William F. Trench

Digital versions PDF
Source available Yes
Exercises Yes
Answers to selected exercises Yes
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NonCommercial-ShareAlike 3.0
  • 583 page text for two semesters of undergraduate real analysis
  • Originally published by Pearson Education
  • Complete solution manual available to verified faculty
  • May be printed and distributed with a nominal charge to cover costs
  • For more information and to download

From an instructor who recently used this book: “I found it mathematically sound, well organized and very instructive for a good upper division undergraduate class. In particular, the exercise sets are well thought out and both the proofs and the narrative speak well to that level of student without sacrificing any rigor.”

The first half of the book covers functions of a single variable and is appropriate for one semester. The second half covers functions of several variables, both real-valued and vector-valued. The last chapter is an introduction to metric spaces. There are 295 examples completely worked out and 760 exercises with selected answers. The solution manual for instructors has solutions to all the exercises. There are two supplementary sections on functions defined by improper integrals and on Lagrange multipliers.

The author welcomes corrections and is updating the book regularly. The most recent version is dated May 2012.