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.
This book, first published in 2004, uses the problem of exact evaluation of definite integrals as a starting point for exploring many areas of mathematics.
'I recommend this book highly as a source of rewarding projects for undergraduates (and others) to home their analytic skills and gain an appreciation for this area of mathematics. The authors clearly had great love for the material and their enthusiasm comes through in an infectious manner.' SIAM Review '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