Department of Mathematics

Van Vleck Hall, 480 Lincoln Drive, Madison, WI

Errata to the Calculus texts


Math 221

  • page 167, problem 7 about the Catenary.  The equation for the catenary in this problem should be $$y=\frac12\bigl(e^x+e^{-x}\bigr)$$ instead of $$y=\frac14\bigl(e^x+e^{-x}\bigr).$$This does not affect problem 7a, but problem 7b now has a nice answer. (reported by Keith Rush, Sept 2015).

Math 222, Math 234

  • none reported (yet).


Typos in older versions

In 2014/15 the following typos were reported.  They have been corrected in the currently posted (fall 2015) versions of the text, but if you are using an older version they may still be relevant:

Math 221

  • page 38: In (P7): k must be an integer, or k can be any real number but then L1 must be positive.
  • page 46, right in the middle of the page it should read limx→a g(x) instead of h(x)
  • page 49, 13.2, third line from the bottom should read f(x) = √x, instead of g(x)
  • Ch3, §16, p.54: the answer to Problem 8 is 0, not -1 [reported by Marc Conrad, and Zach Wachtel]
  • Chapter 8, §8.3:  the correct value for the length of the parabola is $1/2 \sqrt{5} + 1/4 \ln(2+\sqrt{5})$

Math 222

  • Page 10, example 3.1.2: In the last two lines of this example it should say
    I = x/4 + 1/4 sin2x + 1/4 ( x/2 + 1/8 sin 4x)+C
      = 3x/8 + 1/4 sin2x + 1/32 sin 4x + C.
  • Chapter 1, §15 Mixed Integration problem #32:  the hint should be $1+\cos\alpha = 2\cos^2(\alpha/2)$

Math 234

  • Chapter 4, §9.1, equation (79).  In the middle the term $\frac{\partial f}{\partial y}\frac{dy}{dt}$ appears twice.  One of those terms should be$\frac{\partial f}{\partial z}\frac{dz}{dt}$.  [Reported by Zachary Wachtel.]
  • Chapter 4, §10.3: the computation of the partial derivative $F_x$ had a sign error as a result of which the computed value of $g_y(3,6)$ also had the wrong sign [reported by Alex Sharp]

UW-Madison Department of Mathematics
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Madison, Wi  53706

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