Sean M. Stewart

How to Integrate It (eBook, ePUB)

A Practical Guide to Finding Elementary Integrals

• Format: ePub

Produktbeschreibung

While 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 I 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.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 21. Dezember 2017
• Englisch
• ISBN-13: 9781108311144
• Artikelnr.: 50463427

Autorenporträt

Seán M. Stewart is the co-founder and principal teaching fellow at Omegadot Tuition, Sydney. He has had over eighteen years of experience teaching mathematics and physics at both the secondary and tertiary levels. He is a member of numerous professional associations and societies in mathematics and physics. In 2004, he won the Petroleum Institute Outstanding Faculty Award for Teaching. He has written numerous research articles and co-authored the book Blackbody Radiation: A History of Thermal Radiation Computational Aids and Numerical Methods (2016).

Inhaltsangabe

1. The Riemann integral
2. Basic properties of the definite integral - Part I
3. Some basic standard forms
4. Basic properties of the definite integral - Part II
5. Standard forms
6. Integration by substitution
7. Integration by parts
8. Trigonometric integrals
9. Hyperbolic integrals
10. Trigonometric and hyperbolic substitutions
11. Integrating rational functions by partial fraction decomposition
12. Six useful integrals
13. Inverse hyperbolic functions and integrals leading to them
14. Tangent half-angle substitution
15. Further trigonometric integrals
16. Further properties for definite integrals
17. Integrating inverse functions
18. Reduction formulae
19. Some other special techniques and substitutions
20. Improper integrals
21. Two important improper integrals
Appendix A. Partial fractions
Appendix B. Answers to selected exercises
Index.