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

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9780511617041: Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals

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.

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Book Description:

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, including analysis, number theory, algebra and combinatorics. The questions discussed here are as old as calculus itself. This will be a guided tour of exciting discovery for undergraduates and their teachers in mathematics, computer science, physics, and engineering.

Review:

"This book would be perfect in a basic elective course to hone calculus and proof writing skills and as enrichment reading for talented calculus students." Choice

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