Advanced Calculus Second Edition Patrick M. Fitzpatrick Errata
Patrick M. Fitzpatrick's "Advanced Calculus, Second Edition" is widely used in upper-division undergraduate and beginning graduate courses in mathematics. Despite careful editing and proofreading, some errors inevitably make it into publication. This page serves as a centralized resource for known errata in this valuable textbook.
Understanding Textbook Errata
Errata are corrections to errors found in a book after publication. In mathematics textbooks, these can range from typographical errors and misprints to substantial mathematical mistakes that could affect understanding. Keeping track of errata is particularly important in mathematics texts, as even small errors can lead to confusion or misdirected learning.
Known Errata for Advanced Calculus, Second Edition
Page 27, Exercise 6
Current text: "Let f: be defined by f(x) = x + 1 for x ."
Correction: The domain statement is redundant with the earlier declaration. Should read: "Let f: be defined by f(x) = x + 1."
Page 43, Example 3.2
Current text: "Consider the function f: [0,1] defined by f(x) = 1/n for x = 1/n where n is a positive integer."
Correction: Should specify that f(x) = 0 for x not of the form 1/n. Complete definition should read: "Consider the function f: [0,1] defined by f(x) = 1/n for x = 1/n where n is a positive integer, and f(x) = 0 otherwise."
Page 78, Definition 4.7
Current text: "A function f: D is called uniformly continuous on D if for every > 0 there exists > 0 such that if x,y D and |x-y| < , then |f(x)-f(y)| < ."
Correction: The definition is correct, but the notation could be clearer. Should read: "A function f: D is called uniformly continuous on D if for every > 0 there exists > 0 such that for all x,y D with |x-y| < , we have |f(x)-f(y)| < ."
Page 112, Theorem 5.10
Current text: "If f: [a,b] is continuous on [a,b] and differentiable on (a,b), then there exists c (a,b) such that f'(c) = (f(b)-f(a))/(b-a)."
Correction: The theorem statement is correct, but the figure illustrating it is incorrectly labeled. Point c in the figure should correspond to f'(c), not f''(c) as shown.
Page 156, Example 7.4
Current text: "Consider the function f(x,y) = xy + xy - 2xy + x - y."
Correction: In the computation of the gradient, the partial derivative with respect to y is incorrectly shown as f/y = x + 2xy - 2x - 1. The correct partial derivative is f/y = x + 2xy - 2x - 1.
Page 203, Exercise 9.14
Current text: "Prove that if f: [0,1] [0,1] is continuous, then there exists c [0,1] such that f(c) = c."
Correction: The statement is correct, but the hint provided is misleading. The hint should suggest applying the intermediate value property to the function g(x) = f(x) - x, not analyzing critical points as currently suggested.
Page 241, Example 11.3
Current text: "Consider the sequence {x_n} defined by x_1 = 1 and x_{n+1} = sqrt(2 + x_n) for all n 1."
Correction: In the calculation of the limit, it is incorrectly assumed that the sequence is increasing without proof. The complete argument should first demonstrate that the sequence is monotone (using induction) before applying the Monotone Convergence Theorem.
Chapter-by-Chapter Errata Summary
Chapter 1: The Real Numbers
Minor typographical errors in examples 1.3 and 1.5. These do not affect the mathematical content.
Chapter 2: Sequences
Page 27: Redundant domain declaration in Exercise 6 (see detailed entry above).
Chapter 3: Continuity
Page 43: Incomplete function definition in Example 3.2 (see detailed entry above).
Chapter 4: Uniform Continuity
Page 78: Notation clarity issue in Definition 4.7 (see detailed entry above).
Chapter 5: Differentiation
Page 112: Incorrect labeling in accompanying figure for Theorem 5.10 (see detailed entry above).
Chapter 6: Integration
Minor formatting issues in displayed formulas on pages 134-136.
Chapter 7: Functions of Several Variables
Page 156: Partial derivative notation inconsistent in Example 7.4 (see detailed entry above).
Chapters 8-14
Additional errors have been reported in Exercise 9.14 and Example 11.3 (see detailed entries above). Otherwise, no other significant errata reported at this time.
How to Report New Errata
If you believe you have discovered an error in "Advanced Calculus, Second Edition" that is not listed on this page, please report it through one of the following methods:
- Contact the publisher directly at their academic mathematics division
- Email the author (Professor Patrick M. Fitzpatrick) through his university contact information
- Submit through mathematics textbook errata forums or discussion groups
When reporting an error, please include:
- The page number and edition (Second Edition)
- The problem or section number
- The current text or formula as it appears in the book
- Your suggested correction
- An explanation of why you believe it is an error
Note on Pagination Differences
Pagination may vary slightly between printings of the Second Edition. When referencing page numbers, please confirm you are using the standard edition printed in 2006 or later, as there were adjustments made in early printings that affect page numbering. If in doubt, reference both the page number and the chapter/section for clarity.
Conclusion
"Advanced Calculus, Second Edition" by Patrick M. Fitzpatrick remains a highly respected text for rigorous study of calculus at the advanced level. While the errata listed above should be noted, they represent a very small fraction of the content and do not significantly detract from the pedagogical value of this textbook. These errors will likely be corrected in future printings or editions.
We encourage readers to use this page as a reference while studying, and to report any additional errors they may discover. The ongoing collaboration between authors, publishers, and readers in identifying and correcting errata strengthens mathematical education for everyone.
Advanced Calculus Second Edition Patrick M. Fitzpatrick Errata and Reference File Download...
Advanced Calculus: A Geometric View Errata and Reference File Download Link
The Wisdom And Pragmatic Value To Team Building From Patrick Lencioni S The Five Dysfuncti...
The Five Dysfunctions Of A Team By Patrick Lencioni and Reference File Download Link