Description
Book SynopsisIntegration has a long history: its roots can be traced as far back as the ancient Greeks. The first genuinely rigorous definition of an integral was that given by Riemann, and further (more general, and so more useful) definitions have since been given by Lebesgue, Denjoy, Perron, Kurzweil and Henstock, and this culminated in the work of McShane. This textbook provides an introduction to this theory, and it presents a unified yet elementary approach that is suitable for beginning graduate and final year undergraduate students.
Trade Review'… already it is worthy of a place in our standard curriculum … The book of Lee and Vyborny serves well as an introduction and reference for anyone interested in this topic.' J. Alan Alewine and Eric Schechter, American Mathematical Monthly
'… the authors do an excellent job of presenting their material. The book is written with clarity and enthusiasm.' Brian Jefferies
'This is a valuable addition to the literature …'. Jean Mawhin, Bulletin of the Belgian Mathematical Society
Table of ContentsPreface; 1. Introduction; 2. Basic theory; 3. Theory development; 4. The SL-integral; 5. Generalized AC function; 6. Integration in several dimensions; 7. Some applications; 8. List of symbols; Appendices.
