Bill Goodwine's Courses

You may download the updated version of the course text. This may contain additional material and corrections that are not in the printed version. Unless otherwise indicated in class or on a homework, all references to page, section and problem numbers are for the printed version.

Post any errors that you find in the printed version of 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.

There should be an = in eq. 6.5

[quote="sjensen1"]There should be an = in eq. 6.5[/quote]
that is an = instead of a d/dt

I think there should be a hat on the xi in (A-Gamma*I)*Xi = 0

There is also a hat missing on the xi with the n superscript in the expression for Xi(t)

When determining the determinate of (A-lambda*I), the text reads that it is

(1-lambda)*lambda - 2

I think there should be a negative on the outside of (1-lambda) that coomes from the lambda on the outside, on other words

-(1-lambda)*lambda - 2

pg 135 line 6 (last words in the main paragraph)

Equation 6.9 is referenced when equation 6.8 should have been.

page 136 last line

Equation 6.12 is referenced instead of 6.13

Sorry, 6.12 (the original) was the correct equation

I think I found a typo here, the end of the line should be =0 not -0.

". . . is transposed an all the elements are changed . . ." the 'an' should be 'and'

"Thus we make take . . ." either make or take should be omitted

The m and i=1 of are to the right of the summation sign, instead of above and beneath

"ed" should be removed so that the line reads, "For the non-repeated eigenvalues..."

in the second line of example 6.11.3, the xi symbol does not appear (the word "xi" is written instead)

Extra period should be removed for sentence ending ..."independent eigenvector associated with lambda_1 = 1."

The text reads:

"we may to proceed as before and..."


I believe it should read:

"we may proceed as before and..."

The text reads:

"and an simple calculation shows that..."


I believe it should read:

"and a simple calculation shows that..."


The word "an" was changed to "a".

on the right side of the equal sign, ξ3 should be replaced with ξ4

and similarly on 137 in the brackets on the right, ξ5 replaced with ξ6.

In your answer to the determinant, you have (1-lambda)*lambda-2. It should actually be (1-lambda)*(-lambda)-2. Your end result is correct, but the intermediate result is missing the minus sign.

Line six states that lines 7 and 8 will show a combination of the two modes of oscillation, but the first mode of oscillation shows a term
sqrt(k/m) and in both terms in lines 7 and 8, there is just sqrt(k)*m. Similarly for the second mode in lines 7 and 8, the m term needs to be in the denominator of the fraction within the square root sign.

-Tom Banasiak

the eigenvalue \lambda_1 is 1+2i, but you list \omega as 1. It should be a 2.

The Lambda sub i, hat with the complex conj. bar atop it should be a zeta b/c it's an eigenvector corresponding to lambda sub j.

As is written: "Recall, that the whole business..."
correction: drop the comma.
Corrected: "Recall that the whole business"

nb: "the whole business" probably doesn't have an appropriate tone for a textbook. Consider rewording that phrase.

I believe "Note the assume form of the solution is..." should be "Note the assumed form..."

Ashley Meklis

The text reads:

"Also, to distinguish it from addition of real numbers, vector addition will be denoted bold plus sign."

I believe it should read:

"Also, to distinguish it from addition of real numbers, vector addition will be denoted by a bold plus sign."


The words, "by a" were added to the second version.

There is a period missing after the matrix in the last line.

The text reads:

"Note the assume form of the solution..."


I believe it should read:

"Note the assumed form of the solution..."


The word "assume" was changed to "assumed" in the second case.

"...with algebraic multiplicity of 4" should read (I believe) "...with algebraic multiplicity of 3"

In the second equation of equation 7.1 the first x2 should be x1

The t^0 equation is incorrect. It reads lambda(xi2+xi1)*e^(lambda*t) = A*xi2*e^lambda*t

The lambda should not be distributed to xi1. The equation should read

(lambda*xi2+xi1)*e^(lambda*t)=A*xi2*e^(lambda*t)

The equation here showing values being substituted lacks an e^(mu*t) term. The second line of the equation should read:
...+k_2 * e^t * (. . .)

On Figure 7.7, the last spring attached to masses n and n-1 should have a spring a damper labeled k_n and b_n, not k_n-1 and b_n-1. Although it's arbitrary, the counter goes from 1 to n on the masses and 1 to n-1 on the springs and dampers, which is confusing.

There is a bulleted paragraph on the right side of the page that is cut off by the edge of the page making it impossible to read...

When substituting x1(t) and x2(t) into the equations of motion, one should obtain [...] cos wt = 0 for both of the equations.

This should read: "So, lambda = -2 is the solution"

in the equality eqn, I think the first should be \alpha_1, not \alpha_i. (even though it's true anyway)

On pg. 159, where the (A-2I) matrix is calculated, the (1,1) position should be a -1 instead of a 1.

The text reads:

"(A-lambda_1*I)*xi^1 = 0 <---> [matrix]"

I believe the [matrix] should be the "A" matrix from page 158, line -13 with 1*the identity matrix subtracted from it. However, the [matrix] given on line -6 only has the first term after the subtraction with the remaining values on the diagonal still coming from the original "A" matrix.

The [matrix] in the text is:

0 0 0 0 | 0
0 2 1 0 | 0
0 0 2 1 | 0
0 0 0 2 | 0

while I believe it should be:

0 0 0 0 | 0
0 1 1 0 | 0
0 0 1 1 | 0
0 0 0 1 | 0.

all t's in the integrand should be tau's (exponents of e's)

after "which is", the "...= T=..." should be "...= T \psi =..."

The text reads:

"Constructing the augmented matrix for A-2I gives
0 1 | 1
0 0 | 0."

I believe it should read:

"Constructing the augmented matrix for A-2I gives
0 1 | 0
0 0 | 0."


The second version has the last column in the matrix as all zeros instead of as 1,0.

In the first matrix the 1 is the first value in the column but when multiplied by lambda_n it is shown in the second matrix as being the last entry in the column. From the lines preceding in the book, I believe the first matrix should have the 1 as the last entry in the column so when multiplied by the lambda_n the second matrix is correct.

I think the spring constants labeled k(i+1) should be k(i+2) and the one labeled k(i) should be k(i+1).

"Example 6.11.3 Find the general solution to...(equation)"

On the RHS of the equation, I believe there "xi_2" should be "eksi_2"

The last coefficient equation says "sine term, first equation." I believe it should be "cosine term, second equation."

The first interval should read 0 <= t < 1, not t <= t < 1

Wrong form of "to" is used, should read "is not too great."

The line after "and substituting gives" starts xdot+ x = ...

I believe a 3 should precede the term in brackets.

The word "transform" is unnecessarily repeated.

"multiple" should be "multiply"

the equation should read L-1 = (1/2 (1-e^(pi*s)) * (2/s*(s+2)) rather than 1/s*(s+2)

The numerator of the function which the inverse Laplace is being operated on should be 2 and not 1 so that the line reads: inverse Laplace [ 1/2 * (1-exp^-pi*s) * 2/{s*(s+2)} ] =

I think that for Fact 8.1.2, the integral should equal 1/(s-a) and not 1/(s+a). On the last line of page 197 you define the integral using -a.

Someone already pointed out that the omega in this problem should be equal to two. This value needs to be placed in the third line as exp(2*t)*k2*... and line thirteen as exp(2*t)*... . The answer that is given does not take this into account as well.

The equation for E(t) has a plus sign (+) at the end of its third term, but the next line has an equal sign (=) so it appears unnecessary.

The text reads as follows "Edot = aE"

a should be capitalized, so it should be Edot = AE.

-- Arturo Garcia

Similar to my previous post...

There is an unnecessary plus (+) sign immediately before an equal (=) sign for the E(t) equation.

I'm not sure if this is a mistake, but on the homogeneous solution shouldn't there be a ci in front of thing within the parenthesis.

-- Arturo Garcia

the second term in that answer should have c2 in front of e^2t ([ 0 1 0 ] + t * [ -1 -1 0] ) instead of the c1

"servor" should be "servo" as in the footnote.

"inductor" should be plural.
"gives" should be "give."
"May" should have an "n."

"switching" should be taken out.
"The" is repeated.

"The functions step() and impulse() computes and plots an ...": verbs should be plural.

Book states: "The force on mass 2 is f=T2-T3"

I believe this force acts on Mass 1.

Currently it reads "...is attached to a belt that driven by a pulley."
should be ...a belt that IS driven by a pulley.

Currently it reads: "...used to simplify an complicated..."
Should be "used to simplify A complicated..."

zero appears twice

̈x(t) = A cos ωt + B sin ωt --> this should be x(t), not the 2nd deriv. of x(t)

2ζ ωn x --> this should be xdot

There are no sign changes, so all solutions to equation 9.15 should be in the left half plane, not right

under example 9.8.23, the equation should be s+3/((s+1)(s+2)) to match example 9.8.21 and fig 58

pg 245: 1st sentence after 4. (an detailed = a detailed)
pg 247: line 3 (equation 9.2)
pg 254: 2nd eqn from top there might be a missing m*g*l*cos(theta) added on factor
pg 254: the d/dt [x1;x2;x3 eqn for (theta_d - x(1)) should be equal to (theta_d - x(2))]
b/c d/dt (x(3)) = d/dt(T_d - T) and d/dt (theta) = x(2)
pg 279: first line beneath eqn 9.19 -- A plot of O it versus . . . it = /it (italics)
pg 282: 2nd line beneath eqn 9.21 which satisfy the . . . = satisfies
pg 283: line 14 from top "It is necessary component" = is a necessary
pg 292: line 10 from top " in a complex conjugate poles" either in comp. conj. poles or in a pair of CCPoles
pg 292: line 11 for kp>=3 needs a space
pg 295: the black box for the aside review in complex variables is in the wrong spot (just beneath 9.27) It looks like new material was added afterwards that still pertains to hte review. Probably should be just before example 9.8.4
pg 297: 9 from bottom all the arrow = arrows
pg 300: line 7 from top (from the - infinity) just before there is no the or + inf. ( prob erase "the")
pg 300: line 10 there shouldn't be a comma after k since the following is a dependent clause
pg 300: Rule 9.8.5 then At k . . . At = at (lower case)
pg 301: first line after propos. 9.8.8 Figure 9.46 with is the root (with is a typo)
pg 303: line 7 Rule 9.8.9 gives and angle and = an

Solving 1+kG(s)=0 for k gives k=-1/G(s), not 1/G(s) as is said on this page.

There should be negative signs in front of equation 9.29, the second, third, and fourth equations from the top of the page (k and dk/ds in ex 9.8.18), and the second to last equation line on the page (k in ex 9.8.19).

The same error is made here: rule 5 should read d/ds(-1/G(s))=0.

Plan should be plane

pg. 274 line 3

The omega_n in the equation after the arrow should be (omega_n)^2.

Part 2 of Example 9.8.22 Shold be referencing Figure 9.59

First line of Section 9.4 currently reads "gains in section 9.2 practically"

To fit the rest of the book's convention "section" ought be capitalized. Trivial, I know.

The line reads: "constant and the the magnitude of the vector is increased"
The line should read: "constant and the magnitude of the vector is increased"

on pg 228 Figure 8.22 I think that the the block diagram does not match the equation above it. It looks like the mgl/s term should be positive.

on pg. 354 prob 9.9-5 there is a typo. "...by hand, the how the poles..."

proportional controls suffices. should be singular

p 280 L -6 -- the zeta omega_n greater than 1.3 should read as "less than negative 1.3"
p 257 (one line above the eqn for y1(t) = inv Laplace(G(s) / s)) reads "the impulse response is given as . . ." -- impulse should be unit step

"less than 3 seconds . . . in Figure 9.26" the 3 seconds is 1.3 seconds

I made a mistake, the last post on 280 is correct in the book

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

In the footnote, the final sentence reads "The means to to this. . ." I believe the second "to" should be a "do".

This figure depicts the zero of the equation in Example 9.8.7 as being located at -2. The zero occurs at -3.

The sentence "If we desire to determine whether or not a point, indicated by a cross in the figure, we will use the fact that it. . ." is missing a clause. It is unclear what we are determining about the point.

p 301 L 3 "the branches of the root locus start at . . ." instead of "starts at"

page 201 3 lines under the first black box - unnecessary "it" (or comma shortage)
line reads, "Since there impulse has zero width, if the lower limit were simply 0, then it whether or not the impulse is included in the integral would be ambiguous"

page 207 after 3rd equation block Covert-->Convert
Reads "Now we want to covert the right hand side into a combination of terms that appear in Table 8.1."

Professor,

In your matrix representation of the equations, you have a 4x4 matrix added to a 4x1 matrix. You should have the 4x4 matrix multiplied with a 4x1 matrix with values (x_1, x_1 dot, x_2, and x_2 dot).

The ) bracket should be outside of (Xd-X) before factoring in the next line

The sentence reads,

"We considered this previously in Example 9.5.12)."

There's no need for that parentheses.

Page 306, Line 3
"..at the zero and a does grow unbounded." The a is unnecessary

Page 370, Line -5
"it acts like term proportional..." I assume a "a" is needed between the like and term.

the text reads as follows, "...where r = 10, 1, -1 and = 10,..."

I believe that the "=" next to the second 10 in that list should be a negative 10, thus the text should read,

the text reads as follows, "...where r = 10, 1, -1 and - 10,..."

Page 228, in Example 8.6.1 second to last line before the equations & fig 8.22 Extra "it"
Text reads, "Then it it added to the gravity term and finally multiplied by the robot dynamics to give" ...

Page 258, 10th line from the bottom, extra "by" or "in"
Text reads, "This is verified by in Figure 9.8 which compares the two solutions"

Page 258, 3rd line from bottom, first "as" to "at"
Text reads, "impulse response of the two transfer functions with pole locations as the same points as before are illustrated"

In the limit equation, the error should be pointing from left to right not from up to down.

In section 9.5.3, after the first equation, the text states "which as poles at..." when it should be "which has poles at..."

Page 485, last line
"it does not patter which peaks..." should probably read "it doesn't matter which peaks"

Page 486, 3rd equation from the bottom
The text "Since that ..." is attached to the equation for (delta) = ln(0.4/0.7) = -.56

In equation 9.5, I believe the entire denominator should be multiplied by 's.' Thus, the denominator should read: s(Js^2+k_p).

In both equations, you should have the proportionality constant times the integral of theta desired minus theta. Therefore, you should add parenthesis around theta_d(t) - theta(t) in both equations.

pg 483 figure 17.1 the damper is labled as 'k' and the spring is labled as 'b'

The line reads: "it makes sense to use the data t either validate...."
but I think an 'o' was forgotten and it should read "it makes sense to use the data to either validate...."

The problem considers a low pass filter. The Resistance and Capacitance subscripts should therefore be LP, not HP.

a ")" is missing in G(iw)

[quote="sjensen1"]In the second equation of equation 7.1 the first x2 should be x1[/quote]


I believe it is the 2nd x2, of the -k3 x2, that should be x1, not the x2 of (k2 + k3)x2. That one is correct.

The top line under the section title 1.5.5 currently reads:
"If the all the functions..."

I believe it should be changed to:
"If all the functions..."

A few small typos:
Page 14, Line -1: "Then Equation 1.11 has exatcly one solution,"

Last paragraph of 1.7 on Page 15:
"Be careful to propery interpret the theorm"
And: "sufficient condition for exitence"