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Kurzbeschreibung Combining historical coverage with key introductory fundamentals, Real Analysis: A Historical Approach, Second Edition helps readers easily make the transition from concrete to abstract ideas when conducting analysis. Based on reviewer and user feedback, this edition features a new chapter on the Riemann integral including the subject of uniform continuity, as well as a discussion of epsilon-delta convergence and a section that details the modern preference for convergence of sequences over convergence of series. Both mathematics and secondary education majors will appreciate the focus on mathematicians who developed key concepts and the difficulties they faced.
Aus dem Inhalt Preface to the Second Edition
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 Fermat's Calculus
3. Newton's Calculus (Part 1)
3.1 The Fractional Binomial Theorem
3.2 Areas and Infinite Series
3.3 Newton's Proofs
4. Newton's Calculus (Part 2)
4.1 The Solution of Differential Equations
4.2 The Solution of Algebraic Equations
Chapter Appendix. Mathematica implementations of Newton's algorithm