
Book errata:
As you know, the book is new and there might be one or the other typos
still there. If you find an error (or think something is an error),
please email it to math21a@fas.harvard.edu. We will post them here.
It will help to make the book even better in the future.

Discoverer  Date  Typo 
Julia Ye  Oct 2, 2006, 5 PM 
Problem 65 in Section 11.5: The answer is 10/3^{1/2}, not 10 * 3^{1/2}

Shantanu Gaur  Oct 2, 2006, 11 PM 
Page 49, the last sentence in the solution for Example 7 should read,
x=0+3t since 3 is the xcomponent of the vector m.

Kelley Swanberg  Oct 3, 2006, 11 AM 
In problem 49 on page 43, the answer is
<2/3, 0, 0> x <0, 60, 0> = <0, 0, 40> ftlbs which has a magnitude
40 ftlbs. It is not 30 ftlbs as indicated in the solutions.

Michael Pershan  Oct 3, 2006, 3 PM 
On page 32. Numbers 62 and 62 are identical.

Kipyegon Kitur  Oct 4, 2006, 6 PM 
In the solution to Example 5, Section 11.4, pg 37. It
should be 10i2j+2k instead of 10i2j+2j. Also two lines
below, the the vectors have to have the form a i + b j + c k
not a i + b j + c j.

Dan Norman  Oct 4, 2006, 8 PM 
On page 52, in Example 13, substituting x=0 and y=0 in the equation for the
plane gives z=1, not z=1. They go on to represent z
correctly in the coordinates for Q, so it's not a huge deal.

Alice Tzeng  Oct 5, 2006, 11 PM 
On p.96 of our textbook, the directions for Exercises 5156 should
read "Calculate the moving frame (T, N, B) at t_{0}" (t subscript 0 as opposed
to t(0)).

Shiyu Wei  Oct 6, 2006, 8 PM 
On page 76, section 12.1, problem 62. The formula
d^2/dt r(t) + r(t)= 0 should read d^2/dt^2 r(t) + r(t)= 0, (there is a 2 missing in the exponent of dt).

Shiyu Wei  Oct 6, 2006, 9 PM 
On page 90, in the solution of Example 3, there is a
j vector in the arc length formula under the first square root.

Preston Copeland  Oct 31, 2006, 11 PM 
On page 132, example 3. The reader is asked to compute (f + g)(1,2) in the question,
but in the solution, (f + 3g)(1,2) is computed instead.

Kipyegon Amos Kitur  Nov 1, 2006, 9 PM 
On page 184, the solution to example 6 is wrong.
The gradient is (yz,xz,xy) = (2,1,2). The direction
of steapest decent is (2,1,2)/3.

Jenny Zhang and Pawel Zimoch  Nov 6, 2006, 11 PM 
Problem 30 in Section 13.8. The problem should ask for a minimal area and not
maximal area.

Michael Pershan  Nov 10, 2006, 3 PM 
I'm reporting an extremely minor error:
the answer to problem 19 in section 14.8 (on page 419) should list the angle of
theta as 7 pi/4. For the cylindrical coordinates it lists it as 7/4 pi which
could be understood as 7/(4 pi). It should be written more clearly
as pi/4 or (7/4) pi.

Laura Mulvey  Nov 13, 2006, 6 PM 
On page 175 example 8, f_{x} is computed at (1,2) instead of at the point (1,3).

Julia Ye  Nov 17, 2006, 6 PM 
On page 270, example 7, the bound for the angle should be theta from 0 to pi, not
r from 0,pi in the expression in S = { (r,theta) : ... }.

Derek Dietz  Nov 24, 2006, 8 PM 
In Page 291, Problem 20, a z is missing in the definitin of the region R. It should
be (x,y,z), not (x,y).

Linda Chao  Nov 26, 2006, 12 AM 
On page 170, there is a typo in the solution of example 3: resepect > respect.

Antonio Iglesias and
Chris Murphy  Dec 3, 2006, 16 PM 
On p. 324, in Example 6, they ask you to calculate the integral of:
yz dx + z dy + x dz
But then in the solution, they are working with the integral
xy dx + z dy + x dz

Preston Copeland  Dec 7, 2006, 12 PM 
Problem 55 in section 11.5 on page 56 has the answer 3, not
9 sqrt(3)/5 as given on page 401.

Janet Chen  , Dec 10, 2006, 11 AM 
Problem 15.7:32 on page 382: delete =2 in the definition of the surface.
The surface is the elliptic paraboloid z= 1x^{2}/4y^{2}, z>0.

Kelly Swanberg  Jan 4, 2006, 12 PM 
On page 319, Example 1, part 2 (on the line starting, "Similarly, we have..."),
r(t) should read r'(t).

Anna Liu  Jan 20, 2006, 22 PM 
On page 319, under the solution of example 1, the book incorrectly reads
"Thus, we have F(r(t))  r'(t)" when instead it should read "Thus, we have
F(r(t)) (dot product) r'(t)." The book lists the computation as subtraction,
but it should be a dot product both in terms of the equation and the actual
calculation it does.

