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, 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.
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, 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.
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.
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.
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