Harvard University,FAS
Fall 2006

Mathematics Math21a
Fall 2006

Multivariable Calculus

Course Head: Oliver Knill
Office: SciCtr 434
Email: knill@math.harvard.edu
Harvard Mathematics

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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 10/31/2, not 10 * 31/2
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 x-component 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> ft-lbs which has a magnitude 40 ft-lbs. It is not 30 ft-lbs 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 -10i-2j+2k instead of -10i-2j+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 51-56 should read "Calculate the moving frame (T, N, B) at t0" (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, fx 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= 1-x2/4-y2, 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.

Please send comments to math21a@fas.harvard.edu

Math21a, Multivariable Calculus, Fall 2006, Department of Mathematics, Faculty of Art and Sciences, Harvard University

Thu Jan 25 21:36:37 EST 2007