Bill Goodwine's Courses

Post any errors that you find in the course text below. To aid in avoiding any repeats, please do it as follows:

In the subject put something like

• "page xx, line yy"

then in the body of the post put the error. If it's near the bottom of the page put "page xx, line -yy," meaning the error is yy lines up from the bottom. Count equations as lines as well.

Points:

• typos = 1 homework point
• substantive errors = 10 homework points
• really major errors = 10's of homework points

Obviously what constitutes the distinction between these three types of errors is a matter of degree. I'll use my best judgment to allocate points fairly. As time progresses, I will most likely designate certain chapters as "off limits" or offer only reduced credit for any errors since they have not been as thoroughly proofread by the author.

Only the first person to post an error will receive any credit, so try not to repeat any others that have already been posted.

In the Figure 1.5 caption I believe the word "covarieant" is spelt incorrectly and should instead be covariant.

The first sentence of page 30 starts with "This results is"
I believe this should be re-worded to create subject-verb agreement, so probably "These results are".

I believe the problem should be reworded from "...previous problem, fine (del dot u) where u...." to "previous problem, find (del dot u) where u...".

My book and several others are missing page 100.

One, the text suggests adding/subtracting partial(f)/partial(y) * y'' yet eqn (1.111) has partial(f)/partial(y') * y'' added/subtracted. Two, the first component of eqn (1.111): partial(f)/partial(y) * y' seems sufficient to = df/dx without the other component.

I still do not understand the regrouping in (1.112) for the rest.

P.67, Problem 9(b)

I suppose that this problem is given to be solved by the method in P.57 (Riccati Equation). So a special solution is needed to be found at first. Then It seems that one of the two last minus sign should be positive, so that y=x*x is the special solution. Otherwise, I find it hard to find the special solution. I think it may be a typo.

page 79, equation 3.37

In the 2nd line of the equation, Sigma u(i)'y'=0, I think the subscript (i) got dropped from the y' term accidently.

I think the authors intended to write Sigma u(i)'y(i)'=0.

page 47, line 25 (problem 17) should say "find" instead of "fine."

page 47, line 1 (problem 10) should read "function" instead of "functional"

page 76, line 16: r1=-2 and r2 should also equal -2 (since they are repeated roots)

The parenthesis should be like
(1-2()+3()^2+...)

Between the two steps in Example 4.2, there is a change in index of the summation, without adjusting the summation.

It is now:

xy' = sum(n an x^n) from n=1 to inf
xy' = sum(n an x^n) from n=0 to inf

It should probably be changed to reflect the start of the index from 1 to 0.

xy' = sum(n an x^n) from n=1 to inf
xy' = sum(n+1 a(n+1) x^(n+1)) from n=0 to inf

This will result in a change in the solution, however I don't believe it will change the fact that the series will converge.

In the 2nd line of the integrating the diff. eqn. part: x'x"+x'x+epx'x^2, the x^2 should be x^3.

Page 171.
In the identities section I believe that the second one down and second from the left should read:
d/dt(uivi) = ui dvi/dt + dui/dt vi and not the way it is currently written.

Two things:
One is a typo on page 174, middle of the page right after equation 6.97.
The sentence currently reads "...form an orthogonal systems of unit vector." It should read "...form an orthogonal system of unit vector."
So change sytems to system.
Second may not be a typo but I have always written it differently. It is on page 171 in example 6.5 right after At t=1 I don't see why the next equation isn't written r(1) instead of r(t).

Page 193, problem 12(C):

I think the correct expression for this formula should be:

(a cross b) * (c cross d) = (a cross b) cross c * d

Otherwise, the LHS of that equation will be a scalar cross a vector!

Page 199, -line 7.

Condition 2.

I think there may be an error here. The lecture note states that for any x, y from S, (x+y)+z=x+(y+z)

I think it should be: for any x, y, z from S...

And It can be verified from this webpage:
http://en.wikipedia.org/wiki/Vector_space

On pg. 146, eqn 5.125 should read r(x)=1/x

Also, eqn (5.123) should start out Ls=1/x (........)

The right hand sides of the two equations should have opposite signs

"The inner measure of the set is (a-b)..."

I think it should be "(b-a)".

There is a typo in the formula of " ||x||=||x||3=...+||x^2||^3+... "

where, x^2 should be x with the subscript 2.

In the right hand side of the equation:

The sub-bound of the third integral should be "k/n", instead of "i/n".