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Practical guide demystifying the art of integration for beginning calculus students through thorough explanations, examples and exercises.
List of contents
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.
About the author
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).
Summary
This practical guide demystifies the art of integration. Each chapter explains a particular technique of elementary integration through thorough explanations, worked examples and numerous exercises ranging from the routine to the challenging. It may serve as a complete introduction, or as a supplementary text for any beginning course in calculus.
