Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals

ISBN-13: 9780521796361 / Angielski / Miękka / 2004 / 322 str.

Victor H. Moll; George Boros; Victor Moll

Opis

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 nineteenth century analysis and it has now been revived with the appearance of symbolic languages. The authors use the problem of exact evaluation of definite integrals as a starting point for exploring many areas of mathematics. The questions discussed 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. They illuminate connections with many subjects, including analysis, number theory, algebra and combinatorics. This is a guided tour of exciting discovery for undergraduates and their teachers in mathematics, computer science, physics, and engineering.

Recenzje

'The authors have managed to write a very readable account about integrals, accessible even to advanced undergraduates. Some of the topics of the book could be used for undergraduate reading and research projects. This way the book could serve as a 'springboard to many unexpected investigations and discoveries in mathematics.' Zentralblatt MATH

Spis treści

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.