integration in Euclidean Space. Appendix A. Set Theory. Problem Solutions. References. Index.
- ISBN: 978-0-470-23288-0
- Editorial: John Wiley & Sons
- Encuadernacion: Cartoné
- Páginas: 416
- Fecha Publicación: 09/05/2008
- Nº Volúmenes: 1
- Idioma: Inglés
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- MATEMÁTICAS /
- CÁLCULO