Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of IntegralsThe 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. |
Contents
Factorials and Binomial Coefficients | 1 |
The Method of Partial Fractions | 28 |
A Simple Rational Function | 48 |
A Review of Power Series | 70 |
The Exponential and Logarithm Functions | 78 |
8 | 97 |
A Quartic Integral | 137 |
The Normal Integral | 167 |
Other editions - View all
Irresistible Integrals: Symbolics, Analysis and Experiments in the ... George Boros,Victor Moll No preview available - 2004 |
Irresistible Integrals: Symbolics, Analysis and Experiments in the ... George Boros,Victor Moll No preview available - 2004 |
Irresistible Integrals: Symbolics, Analysis and Experiments in the ... George Boros,Victor Moll No preview available - 2004 |
Common terms and phrases
a₁ algebraic Amer an(x Apery's appears in G ascending factorial ax² b₁ Bernoulli numbers binomial coefficients binomial theorem Borwein central binomial central binomial coefficients change of variable Chapter closed form compute Conclude convergence definite integrals denominator derive di(m differentiation discussed dx x² elementary equation establish Euler's constant evaluation example expansion expression Extra factorization gamma function given H₂ harmonic numbers Hint identity In² inequality integer integral representation integrand introduced ln x dx logarithm Master Theorem Math Mathematica Mathematica command Mathematics Moll Monthly number theory obtain parameters partial fractions Pm(a polynomial power series prime numbers primitive produce Project proof Proposition Prove quartic r₁ radius of convergence rational function reader will find recurrence result Riemann zeta function roots satisfies sequence Stirling's formula symbolic Taylor series trigonometric functions Wallis x²+1 x4 2ax² yields