Seán M StewartCambridge University Press, 12/28/2017EAN 9781108408196, ISBN10: 1108408192Paperback, 380 pages, 22.9 x 15.2 x 2.2 cmLanguage: EnglishWhile differentiating elementary functions is merely a skill, finding their integrals is an art. This practical introduction to the art of integration gives readers the tools and confidence to tackle common and uncommon integrals. After a review of the basic properties of the Riemann integral, each chapter is devoted to a particular technique of elementary integration. Thorough explanations and plentiful worked examples prepare the reader for the extensive exercises at the end of each chapter. These exercises increase in difficulty from warm-up problems, through drill examples, to challenging extensions which illustrate such advanced topics as the irrationality of À and e, the solution of the Basel problem, Leibniz's series and Wallis's product. The author's accessible and engaging manner will appeal to a wide audience, including students, teachers and self-learners. The book can serve as a complete introduction to finding elementary integrals, or as a supplementary text for any beginning course in calculus.1. The Riemann integral2. Basic properties of the definite integral – Part I3. Some basic standard forms4. Basic properties of the definite integral – Part II5. Standard forms6. Integration by substitution7. Integration by parts8. Trigonometric integrals9. Hyperbolic integrals10. Trigonometric and hyperbolic substitutions11. Integrating rational functions by partial fraction decomposition12. Six useful integrals13. Inverse hyperbolic functions and integrals leading to them14. Tangent half-angle substitution15. Further trigonometric integrals16. Further properties for definite integrals17. Integrating inverse functions18. Reduction formulae19. Some other special techniques and substitutions20. Improper integrals21. Two important improper integralsAppendix A. Partial fractionsAppendix B. Answers to selected exercisesIndex.
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