George Boros

Irresistible Integrals (eBook, PDF)

Symbolics, Analysis and Experiments in the Evaluation of Integrals

• Format: PDF

Produktbeschreibung

The problem of evaluating integrals is well known to every student who has had a year of calculus. It was an especially important subject in 19th century analysis and it has now been revived with the appearance of symbolic languages. In this book, the authors use the problem of exact evaluation of definite integrals as a starting point for exploring many areas of mathematics. The questions discussed in this book, first published in 2004, are as old as calculus itself. In presenting the combination of methods required for the evaluation of most integrals, the authors take the most interesting, rather than the shortest, path to the results. Along the way, they illuminate connections with many subjects, including analysis, number theory, algebra and combinatorics. This will be a guided tour of exciting discovery for undergraduates and their teachers in mathematics, computer science, physics, and engineering.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 21. Juni 2004
• Englisch
• ISBN-13: 9780511207914
• Artikelnr.: 38200765

Inhaltsangabe

1. Introduction
2. Factorials and binomial coefficients
3. The method of partial fractions
4. A simple rational function
5. A review of power series
6. The exponential and logarithm functions
7. The trigonometric functions and pi
8. A quartic integral
9. The normal integral
10. Euler's constant
11. Eulerian integrals: the Gamma and Beta functions
12. The Riemann zeta function
13. Logarithmic integrals
14. A master formula
15. Appendix: the revolutionary WZ method.