Bill Goodwine's Courses

Posted: **Wed Jan 16, 2008 1:16 pm**

Here is the printed version of the course text.
Here is the updated version.

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.

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

Posted: **Sun Jan 20, 2008 7:29 pm**

There is an inconsistency with your definitions of linear dependence and independence and "Example 6.3.2"

Under "Definition 6.3.1" you give an if-then definition for linear independence and say if the scalars yield a zero total then it is linearly independent. This happens in a non-trivial way in the example and you say it results in the set of vectors being linearly dependent.

This may effect what you write in the line ,
"If the set is non linearly dependent, then it is linear independent."

Posted: **Tue Jan 22, 2008 4:18 pm**

It looks like the Xi_3 in the third row should be Xi_4.

Paul

Posted: **Sun Jan 27, 2008 5:57 pm**

in the 4th line, the (+ b4*xi2) the b4 should be b2

Posted: **Sun Jan 27, 2008 6:12 pm**

The left side of the equation should be multiplied by a Xi_hat

Posted: **Tue Jan 29, 2008 12:14 am**

on page 180, the matrix calculated with an eigenvalue of 1 is incorrect (i think). the (1,1) term was modified to find the eigenvector, but the (2,2), (3,3), and (4,4) terms were not modified.

Posted: **Tue Jan 29, 2008 1:49 am**

on page 166, the superscript for the eigenvector for the lambda-sub 2 is one. it should probably be 2

Posted: **Sat Feb 02, 2008 6:07 pm**

on the paragraph at the bottom of the page, it says "to compute the eigenvalue associated with a particular eigenvalue..." the first "eigenvalue" should be "eigenvector"

Posted: **Mon Feb 04, 2008 9:51 pm**

It's p.218 in the pdf.

"Thus, Î» = 2 is an eigenvalue with algebraic multiplicity of 4."

I think the algebraic multiplicity should be 3, as the eigenvalues are 2,2,2,1.

Anthony

Posted: **Mon Feb 04, 2008 11:03 pm**

"...and lambda sub i an eigenvector"

should be

"...and lambda sub i an eigenvalue"

Posted: **Wed Feb 06, 2008 10:27 pm**

for some reason the augmented matrix has a 1 in the third column

0 1 |1
0 0 |0

it should be a 0

0 1 |0
0 0 |0

Posted: **Mon Feb 11, 2008 10:29 pm**

resut should be result

Posted: **Tue Feb 12, 2008 4:36 pm**

153 line 10 ..."in this chapter are are systems of of n first order....

also later on equation 6.5, should there be two d/dt s in that line?

for page 156 line 2
i think you meant convert not "confert"

Posted: **Tue Feb 12, 2008 8:09 pm**

Proposition 6.6.2: Lambda-i should be a xi-i for the eigenvector corresponding to Lambda-j.

Posted: **Tue Feb 12, 2008 8:11 pm**

First sentence on page: Should be n linearly independent eigenvectors, not eigenvalues.

Posted: **Wed Feb 13, 2008 12:49 am**

"So, lamba = 2 is the solution"

I believe the solution should be -2

Posted: **Sun Feb 17, 2008 10:24 pm**

the page numbers mesh with the title of the page

Posted: **Sun Feb 17, 2008 10:29 pm**

Throughout all of chapter 6.11 and 6.12, not only does it happen once, but happens on every page. It may not be a typo, but I'd just like your book to look classy.

Adam Mathews

Posted: **Wed Feb 20, 2008 11:30 am**

The integrals for v_1,v_2 and v_3 should be e^2*tau and not e^2*t

Posted: **Fri Feb 22, 2008 12:06 am**

Correction For the Matrices of the form d/dt xi = [A] [xi] + g(t) in the middle of the page:

3rd row of the A matrix should read 0, 0, 0, 1 instead of 0, 0, 1, 0.

Right now you have xi_3 dot = xi_3 instead of xi_4 plus some f(t).

Posted: **Fri Feb 22, 2008 12:15 am**

For the fourth of equation from the bottom of the page of the form:

psi dot = lambda_i*psi + h_i(t)

The psi on the right hand side of the equation should have a subscript i as well.

so: psi dot = lambda_i*psi_i + h_i(t)

Posted: **Wed Mar 12, 2008 1:04 am**

Right now it reads "xi dot = A + f(t)"

It should read "xi dot = [A + f(t)]*xi,

so that the standard equation xi dot = A*xi is satisfied.

Posted: **Wed Mar 12, 2008 11:21 pm**

Last sentence of the footnote on p.255.

"The means to to this will be covered ..."

Duplicate 'to'.

Posted: **Sun Mar 16, 2008 9:15 pm**

"Covert" should be "convert."

Posted: **Sun Mar 16, 2008 9:17 pm**

First text line below paragraph one..the word expansion has an exponent.

Posted: **Sun Mar 23, 2008 4:15 pm**

"The" is written twice on the last line of the page:

The "the" block containing...

Posted: **Sun Mar 23, 2008 4:18 pm**

In the second to last equation the second term on the RHS says c1c2 (b/(s+a)^2 + b^2)

It should just be c2

Posted: **Sun Mar 23, 2008 4:19 pm**

which as poles at.... you forgot the h in has

should be: which has poles at ...

Posted: **Sun Mar 23, 2008 4:22 pm**

you wrote: transfer function has "a" multiple left poles in the .... need to delete the a

should be: transfer function has multiple left poles in the...

Posted: **Sun Mar 23, 2008 4:23 pm**

The last equation on the page says cost2

should be: cos2t

Posted: **Sun Mar 23, 2008 4:24 pm**

wnx should be (wn^2)x

Posted: **Sun Mar 23, 2008 4:25 pm**

remove the word if if the sentence: Hence, if the effects of moving the location...

Posted: **Sun Mar 23, 2008 4:27 pm**

Oops the last post was supposed to say remove the word if in the sentence

Posted: **Sun Mar 23, 2008 4:29 pm**

remove the word it in the sentence: A plot of O it versus...

Posted: **Sun Mar 23, 2008 4:30 pm**

in the sentence ...to satisfy this specification are illustrated in Figure 9.43- "are" should be changed to "is"

Posted: **Sun Mar 23, 2008 4:32 pm**

the = sign in =10 should be a minus sign

should be: where r = 10,1,-1 and -10

Posted: **Mon Mar 24, 2008 3:20 pm**

There's a page number in the index with no reference.
It just says " , 389"
This shouldn't be there

Posted: **Mon Mar 24, 2008 3:58 pm**

noun and verb don't agree

currently: "whether or not the change in the step response when the pole is moved in one of the three directions indicated are as predicted."

needs to either be
changes and are
or

change and is

Posted: **Mon Mar 24, 2008 10:30 pm**

currently 0-e^s*tau

should be 0-e^-s*tau

The mistake did not carry through to the solution.

Posted: **Mon Mar 24, 2008 10:38 pm**

the word transform is repeated.

"The Laplace transform transform of a derivative..."

Posted: **Mon Mar 24, 2008 11:55 pm**

ascott5 wrote:Right now it reads "xi dot = A + f(t)"

It should read "xi dot = [A + f(t)]*xi,

so that the standard equation xi dot = A*xi is satisfied.

CORRECTION to the correction

It should read "xi dot = [A]*xi + f(t)

Sorry for the confusion

Posted: **Wed Mar 26, 2008 12:53 am**

"match the plots of the pole and zero zero locations..."

zero should only be there once

"pole and zero locations"

Posted: **Sat Mar 29, 2008 1:31 pm**

In the Xi vector, "xi2" is written instead of the greek symbol for it.

Posted: **Sun Mar 30, 2008 2:54 pm**

Short explanation: multiply whole denominators of eq 9.5 and 9.6 by s.

I believe that equation 9.5 should have its whole denominator multiplied by s.

equation 9.5 currently reads:

theta(s) = (kp*s*theta_d - m*g*l)/(J*s^2 + kp)

It should read:

theta(s) = (kp*s*theta_d - m*g*l)/(J*s^3 + kp*s)

You got it correct when you referenced 9.5 on page 266 in the block diagram example.

equation 9.6 should also be adjusted by multiplying the denominator by an additional s.

Posted: **Sun Mar 30, 2008 3:04 pm**

Equation 9.6 was fine the way it was.

in equation 9.5 you may want to write theta_d(s) in the numerator instead of theta_d.

Posted: **Sun Mar 30, 2008 3:06 pm**

The second comparator in the block diagrams should have a negative on the arrow leading from the (mgl/s) term in order to be consistent with the first stand-alone equation on the page.

This applies to both block diagrams.

Posted: **Sun Mar 30, 2008 5:04 pm**

A somewhat major mistake I think: You list that the row does not exhibit a sign change, but I believe it should be the column, that does not contain a sign change.

Posted: **Sun Mar 30, 2008 5:41 pm**

In the T = [yadda yadda yadda] matrix, there is an unnecessary asterisk (*) where it should just be the "..."

Posted: **Sun Mar 30, 2008 5:43 pm**

in the square matrix, the last entry in the first column is a ")" - it should be a "0"

Posted: **Sun Mar 30, 2008 5:46 pm**

in the "T^-1*A*Xi_hat_n" equation, the lambda_n in the vector at the end is not multiplied by 1 as it is in the vectors directly above it.

Also, the first vector in that equation is wrong. It lists the first entry as a 1 when it should be a 0 and the last entry should be a 1.

Posted: **Sun Mar 30, 2008 6:09 pm**

typo:
"if the all the nonhomogeneous terms"

should be changed to

"if all the nonhomogeneous..."

Posted: **Sun Mar 30, 2008 6:26 pm**

"This is because of the the term in the homogeneous solution..."

the "of the" should be removed to make the sentence work:

"This is because the term in the homogeneous solution..."

Posted: **Sun Mar 30, 2008 6:35 pm**

"since, at least in Chapter 3 the derivation was rather complicated"

a comma should be added after "chapter 3"

"since, at least in Chapter 3, the derivation...."

Posted: **Sun Mar 30, 2008 6:35 pm**

"i really want to reference equation 6.31"

is there a point to this line?

Posted: **Sun Mar 30, 2008 6:43 pm**

line 3

a comma is needed after "details" so it becomes:
"Skipping the details, the general solution was"

line 7

a comma is needed after "ci"
"Since each term that is multiplied by a constant, ci, is a homogeneous solution..."

Posted: **Sun Mar 30, 2008 8:14 pm**

Fact 8.1.2 on 209 says that the integral of e^at * e^-st = 1/(s+a)
but on page 210, line 12 says that it equals 1/(s-a)

fact 8.1.2 needs to be fixed

Posted: **Sun Mar 30, 2008 8:49 pm**

"but has, for positive values of sigma a multiplicative..."

should be a comma after sigma

"but has, for positive values of sigma, a multiplicative..."

Posted: **Sun Mar 30, 2008 9:12 pm**

"proper interpretation of HeavisideTheta(t - tau) is that the function 1(t) is shifted"

it should be:

"of HeavisideTheta(t - tau) is that the function HeavisideTheta(t) is shifted"

*HeavisideTheta refers to the capital 1 function thing*

Posted: **Sun Mar 30, 2008 9:17 pm**

"then it whether or not the impulse..."

the "it" should be removed

"then whether or not the impulse..."

Posted: **Sun Mar 30, 2008 9:22 pm**

"Laplace transform of a function, f(t) is L(f(t)) = F(s)..."

comma needed after "f(t)"

"of a function, f(t), is..."

Posted: **Sun Mar 30, 2008 10:56 pm**

"sine term, first equation ==> 4b2 = 3a2+1"

should be

"cosine term, second equation..."

Posted: **Mon Mar 31, 2008 4:45 pm**

"contain a term of the form c_0, it i.e.,"

remove the "it" at the end:

"of the form c_0, i.e.,"

Posted: **Wed Apr 02, 2008 2:49 pm**

In the footnote: "The means to to this will be covered..."

should read, "The means to DO this..."[/quote]

Posted: **Wed Apr 02, 2008 3:02 pm**

"This chapter provides an detailed introduction to..."

should read, "This chapter provides a detailed introduction to..."

Posted: **Wed Apr 02, 2008 3:13 pm**

The term, m*g*l/s, should be subtracted at the comparator in the middle of both block diagrams as stated on p. 255 and line 8 of p. 266.

i.e. the plus sign on that arrow needs to be changed to a minus sign.

Posted: **Wed Apr 02, 2008 3:22 pm**

In line 8, the equation states:
y(t) = the inverse Laplace transform of (G(s)*(1/s))

The following line doesn't include the (1/s) in the inverse transform.

i.e. (1/s) needs to be multiplied within the parenthesis of the inverse transform on line 9.

Posted: **Thu Apr 10, 2008 6:58 pm**

The transfer function should be asking for Theta(s)/Theta_d(s)

Posted: **Thu Apr 10, 2008 7:00 pm**

"...occurs if a transfer function has two more poles or zeros..."

should be

"...function has two or more poles..."

Posted: **Tue Apr 29, 2008 10:06 pm**

the values of the subscripts of R and C don't match up with the subscripts of R and C in figure 9.103

Posted: **Sat May 03, 2008 3:25 pm**

alpha 3 should be -1 instead of 1

Posted: **Sun May 04, 2008 1:44 am**

The first element of the first matrix should be -1 instead of 1.

currently is 1 0 0 0
0 0 1 0
0 0 0 1
0 0 0 0

Should be: -1 0 0 0
0 0 1 0
0 0 0 1
0 0 0 0

Posted: **Sun May 04, 2008 1:51 am**

The long equation in the middle of the page should have a negative instead of a positive sign between the omega^4 and (k1+k3)/m1 . . . .

I expanded the proportion equation before it and kept getting a negative after the omega^4

Posted: **Sun May 04, 2008 1:55 am**

Looks like the LaTex didn't take the backslash denoiting \xi2

Its in the matrix equation immediately following example 6.11.3

Posted: **Sun May 04, 2008 10:09 pm**

I dont know if you left it out on purpose, but after you write the laplace inverse (G(s)*1/s) you leave out the s in the next line.

I know you might have done this since the laplace inverse(1/s) is the one's function, but I wasn't sure if you meant to include it or not since you didn't mention that simplification in the following paragraph.

Posted: **Sun May 04, 2008 10:31 pm**

missing word

currently:

"can written"

should be:

"can be written"

Posted: **Sun May 04, 2008 10:43 pm**

plural agreement

"will result in a complex conjugate poles"

change to either

"will result in a complex conjugate pole"

or "will result in complex conjugate poles"

Posted: **Sun May 04, 2008 10:45 pm**

"The real part of the poles for kp>=3 ...."

there is a space missing between "for" and "kp"

Posted: **Sun May 04, 2008 10:48 pm**

"or a overshoot specification..."

needs to be:

"an overshoot..."

Posted: **Sun May 04, 2008 10:50 pm**

"point of the example, though is that once..."

remove the comma

Posted: **Sun May 04, 2008 11:06 pm**

"length of all the arrow from the"

should be

"all the arrows"

Posted: **Sun May 04, 2008 11:07 pm**

"to s and multiply them for zeros"

should be

"and multiply by them for zeros"

Posted: **Sun May 04, 2008 11:08 pm**

"and by subtracting the angle from all the poles"

should be

"subtracting the angles from all the poles"

Posted: **Sun May 04, 2008 11:21 pm**

"then At k = 0, one of each"

"At" should not be capitalized

Posted: **Sun May 04, 2008 11:28 pm**

"Rule 9.9.9 gives and angle..."

should be

"gives an angle"

Posted: **Sun May 04, 2008 11:47 pm**

"The final rule is addresses a feature not present"

should be

"final rule addresses a feature"

Posted: **Sun May 04, 2008 11:50 pm**

"The first rule will will apply is Rule 9.9.14..."

should be

"first rule we will apply..."

Posted: **Thu May 08, 2008 6:16 pm**

non-repeated eigenvalues should (need to remove the ed)

Posted: **Thu May 08, 2008 6:18 pm**

assume should be assumed

Posted: **Thu May 08, 2008 6:19 pm**

contains function should be contains a function

Posted: **Thu May 08, 2008 6:20 pm**

i should be capitalized

Posted: **Thu May 08, 2008 6:20 pm**

determine inverse Laplace should be determine the inverse Laplace

Posted: **Thu May 08, 2008 6:23 pm**

transform written twice

Posted: **Thu May 08, 2008 6:26 pm**

should be a two in the numerator and not a 1 for 1/(s(s +2))

Posted: **Thu May 08, 2008 6:27 pm**

missing a minus sign in between 1/s+1 and 1/s+2

Posted: **Thu May 08, 2008 6:29 pm**

graphically represented by rectangle- should say graphically represented by a rectangle - forgot the "a"

Posted: **Thu May 08, 2008 6:30 pm**

it is "the" natural- forgot "the"

Posted: **Thu May 08, 2008 6:31 pm**

switching/moving- pick one or the other

Posted: **Thu May 08, 2008 6:33 pm**

"an" should be "a"

Posted: **Thu May 08, 2008 6:36 pm**

this is verified by- take out the "by"

Posted: **Thu May 08, 2008 6:39 pm**

forgot "a" after it is _ necessary...

Posted: **Thu May 08, 2008 6:42 pm**

these to extremes- should be these "two" extremes

Posted: **Thu May 08, 2008 6:43 pm**

C_3(s) should be G_3(s)

Posted: **Thu May 08, 2008 6:44 pm**

a belt that driven by a pulley should be a belt that "is" driven by a pulley

Posted: **Thu May 08, 2008 6:45 pm**

Theta(t) should be Theta(s)

Posted: **Thu May 08, 2008 6:46 pm**

after Example 9.6.12))- ) doesn't have a matching (

Posted: **Thu May 08, 2008 6:48 pm**

a = -1/2 should be s = -1/2

Posted: **Thu May 08, 2008 6:52 pm**

the 1 in the first row, first column should be a -1

Posted: **Thu May 08, 2008 6:54 pm**

the first and third components... don't you mean the second and fourth components

Bill Goodwine's Courses

Course Text

Course Text

page 181

page 151, equation 6.3

page 151, equation 6.3

page 155, line -11

page 161

Pg. 190, Line 6 (excluding eqns)

pg. 179, line that begins "Theorem 6.7.13"

page 174, line 4

pg 171, 4 lines up

page 153 and page 156 (of updated online version)

Page 165

Page 175

Page 175 in Course Text, Line 13

p 201, 203

Text Errata

page 193, 8-11

page 189, Middle set of Matrices

page 191, 7th from bottom

page 236, top of page

p.255, footnote, line 4

p224 1st paragraph

p224

page 271 line -1

page 280 line -4

page 280 line 2

page 286 line 2

page 286 line -4

page 294 line 2

page 296 line 4

page 299 line -6

page 300 line 5

page 308 line 7

page 587, line 2

page 362, lines 12 and 14

page 217, line 4 (middle of page)

page 220, line 3

Re: page 236, top of page

page 362, line 16

page 194, line -9

page 255, equations (9.5); (9.6) (middle of page)

page 255, correction to above post.

page 266, top of page (2 figures)

Page 291, after the array

page 189, line -1

page 190, line 7

page 190, line -3

page 194, line 11

page 199, line -14

page 201, line 10

page 201, line 16

page 202

page 209 and 210

page 213, line 3

page 216, line -3

page 219, lines 3 and 4 after Table 8.1

page 220, line 8

page 195, line 7

page 277, line -4

page 242, -2 lines from bottom

page 251, line -13

page 266, Figure 9.10 and 9.11

page 286, lines 8,9

page 366, problem 3

page 367, problem 15

page 370, the problem 9.22 description

page 153, line -3

page 181, line 7

page 183, line 11

page 194, line -11

page 286, line 9

page 314, line 4

page 315, lines 6 and 7

page 315, line 7

page 315, line 21

page 315, line -10

page 321, line -14

page 321, line -13