ÍNDICE: Preface. Acknowledgments. 1. Archimedes and the Parabola. 1.1 The Area of the Parabolic Segment. 1.2 The Geometry of the Parabola. 2. Fermat, Differentiation, and Integration. 2.1 Fermats Calculus. 3. Newtons Calculus (Part1). 3.1 The Fractional Binomial Theorem. 3.2 Areas and Infinite Series. 3.3 Newtons Proofs. 4. Newtons Calculus (Part 2). 4.1 The Solution of Differential Equations. 4.2 The Solution of Algebraic Equations. Chapter Appendix. Mathematica implementations of Newtons algorithm. 5. Euler. 5.1 Trigonometric Series. 6. The Real Numbers. 6.1 An Informal Introduction. 6.2 Ordered Fields. 6.3 Completeness and Irrational Numbers. 6.4 The Euclidean Process. 6.5 Functions. 7.Sequences and Their Limits. 7.1 The Definitions. 7.2 Limit Theorems. 8. The Cauchy Property. 8.1 Limits of Monotone Sequences. 8.2 The Cauchy Property. 9. The Convergence of Infinite Series. 9.1 Stock Series. 9.2 Series of Positive Terms. 9.3 Series of Arbitrary Terms. 9.4 The Most Celebrated Problem. 10. Series of Functions. 10.1 Power Series. 10.2 Trigonometric Series. 11. Continuity.11.1 An Informal Introduction. 11.2 The Limit of a Function. 11.3 Continuity.11.4 Properties of Continuous Functions. 12. Differentiability. 12.1 An Informal Introduction to Differentiation. 12.2 The Derivative. 12.3 The Consequences of Differentiability. 12.4 Integrability. 13. Uniform Convergence. 13.1 Uniform and Non-Uniform Convergence. 13.2 Consequences of Uniform Convergence. 14. The Vindication. 14.1 Trigonometric Series. 14.2 Power Series. 15. The Riemann Integral. 15.1 Continuity Revisited. 15.2 Lower and Upper Sums. 15.3 Integrability. Appendix A. Excerpts from Quadrature of the Parabola by Archimedes. Appendix B. On a Method for Evaluation of Maxima and Minima by Pierre de Fermat. Appendix C. From a Letter to Henry Oldenburg on the Binomial Series (June 13, 1676) by Isaac Newton. Appendix D. From a Letter to Henry Oldenburg on the Binomial Series (October 24, 1676) by Isaac Newton. Appendix E. Excerpts from Of Analysis by Equations of an Infinite Number of Terms by Isaac Newton. Appendix F. Excerpts from Subsiduum Calculi Sinuum by Leonhard Euler). Solutions toSelected Exercises Bibliography. Index.
- ISBN: 978-0-470-87890-3
- Editorial: John Wiley & Sons
- Encuadernacion: Cartoné
- Páginas: 320
- Fecha Publicación: 15/07/2011
- Nº Volúmenes: 1
- Idioma: Inglés