Marsden/Weinstein Textbook Information
Fall 2009
Books for Calculus at Truman
College
- The Math 207 textbook is Calculus
I, 2nd Edition, by Marsden and Weinstein, 1985, ISBN # 978-0-387-90974-5.
There is also have an optional supplement, Student's Guide to
CALCULUS by J. Marsden and A. Weinstein I, by Frederick H. Soon, ISBN
# 978-0-387-96207-8.
- The Math 208 textbook is Calculus
II, 2nd Edition, by Marsden and Weinstein, 1985, ISBN # 978-0-387-90975-2. There is also have an optional
supplement, Student's Guide to CALCULUS by J. Marsden and A. Weinstein
I, by Frederick H. Soon, ISBN # 978-0-387-96234-4.
- The Math 209 textbook is Calculus
II, 2nd Edition, by Marsden and Weinstein, 1985, ISBN # 978-0-387-90985-1. There is also have an optional
supplement, Student's Guide to CALCULUS by J. Marsden and A. Weinstein
I, by Frederick H. Soon, ISBN # 978-0-387-96348-8.
Available Online
- If you are using a computer at
Truman College you should also be able to download these books as PDF files. You can do this by going to http://www.cds.caltech.edu/~marsden/volume/Calculus/
and clicking on the cover of the book.
- Although you are welcome to use
these, all students are strongly encouraged to purchase a copy of the
textbook (and possibly the student guide) as soon as possible. Reading PDF files is simply not as
effective as reading a book.
However, feel free to use these PDF files while you order your book
or if you misplace it, etc.
Typos and Corrections
There have been a number of typos found in the second edition since its publication. The textbook Web site includes many of these. Below you can find various typos and corrections, nearly all of which were found by me or previous students of mine. Most of these have been incorporated into the textbook Web site maintained by the authors. If you find additional items, please e-mail mmaltenfort@ccc.edu (I generally give extra credit for new typos found!). Thank you.
The corrections for Calculus II and Calculus
III appear below those for Calculus I, or click on these links to
jump directly to Calculus II or Calculus III.
p. 87: In
the statement of the Integer Power Rule, the parenthetical sentence should
specify that x is nonzero if n < 1, not n < 0.
p. 93, Example 6:
In the original statement of the problem, the numerator should be
2. This only needs to be corrected in
original statement of problem. More
recent printings of the textbook include this correction.
Towards the top of page 146, when the authors define
decreasing, they mean to say "if there is an interval (a, b)
containing x0," but they say x instead of x0. The definition of increasing is
written correctly without this typo.
On page 216, in the paragraph above the drawing
of buses, the first summation is from i = 0 to n and the second
is from i = 0 to infinity. Both
should be from i = 0 to n.
The solution in the back of the book for 3.5 #27 is
incorrect. The critical points should
be 1 and 1; the minimum is (1,1/2).
In Figure 4.4.2 on page 227, the horizontal axis is
labeled entirely in terms of t even though the independent variable is x.
Page 231:
The answer in the back of the book to Exercise 4.4 #21 should be 319/24,
not 367/24.
Exercise 54 in Section 4.5
(page 239): the assumption that F '
= f is continuous must be added.
(This comment comes from having read Michael Spivak's Calculus.)
Page 247:
the answer to Review Exercise #15 should be 5/4.
Exercise 5.1 #15 should end with a period (as
#16 does), not a question mark.
In Exercise 5.3 #31, the function g has
domain [11/12, 11/12], so technically g'(11/12) is undefined. In the original problem, the domain of f
should be bigger, e.g. [2, 2].
Exercise 5.4 #51a: the answer in the back of the book for the domain should include
two intervals. (As in the graph in the
back of the book for 51b.)
Page 306, review exercise 79a: Judging from the answer in the back of the
book, π1020 is intended where π+1020
appears.
Page 311:
Exercises #14 and #15 in Section 6.1 are printed in reverse order.
Page 328: In
the box at the top of the page, in both limits of #3 (and the concluding
sentence of #3), ln |x| rather than ln x should appear. (Alternatively the limits could be made
one-sided limits, but one-sided limits are not introduced until the following
textbook.)
Page 329:
The footnote at the bottom of the page (referring to the irrationality
of e) should refer to Review Exercise 129, not Review
Exercise 128.
The function cosh1 x is defined
for x ≥ 1, and it is differentiable for x > 1. This domain is correctly given in equation
(3) on page 394, but the domain is incorrectly given as |x| > 1
at the top the table on page 396.
A related change, later in the same table, must be made: when
integrating 1/(x2 1)1/2, one of the
antiderivatives given is cosh1 x + C. Instead the antiderivative should be cosh1
|x| + C. This latter
change also must be made in formula #44 in the table of integrals given at the
back of all three volumes of the textbooks.
page. 364 The answer in the back of the book for 7.4
#45 should be (π + 4)/(8√2) ½.
page 366 Review Exercise #8: In some books, the cube root sign in the numerator
covers the entire numerator, but it should only cover the first term. I.e., the numerator should equal x^(2/3)
x^(5/2).
page 407 The answer in the back of the book for 8.5
#25 should be (b) y' = 3y/x and (c) y = ± √(C
x2/3)
page 407 The answer in the back of the book for 8.5
#35 has the correct picture, but as x goes to infinity, y goes to
2, not to 1.
Exercise 9.5 #22:
the ball has a mass (not weight) of 20 grams.
page 413:
the solution in the back of the book to 8.6 #1 should be y = (3x2
10x + C)/(2x-2).
Alternately, to get the answer in the back of the book, one can change y
to y in the numerator of the first term of the right hand side. The Student's Guide incorrectly solves this
problem (chain rule errors).
page 444: in
older textbooks, the solution in the back of the book to 9.4 #17 is mistakenly
3ln (3/2) rather than 3(ln 3)/2
p. 464: in
older textbooks, the solution in the back of the book to 10.1 #17 mistakenly
has 2cos1(2/|x|) rather than 2cos1(2/x).
page 464:
In the answer in the back of the book for 10.1 #27, the first square
root should be multiplied by 1/√3.
page 476:
In 10.2 # 1, the denominator should end with (x2 + 1)2;
older books omit the outer exponent.
page 476:
In the answer in the back of the book for 10.2 #9, the x21
should be in absolute values, instead of parentheses.
page 498:
In the first equation of the solution to Example 11(b), it says that A
equals the integral from 0 to 2π of y dx and also the
integral from 0 to 2π of y dx/dθ dθ. The first integral, however, since it's in
terms of the variable x, should have limits of integration which go from
0 to 2πa.
page 504:
The solution in the back of the book for Exercise 10.5 #1 is wrong. It should be 24, not 12√2. The error probably occurred because of
sloppiness with absolute values.
Exactly this error was avoided in Example 2, page 501. This error also appears in the Student
Guide.
page 504:
The solution in the back of the book for Exercise 10.5 #13 is wrong,
because the exponent of secant should be 4, not 2.
page 505:
The solution for Chapter 10 Review Exercise #7 should be √(x216)
4arcsec (x/4) + C.
page 505:
In the solution in the back of the book for Chapter 10 Review
Exercise #27, both terms should have coefficient 2 (not just the first).
page 507 #93:
"integrals" should be "integers."
page 510:
In the solution to Example 1(a):
"A useful general rule is to write down f(x) = L
..." but it seems clear that f(x) L is intended.
page 519:
In the solution (hint) to 11.1 #3 in the back of the book, 2[x3]2
is written where clearly 2[(x3)+3]2 is intended.
page 520:
remove superfluous parenthesis in Exercise 11.1 #66.
page 520: In
Exercise 11.1 #67, (a) is probably supposed to ask for f '(x) and
its graph, rather than f(x).
page 520: In
Exercise 11.1 #76, δ1 should be chosen so that |f(x)
L| is less than ε/2 times (|M| + 1), not times M. The absolute values are needed because M
might be negative; the +1 in case M is zero. (This comment also derives from Spivak's Calculus.)
Suggestion:
in the "Preliminary Version" of L'Hτpital's rule, on page 522,
the hypotheses could be weakened: f
and g need only be differentiable at x0 itself, not in
an open interval.
p. 527 Exercise 11.2 #11 and 13: Use ln |x| rather than ln x so
that the limit makes sense.
p. 549 To have consistent notation, in Exercise 11.4
#55a, the question should ask for a B-N definition, rather than
an A-N definition.
p. 568 In the back of the book, the second partial
sum for 12.1 # 3, while correct, should be reduced from 30/27 to 10/9.
p. 615: In
the answer in the back of the book for 12.6 # 21, some books don't have the
correct answer, which is ±i√3.
p. 615: In
the answer in the back of the book for 12.6 # 23, the real part of the
numerator should be 1, not 1.
p. 631 In the answer in the back of the book for
12.7 # 27, (1 √2) appears where it should be (1 2√2).
page 643, Chapter 12 review exercise #123: Should prove that 
because result as stated is trivial and
unhelpful.
The solution in the back of the book for
Exercise 12.6 #87 has 0,46 where 0.46 is intended.
p. 652: In
Exercise 13.1 #27b, the back of the book claims (1/2)a = e, which is incorrect: visually a and e are not
parallel, and computationally a=(3,-2) and e=(2,-1), as can be confirmed
by looking at the answer in the back of the book for Exercise 13.1 #29.
page 734:
The answer in the back of the book for Exercise 14.5 # 13 is the graph
for the equation r = 1 + 2 sin θ, but it should be for r = 1
+ 2 cos θ.
page 753:
Exercise 14.7 # 16 should be asking for the curvature (not the curvature
vector).
page 771:
In Example 10, we must choose ε1 to be the smaller
of 1 and ε/[3(|g(y0)|+|f(x0)|+1)]. That is, an additional factor of three is needed
in the denominator (to be used at the conclusion of (a)). Here and on the line above, f(y0)
must be corrected to f(x0).
page 771:
In proving the equality of mixed partial derivatives, the limit at the
very bottom of the page is undefined.
This is because the fraction is often undefined, even if (Δx,Δy)
is not (0,0) (e.g. if Δx is zero and Δy is not). To correct this, throughout the proof change
all Δx and Δy to Δt, and make the limit at
the bottom of the page into the one-variable limit as Δt approaches
zero.
page 783:
Exercise 15.3 # 20 gives a sketch of a proof of the chain rule, but
it only works under the additional assumption that g and h have
continuous partial derivatives.
page 792:
Exercise 15.4 # 40(c): z
= rcos φ. Some editions have
some missing letters.
page 801:
At the end of the solution to Example 7(d), the second term listed after
"the directional derivative is" should be 1(-1/√3), not
1(-1√3).
page 812:
The equation in Exercise 16.2 # 19 should be cos(x + y) =
0, not =1/2.
page 812:
The solution in the back of the book for 16.2 #39 should be dx/dt
= (-x2/y)dy/dt.
page 821:
Towards the end of the Supplement to Section 16.3,
"minima" is a typo for "minimum."
page 853:
Exercise 17.2 # 23: the region D
doesn't make sense (x=2??), but it is unclear where the typo is.
page 859:
Exercise 17.3 # 25 should specify z ≥ 0.
page 875:
Exercise 17.5 # 13: Unclear
problem, since the region could be inside both figures, or outside the cylinder
and inside the sphere. From the back of
the book's answer, the former is intended.
page 881:
Exercise 17.6 # 1b should have z2 instead of z
to match the solution manual. However,
the solution manual and the back of the book have the wrong answer. The answer should be 41/12, not 41/3. The answer to the problem as printed in the
book is 37/12.
page 889:
Italics are missing from one instance of f(u), and a
separate instance of u, in the statement of the Independence of
Parameterization Theorem.
page 901:
Exercise 18.2 # 21: Change y
> 0 to x > 0. This way the
hint works.
page 901:
Continuity must be assumed in Exercise 18.2 # 36.
page 907:
Exercise 18.3 # 10: The
path should be (x√t, ty), not (x√t,
tx).
page 916:
At the top of the page, in the formula following "The circulation
of V about the circle..." the coefficient of "(area of
disk)" should be 2, not 2.
Section 18.5:
The introduction of the Mean Value Theorem for double and triple
integrals at the top of the page 922 should instead appear in the middle
of page 916, where it is first used.
page 923:
Exercise 18.5 # 5: the answer in
the back of the book should be 8, not 8.
page 923:
Exercise 18.5 # 17 should specify that S and C do not
intersect the plane y + z = 0.
page 930:
Exercise 18.6 # 3: the answer in
the back of the book should be ycos(xy)+x2sin(x2y),
not ycos(xy)x2sin(x2y).
Revised Friday, May 1, 2009. E-mail corrections, suggestions to mmaltenfort@ccc.edu