This is the third edition of this popular text on Real Analysis by two well-established authors. In this new edition there has been a small amount of revision in the exposition some new exercises have been set and there is a totally new chapter on the generalised Riemann integral.
The content is fairly typical of an analysis text. Topics covered include sequences series limits the derivative sequences of functions and infinite series. In addition there are chapters on the Riemann integral and the generalised Riemann integral. The authors’ justification for this latter chapter being that the generalised Riemann integral (also known as the Henstock-Kurzweil integral) has a greater range of application than the Lebesgue integral. There are appendices on methods of proof countability approximate integration and integrability criteria. Each section of every chapter has a generous set of exercises of varying difficulty although the harder exercises are not starred and there are no slightly longer “project exercises” which characterise Bartle’s solo text “The Elements of Real Analysis”. About half of all exercises have answers or at least hints to the solution. (A teacher’s manual with almost all solutions is available upon request to the publisher).
