Bill Goodwine's Courses

Posted: **Wed Aug 26, 2009 9:43 am**

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.

Posted: **Sat Aug 29, 2009 3:58 pm**

page 1, line -3 states that there are 2^5=32 possible classifications based on the five categories listed. However, I do not believe that this is actually correct because some possibilities are restricted. For example, we do not classify nonlinear equations as homogeneous or inhomogeneous. Therefore, there are actually less than 32 possible categorizations (20, I think). The 32 categorizations are also mentioned on the first line of page 2.

page 5, line -13 is the definition of the partial derivative. The first t after the limit is missing the subscript 1.

Posted: **Sat Aug 29, 2009 4:00 pm**

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..."

Posted: **Sat Aug 29, 2009 4:15 pm**

(this is on the second page of the preface)
the end of the line reads "...methods (section and 1.9)."
there is an extra 'and' added or a section number missing.

Posted: **Sun Aug 30, 2009 10:18 am**

page 14: Under Theorem 1.7.1, the second bracket should be closed instead of open.
page 15: In the last paragraph in section 1.7, I think 'propery' should be changed to 'properly' and 'exitence' to 'existence.'

Posted: **Sun Aug 30, 2009 10:57 am**

page i, line 2 "and students other disciplines" should read "and students of other disciplines"
line 4 "This material that is traditionally" should read "This is material that is traditionally" or "This material is traditionally"
line 7 There should be a comma after the word "Specifically"

page ii, line 12 "would simply to bring" should read "would be simply to bring"

Posted: **Sun Aug 30, 2009 11:01 am**

p. xvii, xix, xx

This is just a formatting mistake... There should be a space inbetween the listing of each chapter-section number and the title of each section, but often the space is missing (i.e. "12.10The first five terms..." to "12.10 The first five terms...").

Posted: **Sun Aug 30, 2009 11:03 am**

Oops, I forgot to put the label above so I re-posted it.

p. xvii, xix, xx

This is just a formatting mistake... There should be a space inbetween the listing of each chapter-section number and the title of each section, but often the space is missing (i.e. "12.10The first five terms..." to "12.10 The first five terms...").

Posted: **Sun Aug 30, 2009 11:45 am**

"theorm" should be "theorem"

Posted: **Sun Aug 30, 2009 12:11 pm**

I'm not sure how to fix this exactly, but I think you need to eliminate either "will always be orthogonal to r and h about the center of the hoop" or "will always be orthogonal to the plane of the hoop."

Posted: **Sun Aug 30, 2009 12:22 pm**

In this phrase "...properly modeling some of them are necessary in this book." I think "are" should be "is"

Posted: **Sun Aug 30, 2009 12:39 pm**

Sorry, I forgot to post the subject heading in my earlier post so I listed it here.

On page 18 line 16, there should not be a period in
"the first law follows. and is given by"

Posted: **Sun Aug 30, 2009 1:49 pm**

The angular momentum (line 6) should be h = m*r^2*(thetadot).
The moment r X F (line 9) should be = rmgcos(theta).

These would make the differential equation (line 15) be thetadubdot = g*cos(theta)/r

Posted: **Sun Aug 30, 2009 1:55 pm**

13: Bounday should be Boundary

14: exatcly should be exactly

30: should be a space between t_o and in

Posted: **Sun Aug 30, 2009 1:56 pm**

{1,....,n} should be {0,....,n}

Posted: **Sun Aug 30, 2009 10:05 pm**

On page iii under second semester, chapter 6 uses a colon to separate 'covered in detail' while all other chapters are separated by a comma.

Posted: **Mon Aug 31, 2009 1:32 pm**

For Problem 1.1 in the 1.10 Exercises, neither #7,10,12 nor 13 should have time differentials for intial conditions as time is not an independent variable.

Posted: **Mon Aug 31, 2009 3:56 pm**

On page 43, the first sentence under the graph, "biological process" should be "biological processes"

Posted: **Mon Aug 31, 2009 9:22 pm**

The sentence is incomplete:
"This text will only consider nth order ordinary differential equation may be written in the form..."
should be: "This text will...equations that can be written in the form..."

Posted: **Tue Sep 01, 2009 12:00 am**

Page 541: The program still needs to be written.

Page 546: The header reads Appendix D. Example Problems, despite being in the Nomenclature section.

Posted: **Tue Sep 01, 2009 12:42 pm**

This line shows a Matlab command format. TSPAN is skipped in the subsequent definitions of each part of the command. Even though it is fairly obvious what TSPAN might be, it seems strange that it is omitted.

Posted: **Fri Sep 04, 2009 11:32 am**

In equation 2.2, the units of h, the convection heat transfer coefficient are shown as W/(m^2)*K (equivalent to WK/(m^2). They should be W/(m^2*K).

Posted: **Fri Sep 04, 2009 12:40 pm**

"A particle is an object" instead of "A particle is a object"

Posted: **Fri Sep 04, 2009 1:23 pm**

You wrote "...the Boit number, , which is defined as..."
I think you meant to have a variable between the commas, otherwise you just have too many commas.

Posted: **Fri Sep 04, 2009 1:24 pm**

"will be emphasized in the first few example" should be "will be emphasized in the first few examples"

Posted: **Fri Sep 04, 2009 1:32 pm**

I'm not completely sure how to fix this, but its just an inconsistency. I think that x_p(t)=c_0e(t) should probably be defined as x_p(t)=c_1e(t) because when you substitute it into the equation, you use c_1 instead of c_0.

Posted: **Fri Sep 04, 2009 1:39 pm**

Again I'm not sure how to fix it, but there's something wrong here. The last 2 isn't a subscript, and I don't think it should even be a 2.

"c_1-c_2-c2=0"

Posted: **Fri Sep 04, 2009 1:40 pm**

The same thing happens for equation 2.3. The specific heat of the material is said to have units of J/kg*K (equivalent to J*K/kg) when it should have units of J/(kg*K).

Posted: **Sat Sep 05, 2009 2:56 pm**

the 4th line of equations should be Integral [ (sin t)*(t^3) dt] not Integral [ (sin t)/t^3]

Posted: **Sun Sep 06, 2009 10:33 am**

in "will yield and equation..." the 'and' should be changed to 'an'

Posted: **Sun Sep 06, 2009 10:38 am**

I think it should read "only x(t)=sin(t) satisfies the latter" rather than x(t) = -sin(t)

Posted: **Sun Sep 06, 2009 4:33 pm**

In example 2.3.19, a - is dropped from the integral of sin(t), this error is carried through to the end of the example.

On page 43, 14 lines from the bottom, the phrase "the change in plasma glucose concentrations due to uptake by, say in, skeletal muscle" needs to be rewritten

Posted: **Tue Sep 08, 2009 12:57 am**

p. 14, line 36
One of the brackets is backwards; " [0, infinity symbol[ there exist..." to " [0, infinity symbol] there exist..."

Posted: **Tue Sep 08, 2009 1:30 pm**

The line currently reads "may be used to in some way to satisfy"

I believe it should be changed to "may be used in some way to satisfy"

Posted: **Tue Sep 08, 2009 1:37 pm**

The first part of this paragraph currently reads:
"The distinction between initial conditions and boundary conditions are that..."

I believe the "are" in this statement should be changed to "is".

Posted: **Tue Sep 08, 2009 7:40 pm**

the statement of example 2.2.4 cites cocaine as an illicit example of a drug, just seems out of place and there is no previous reference to cocaine, example 2.2.3 is about alcohol and might have been about cocaine at one point but other that that the statement just feels very out of place and unnecessary

Posted: **Wed Sep 09, 2009 10:07 am**

In Step 4 in the algorithm for Euler's method for a given delta t, there should be a delta t on the f(x(t0+(n-1)deltat),t0+(n-1)deltat) term: f(x(t0+(n-1)deltat),t0+(n-1)deltat)DELTAt.

Posted: **Sat Sep 12, 2009 1:29 pm**

the derivative of z(t) should be bZ(omega)*cos(omega*t)
not bZ*cos(omega*t)

Posted: **Sat Sep 12, 2009 1:44 pm**

"i.e.,," has an extra comma.

Posted: **Sat Sep 12, 2009 1:52 pm**

On lines 13 and 14, you defined
x1^=sin (natural frequency*t) and x2^=cos(natural frequency*t), but then on line 27 when you substituted them in you did the opposite. I think based on the convention used for c1^ and c2^ it should be x1^=cos(natural frequency*t) on line 13 and x2^=sin(natural frequency*t) on line 14.

Posted: **Sat Sep 12, 2009 1:58 pm**

"then" should be changed to "when"

Posted: **Sat Sep 12, 2009 2:13 pm**

In "W(x1,x2)" the 1 and 2 should be subscripts

Posted: **Sat Sep 12, 2009 2:54 pm**

I think "equation 3.10 can be rewritten as" should be changed to "equation 3.6"

Posted: **Mon Sep 14, 2009 3:59 pm**

page 69, line -3 (of text, excluding equation lines)

You write "equation 3.10.."

I am pretty sure you meant to reference equation 3.6, as 3.10 does not appear until the discussion on complex roots.

Posted: **Tue Sep 15, 2009 1:42 am**

In problem 3.11, there is an extra Zeta symbol in the middle term on the left-hand side of the equation. I believe there only needs to be one in that term.

Posted: **Tue Sep 15, 2009 1:34 pm**

There is an extra + in the equation (++1/4sin2t).

Posted: **Sun Sep 20, 2009 4:35 pm**

The end of the first paragraph of text on page 69 currently reads: "because it simplifies notation the problem."

I think it should be changed to "because it simplifies notation in the problem" or "because it simplifies notation of the problem".

Posted: **Sun Sep 20, 2009 10:07 pm**

The equation on the bottom of page 73 currently reads x(t) = c1e^λ1t + c2e^ λ2t. Because this section is describing repeated roots, however, the two λ values (λ1 and λ2) are the same and therefore do not need to be distinguished from each other. This means that the subscripts of 1 and 2 can be eliminated from the λ variables. In the first part of Theorem 3.3.6 (giving the x(t) functions) this convention is used and the λ variables are written without subscript.

Posted: **Sat Sep 26, 2009 10:33 am**

"Now consider the problem of a coupled by a spring to a vibrating base."
should read:
"Now consider the problem of a spring coupled to a vibrating base."
or something along those lines.

Posted: **Sat Sep 26, 2009 11:54 am**

'they' should be changed to 'the'

Posted: **Sat Sep 26, 2009 12:24 pm**

On page 92 line -10, there should be a 'the" before most. It should read "is probably the most expedient solutoin method."

On page 93 line -13, in equation (4.8) the xdot term before the sin (w_n*t) is missing its subscript and should be xdot_0.

Posted: **Sat Sep 26, 2009 1:04 pm**

p. 74, line 25
The sentence "While not necessary to simply find..." seems to lacks a verb in this clause ... perhaps it should be "While it is not necessary to simply find..."

Posted: **Sat Sep 26, 2009 1:05 pm**

On page 95 line 9, I think the equation for x(0) should be positive rather than negative in order to make the homogeneous solutions zero so that the complete solution is the particular solution.

On page 97 line 7, in equation (4.9) I think the inhomogeneous term should include the natural frequency rather than omega.

page 101 line 5: "is" should be changed to "are"
page 109 line 18: "good" should be added so it reads "is probably a good idea"

Posted: **Sat Sep 26, 2009 3:10 pm**

"...the method of undetermined coefficients is probably most expedient solution method." needs to have a "the" inserted so it says "...the method of undetermined coefficients is probably THE most expedient solution method."

Posted: **Sat Sep 26, 2009 3:12 pm**

"Now consider the problem of a coupled by a spring to a vibrating base..."
I feel like something's wrong here..not sure how to fix it.

Posted: **Sat Sep 26, 2009 4:37 pm**

The line currently reads "which in this case will by y(t)-x(t)."

I think this should be changed to "which in this case will be y(t)-x(t)."

Posted: **Sun Sep 27, 2009 3:34 pm**

I think you meant "If not, be sure to determine.." rather than "If so, be sure to determine.."

Posted: **Mon Sep 28, 2009 6:00 pm**

Page 91, line -12: I believe the omega n in the equation for example 4.1.1 should be squared.

Page 97, line 1: The caption for figure 4.9 should say "out of phase for" rather than "in phase for"

Page 104, line 2: this should just be "xp=" not "xp..="

Page 109, line -11: This sentence reads, "This is in contrast to the magnitude factor for a an applied force..." The "a" should be removed.

Posted: **Mon Sep 28, 2009 8:19 pm**

at the top of the page it says assume the particular solution and then says x''=Acoswt+Bsinwt. I believe it is simply supposed to be x= not x''=

Posted: **Tue Sep 29, 2009 5:14 pm**

It currently states "It is left as an exercise to show that if there is gravity if x is measured..."

I believe it's supposed to say "It is left as an exercise to show that if there is gravity and x is measured..."

Posted: **Wed Sep 30, 2009 5:50 pm**

line 11

"to the since function" should read: "to the sine function"

Posted: **Thu Oct 01, 2009 1:05 am**

equation (4.17) is missing the x(dot) term; currently it is 2*zeta*wn*x << should be xdot

Posted: **Sat Oct 03, 2009 6:58 pm**

p.101, line 24
M = -1 at r=sqrt(2), not M = [positive] 1.

Posted: **Sat Oct 03, 2009 7:03 pm**

I'm not sure if maybe "a" or "the" should be added to the sentence "This is in contrast with multiple degree of freedom system..." so it becomes "This is contrast with a multiple degree of freedom system..." or "This is in contrast with the multiple degree of freedom system...".

Posted: **Wed Oct 07, 2009 12:40 am**

p.109

Last sentence in the first paragraph below the big messy square root (transmissibility): "Plotting the transmissibility as a function..."

The word "good" should be inserted so it reads, "Plotting ... is probably a GOOD idea ...".

Posted: **Sat Oct 10, 2009 12:33 pm**

pg 115 line 11: "to obtain an better approximation" should be changed to "obtain a better approximation"

pg 119 line -2: "more an more" should be changed to "more and more"

pg 120 lines 18-21 I think this sentence should be broken into two. Perhaps add a period after "independent variable." Then start the next sentence with "Attempts to increase the accuracy..."

Posted: **Sat Oct 10, 2009 12:35 pm**

p 121 line -5 "properties of a series approximation depends" should be changed to "depend"

p 123 line 2 "then it is analytic an any" should be changed to "analytic at any"

p 123 line 10 "In other works," should be changed to "In other words"

Posted: **Sat Oct 10, 2009 12:37 pm**

The first derivative should be negative instead of positive.

Posted: **Sat Oct 10, 2009 12:39 pm**

"seris" should be "series"

Posted: **Sat Oct 10, 2009 12:41 pm**

line 19: "furhetermore" should be "furthermore"

line -3: the sum should be (n+2)(n+1) instead of (n+1)(n+1)

Posted: **Sat Oct 10, 2009 12:49 pm**

"Determining" shouldn't be capitalized.

Posted: **Sat Oct 10, 2009 1:01 pm**

p 127 line -12: "initial condition" changed to "initial conditions"
p 129 line -10: "Figure 5.3" should be changed to "Figure 5.6"
p 130 line 3: "where lambda is an positive integer" should be changed to "a positive integer"

Posted: **Sun Oct 11, 2009 7:51 pm**

The word "the" is repeated in the first sentence.

Posted: **Tue Oct 13, 2009 10:38 pm**

The book currently reads:

Equating powers of t gives
. . . .
a3 = -1/6 a3
. . . .

Instead it should read a3 = -1/6 a1

With the 3's and 1's being subscripts.

Posted: **Thu Oct 15, 2009 9:45 pm**

Page 122, Line 20

"funciton" should be "function"

Posted: **Fri Oct 16, 2009 1:32 am**

"substituion" should be "substitution"

Posted: **Thu Oct 22, 2009 2:49 pm**

Also, the term in the third derivative starting with "48t^3" should be negative (-).

Posted: **Thu Oct 22, 2009 2:53 pm**

p. 127, line 15 (not counting figure and caption):

the second derivative should be t^(n-2), not t^(n-1)

Posted: **Thu Oct 22, 2009 3:09 pm**

p. 120, line 10

Actually, I am pretty sure that that the Taylor series given in line 10 is incorrect:
1/(1+t^2)= 1 - t + t^2 - t^3 + t^4 ...

If you actually calculate out all the derivatives and evaluate them at t=0, I am pretty sure that all the odd powers of t cancel out.

It should be: = 1 + x^2 + x^4 + x^6 ....

I think.

Posted: **Thu Oct 22, 2009 3:53 pm**

p. 123, line 1 and 11:

"theorem" is spelled incorrectly in both lines.

Posted: **Thu Oct 22, 2009 6:18 pm**

In the definition 5.3.1 whree should be changed to where

Posted: **Fri Oct 23, 2009 11:15 am**

p. 130, line 5 (not counting figure and caption)

This seems like something so obvious I think it might have been done on purpose, but are you aware that there is no section 5.4?
The title reads, "5.4 Series Solutions about a Singular Point," and then the book promptly skips to the title "5.5. A Collection of Famous Series Solutions." There is no text at all between Sections 5.4 and 5.5. Is there something missing, or was that done temporarily on purpose for now?

Posted: **Fri Oct 23, 2009 11:36 am**

Oops, ignore the above... I have in my notes that you already told us the topic of solutions about singular points isn't in the book anyway.

Posted: **Sun Oct 25, 2009 12:22 pm**

"/omega_n = 1,2,3,4 and 5" but the figure (Figure 4.3) only reflects cases 1,2, and 3

Posted: **Sun Oct 25, 2009 4:18 pm**

"...then it is analytic an any point"
"an" should be changed to "at"

Posted: **Sun Oct 25, 2009 5:52 pm**

line 15: "...covering what has been traditionally been the subject..." One too many beens
line 23: "...label of "engineering analysis" many homework problems..." Should be a comma after analysis

Posted: **Sun Oct 25, 2009 5:57 pm**

where it reads "there may be, in fact, up to n different solutions to the form x = e^..."
it should be x = ce^...
without the c, you don't know what to vary to get the different forms

Posted: **Sun Oct 25, 2009 6:00 pm**

reads "which is more obviously in such a form"
I can't offer a suggestion to fix it because I don't really know what it's supposed to mean

Posted: **Sun Oct 25, 2009 6:07 pm**

It says that the force is always directed in the opposite direction of the velocity of the mass
In actuality, the force is always directed in the opposite direction of the POSITION/DISPLACMENT of the mass

For confirmation, see figure 4.9:
at the point t = 1, the displacement is negative, the velocity is the slope of the x(t) graph, and has a positive value, and the force has a positive value

Posted: **Sun Oct 25, 2009 11:35 pm**

p 124: In the numerator, for the quantity a_(n+2) it reads n(n+1)+1, but it should be n(n-1)+1.

p 126: In the numerator, for the quatity a_(n+2) I think there should be a 20 multiplied by the (n(n+1)a_(n+1)) term.

Posted: **Tue Oct 27, 2009 2:26 am**

Should say Table 5.1

Posted: **Tue Oct 27, 2009 9:36 am**

Should also say Table 5.1 (instead of 5.2)

Posted: **Tue Oct 27, 2009 1:28 pm**

Example 5.4 says the first derivative of f(t)=1/(1+t^2) is 2t/(1+t^2)^2 but i believe this quantity should be negative (-2t/(1+t^2)^2).

Posted: **Tue Oct 27, 2009 1:46 pm**

On the new chapter 5, on page 159, third line of equations. I believe a_3 = (-1/6)*a_1

instead of the currrent:

a_3 = (-1/6)*a_3

Posted: **Tue Oct 27, 2009 1:53 pm**

The first line has the word "the" twice. "This chapter presents the the use of power series..."

Posted: **Tue Oct 27, 2009 7:24 pm**

Both of the following are in the new Chapter 5 Handout.

page 172, line 5: should be "point" instead of "oint"

page 158, line 7: should be (n+2)(n+1) not (n+1)(n+1)

Posted: **Tue Oct 27, 2009 9:32 pm**

Chapter 5 Handout

page 162, line 2 of last paragraph: 'give' should be 'given' and there should be a comma after 'test'

page 172, line 11 (after the recurrence relation equation): 'specify' should be 'will specify'

page 173, line 1: 'substituion' should be 'substitution'

Posted: **Tue Oct 27, 2009 10:23 pm**

p 95 1st equation.

according to equation 4.8, for the homogenous solution to be zero, x(0) would need to be positive, not negative.

If points are given, split them edward "wagner" hitchler, as he is right next to me and we discovered this as a team. Thanks

Posted: **Tue Oct 27, 2009 11:59 pm**

After line 6, the summation of cos(omega*t) should be omega^2n not omega^n

Posted: **Sun Nov 01, 2009 12:23 pm**

The middle of this line currently reads "the number of time steps necessary to for the algorithm"

I believe it shoudl be revised to read "the number of time steps necessary for the algorithm"

Posted: **Sun Nov 01, 2009 12:27 pm**

The line currently reads: "thing to do is to starting including higher order terms"

I believe it should be revised to read "thing to do is to start including higher order terms"

Posted: **Sun Nov 01, 2009 5:04 pm**

Take out the word "compute"

Posted: **Sun Nov 01, 2009 5:05 pm**

Take out "A" and capitalize "the"

Posted: **Sun Nov 01, 2009 5:06 pm**

"As has already been stated, the dependence of f on x and t is specified, but the dependence of x on t"...you should probably add "has not been specified"

Posted: **Sun Nov 01, 2009 5:07 pm**

I feel like this first sentence of 2. is a runon. I don't know how to best fix it.

Posted: **Sun Nov 01, 2009 5:08 pm**

"necessary in a straight-forward Taylor series computations"
You should take out "a"

Posted: **Sun Nov 01, 2009 5:09 pm**

take out "is" in "term is contains"

Posted: **Sun Nov 01, 2009 5:10 pm**

"As a matter of substance is is a matter of considering multivariable Taylor series expansions"
Not sure how to fix it.

Posted: **Tue Nov 03, 2009 6:17 pm**

The line currently says "...obviously, to expand f(x(t) + c2 f(x(t),t)..."

I believe the subscript of 2 in this equation should be changed to a 3.

In this manner the line will read, ""...obviously, to expand f(x(t) + c3 f(x(t),t)..."

Posted: **Wed Nov 04, 2009 7:16 pm**

Appendix D.2

Program for example 13.3.4

You need to declare the variable 'f' as double precision.

Posted: **Wed Nov 04, 2009 10:19 pm**

equation should be x(t + delta t) = f(x(t),t)*(delta t) + x(t)
because each term builds on the previous

Posted: **Wed Nov 04, 2009 10:22 pm**

line should begin "Because of the form of..."

Posted: **Wed Nov 04, 2009 10:24 pm**

last equation, if it is supposed to be a direct simplification of the above equation, is incorrect.
the part above the division line should read:
x(2.5) - 2x(2.0) + x(1.5)
instead of
x(2.5) - 2x(1.5) + x(1.5)

Posted: **Wed Nov 04, 2009 10:27 pm**

across the two lines it reads "in a Taylor series."
this should be "into a Taylor series"

Posted: **Thu Nov 05, 2009 5:34 pm**

"decided" should be "decide"

Posted: **Mon Nov 16, 2009 11:26 pm**

On page 360 Line 10, the first line of Equation 12.2, I believe the first equal sign should be multiplication

On page 369, Figure 12.7, I think the label on the vertical axis is incorrect (it is the same as the one on Figure 12.6, which was a different example)

On page 383 Line 12 and line 16, after the summation symbol there is an infinity that should be above the summation symbol

On page 387 Line 5, the sentence ends with "in Figure 12.19 through ??", which should be through Figure 12.22

On page 393 Line 25, starting with "which has a general solution Y(y)= ..., both exponents of e have 'pi' rather than the symbol for pi

On page 396, very last line, I believe that the X(x) should be d2*sin(sqrt())...the sin has been omitted

On page 397 line 9, the index for the Y(y) should be 'm', not 'n'

On page 401 the second line, first equation: the last term should be a partial du_ss not du_tr

On page 403 line 14 "We need to relate" not "related"

Posted: **Tue Nov 17, 2009 12:26 am**

"defined by Figure ??" should be Figure 35 I believe.
Sorry I did not remember to sign my previous email,
-Maria Gaither

Posted: **Wed Nov 18, 2009 4:43 pm**

pg 402 eq. 12.38

there is a typo: one of the dy^2 should probably be dx^2

Posted: **Sat Nov 21, 2009 1:53 am**

p 367: Figure 12.5 -- the x axis label should be 'x'

Posted: **Sun Nov 22, 2009 1:28 pm**

The line currently reads "the other two functions have a the same sign".

I believe it should be revised to "the other two functions have the same sign".

Posted: **Sun Nov 22, 2009 1:30 pm**

The italics text currently reads "the degree of 'alignment' the functions".

I believe it should be revised to "the degree of 'alignment' of the functions".

Posted: **Sun Nov 22, 2009 3:40 pm**

The second boundary condition currently reads "u(L,t) = T2"

Keeping with the convention used throughout the rest of the section, this should be "u(L,t) = TR", where the R is a subscript.

Posted: **Mon Nov 23, 2009 3:00 pm**

p. 382 6th line of text from the bottom

"which may the case for a second order equation"..

probably supposed to be "which may BE the case..."

Posted: **Mon Nov 23, 2009 6:54 pm**

On page 367, figure 12.5, the horizontal axis should be labeled x not t.

Posted: **Mon Nov 23, 2009 7:15 pm**

Page 382, Line -4

the equation should be X(x) = c1sin(sqrt(lambda)*x) + c2cos(sqrt(lambda)*x) instead of
X(x) = c1sin(sqrt(lambda*x)) + c2cos(sqrt(lambda*x))

Posted: **Mon Nov 23, 2009 10:06 pm**

The upper limit of integration is missing for the last term of the function.

Posted: **Mon Nov 23, 2009 11:42 pm**

on page 362, at the bottom it should say 'where the constantS were combined into an and bn.' right now it just says constant.

Posted: **Tue Nov 24, 2009 1:51 am**

It currently reads X(x)T" = alpha^2X"(x)T(t)

it should read X(x)T"(t) = alpha^2X"(x)T(t)

Posted: **Wed Nov 25, 2009 6:38 pm**

p 128 line -4 the subscript should be a_10 not a_11

p 425 line -3 there is a missing delta t to be multiplied by the c2(f(x(t),t)+partial...) term

p 427 line 7 and f(x(t)+f(x(t),t)delta t, x+delta t) should be changed to (f(x(t)+f(x(t),t)delta t, t+delta t)

p 427 line 9 the equation for x(t+delta t) I think the negative sign was dropped from the equation in front of x^3

p 435 line -5 the f_1(x1(t), x2(t),...xn(t),t) should be f_n not f_1

Posted: **Sun Nov 29, 2009 11:47 am**

It says "The string is assumed to elastic.."
which I think should be "The string is assumed to be elastic.."

Posted: **Sun Nov 29, 2009 11:48 am**

f_3(s) should be f_3(x)

Posted: **Sun Nov 29, 2009 11:52 am**

You say you're substituting into Equation 12.3.1, but that's not an equation number. I think you meant to say the first equation in section 12.3.1 which doesn't have a number.

Posted: **Sun Nov 29, 2009 11:59 am**

"Analogous to ordinary differential equation, in.." should be "Analogous to ordinary differential equationS, in.."

Posted: **Sun Nov 29, 2009 12:14 pm**

it says "sting" instead of "string"

Posted: **Sun Nov 29, 2009 12:52 pm**

"proporational" should be "proportional"

Posted: **Sun Nov 29, 2009 12:53 pm**

same thing as above..
"proporational" should be "proportional"

Posted: **Sun Nov 29, 2009 12:54 pm**

"convering" should be "converting"

Posted: **Mon Nov 30, 2009 12:16 pm**

p. 423 line 2

first line of section 13.3

"the main idea behind the so-called Runge-Kutta methods is.."

should be either "methods are" or "method is"

Posted: **Mon Nov 30, 2009 3:02 pm**

p 441 line 3 (the 2nd line below eq. 13.30)

".. and delta x << 1 is a fixed."

probably should remove the "a"

Posted: **Mon Nov 30, 2009 3:05 pm**

p 443 figure 13.15

the x-axis is labeled "t". I'm pretty sure it should be labeled "x"

Posted: **Mon Nov 30, 2009 3:07 pm**

p 367 figure 12.5

the x axis is labeled "t", and it should probably be labeled "x"

Posted: **Tue Dec 01, 2009 10:31 pm**

The text reads "Example 12.3.3 Ths solution.."
It should probably ready "Example 12.3.3 The solution.."

Posted: **Tue Dec 01, 2009 10:36 pm**

p 383 line 4

you refer to equation 12.3.1...

i cant seem to find equation 12.3.1, not sure which equation it is supposed to refer to

Posted: **Tue Dec 01, 2009 10:50 pm**

p 383 line 7

in the general solution for T(t), you are missing a constant, probably c1.

Give credit to Edward Hitchler for this find

Posted: **Wed Dec 02, 2009 1:11 am**

The equation for b_0= 1/2L... should not have the divided by 2. It should only be divided by 'L'.

Posted: **Wed Dec 02, 2009 1:58 am**

p. 383
when solving for the coefficient cn in the step where you have multiplied by the integral from 0 to L and sin(m*pi*x/L) you drop cn from the equation and just have the integral of sin squared equals the integral of sin time f(x)

p. 401

when you express the boundary conditions in the middle of the page you are missing equals signs at the end of three of them so it looks like you are multiplying. u(Lx,y,t)=utr(Lx,y,t)+uss(Lx,y,t)0 and the next two.

Posted: **Wed Dec 02, 2009 12:07 pm**

the equation at the bottom of the page reads X(a)....

it should read X(Lx)....

Posted: **Sat Dec 05, 2009 8:46 pm**

the sentence says "about x = and nonlinear equation...."

Posted: **Sun Dec 06, 2009 2:25 pm**

I think that where you have x=sqrt(2) it should really be x_0=sqrt(2)

Posted: **Sun Dec 06, 2009 2:27 pm**

"differential equations to s system" should be "differential equations to a system"

Posted: **Sun Dec 06, 2009 8:27 pm**

in equation 14.22, the second equilibrium point should be [2 0] not [0 2]

Posted: **Mon Dec 07, 2009 12:24 am**

line 6:
reads: which is to simply determine the ...
should read: which is simply to determine

line 9:
reads: introduces the the phase plane
should read: introduces the phase plane

Posted: **Mon Dec 07, 2009 12:28 am**

reads: will be to simply compute
should read: will be simply to compute

Posted: **Mon Dec 07, 2009 12:00 pm**

reads " other numerical packages may give a slightly different answers"

probably should read "other numerical packages may give slightly different answers"

(eliminated the "a")

Posted: **Mon Dec 07, 2009 12:06 pm**

in the last line before example 14.1.5, it states that t = 0,2pi,3pi,4pi...

then, in example 14.1.5, t is defined as t = 2m*pi.

Then, both claim to refer to the same figure, 14.5.
If m is an integer, which it usually is, then the initial definition for t should not include the 3pi term.

Posted: **Mon Dec 07, 2009 1:42 pm**

p 464, under number 4(b)
should say "linear approximation about x = 0"

p465, both plots should be xdot vs x, not x(t) vs t

Posted: **Mon Dec 07, 2009 7:55 pm**

p. 466

point 6 part a
the general solution says c1 should be then multiplied by the vector -2 1 but i believe it should be -1 2

Posted: **Tue Dec 08, 2009 1:36 pm**

on page 464, in equation 14.22, the vector [0,2] should be [2,0]. because x1 is supposed to be 2 and x2 should be 0.

Posted: **Tue Dec 08, 2009 10:05 pm**

the last line before example 14.3.7 says "by the simply coordinate transformation"

probably should be "by the simple coordinate transformation"

Posted: **Sun Dec 13, 2009 9:26 pm**

for line 7, should the index begin at n = 0, instead of n = 1?

for line 9, should a_(n+1) be a_(n+2)?

Posted: **Sun Dec 13, 2009 10:32 pm**

line 21 (equation 5.15) - I believe the first term of the numerator should be multiplied by '20'.

Posted: **Wed Dec 16, 2009 5:16 pm**

reads "and noting that since x1 and x2 the terms in the parentheses..."
should read "and noting that since x1 and x2 are the terms in the parentheses.."

Posted: **Wed Dec 16, 2009 5:18 pm**

"try to make the term in the left set of parentheses zero"
From looking at the work, I believe that the term which becomes zero is actually the term in the RIGHT parentheses

Posted: **Wed Dec 16, 2009 5:23 pm**

reads "a Taylor series that only converge for a limited ..."
should read: "a Taylor series that only converges for a limited.."

Posted: **Wed Dec 16, 2009 5:25 pm**

reads "be referred to a a or the differential equation"
should read: "be referred to as a or the differential equation"

Posted: **Wed Dec 16, 2009 5:26 pm**

reads: "A compete consideration of all..."
should read: "A complete consideration of all..."

Posted: **Wed Dec 16, 2009 5:28 pm**

reads: "in the general solution to be in terms of the..."
should read: "in the general solution be in terms of the..."

Posted: **Wed Dec 16, 2009 5:32 pm**

equation 12.24 has a 1/alpha, when the heat equation listed before on page 382 uses alpha^2

Posted: **Thu Dec 17, 2009 7:16 pm**

the statement sin(sqrt(lambda)*Lx = n*pi ... should probably read sqrt(lambda)*lx = n*pi

this is just based on the fact that we want the expression to equal zero, and to do that, we need sqrt(lamba)*pi to equal n*pi, not the sine of that.

Bill Goodwine's Courses

Course Text

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