What are the Errata in Thomas' Calculus 11th Edition?

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In summary, the conversation discusses a few errata found in a copy of the book "Thomas' Calculus Early Trancendentals Media Upgrade 11th edition." One of the errata is found on page 179 and discusses a photograph that may be an artist's rendition rather than an actual photograph. The other errata, found on page 242, discusses a statement about the linearization giving 2 as an approximation for the square root of 3, which the author believes is not accurate to one decimal place. However, it is debated whether the author meant one decimal place or one significant digit.
  • #1
Jimmy Snyder
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I have a copy of the book Thomas' Calculus Early Trancendentals Media Upgrade 11th edition. I have found a couple of errata. While neither of them is important, I found them entertaining.

On page 179 at the bottom right hand corner there is what purports to be a multiflash photograph of falling balls. This cannot be a photograph but perhaps is an artist's rendition. Near the top of the figure, the later images of the falling balls appear beneath the earlier ones.

On page 242 in the middle of the page it says "the linearization gives 2 as the approximation for [tex]\sqrt{3}[/tex], which is not even accurate to one decimal place." I assume the author means that since the first digit of the square root is 1, 2 is off even in this place. However, it is necessary to round off the square root before making the comparison. Otherwise we would say that 2 is a terrible approximation to 1.9999999999999, it is not even accurate to one decimal place.
 
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  • #2
Jimmy Snyder said:
On page 242 in the middle of the page it says "the linearization gives 2 as the approximation for [tex]\sqrt{3}[/tex], which is not even accurate to one decimal place." I assume the author means that since the first digit of the square root is 1, 2 is off even in this place. However, it is necessary to round off the square root before making the comparison. Otherwise we would say that 2 is a terrible approximation to 1.9999999999999, it is not even accurate to one decimal place.
It's cool you find errata entertaining and all, but you're off on this one. 2 is accurate to one decimal place in regards to 1.9999999999999, and I don't see anything wrong with the statement in the book. 1.7 as the approximation of the square root of 3 would be an example of a figure accurate to one decimal place.

I don't have the book, so I can't comment on the first "error" you mentioned.
 
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  • #3
Ryker said:
2 is accurate to one decimal place in regards to 1.9999999999999
Is 2 accurate to one decimal place in regards to 1.73?
 
  • #4
Like mentioned in the book and in my post, it's not.
 
  • #5
So as I understand it, If I approximate 1.9999999999999 with 2, that's accurate to 1 decimal place. If I approximate 2.0000000000001 with 2, how many decimal places?

If I approximate 2001 with 2000, how many decimal places of accuracy would you assign it?
 
  • #6
Anyway, I stand by my original post. I say that 2 approximates 1.9999999999999 to many decimal places and therefore, 2 approximates [tex]\sqrt{3}[/tex] to one decimal place. After all how would you approximate 173 to 1 decimal place?
 
  • #7
Jimmy Snyder said:
So as I understand it, If I approximate 1.9999999999999 with 2, that's accurate to 1 decimal place. If I approximate 2.0000000000001 with 2, how many decimal places?
Yes, although this is accurate to more than one decimal place, same with 2.0000000000001.
Jimmy Snyder said:
If I approximate 2001 with 2000, how many decimal places of accuracy would you assign it?
None.
Jimmy Snyder said:
Anyway, I stand by my original post. I say that 2 approximates 1.9999999999999 to many decimal places and therefore, 2 approximates [tex]\sqrt{3}[/tex] to one decimal place. After all how would you approximate 173 to 1 decimal place?
By, say, 173.03, 172.99, 173.343444444444444444444444444444444 etc.
 
  • #8
You have to count the decimal places on both sides of the decimal point.
 
  • #9
Jimmy Snyder said:
You have to count the decimal places on both sides of the decimal point.
Decimals do not equal significant digits.
 
  • #10
That's pedantry and doesn't fit with what the author meant.
 
  • #11
There is a pair of errata in the book Thomas' Calculus Early Trancendentals Media Upgrade 11th edition. On page 242 in the middle of the page it says "the linearization gives 2 as the approximation for [tex]\sqrt{3}[/tex], which is not even accurate to one decimal place." The author means "not even accurate to one significant digit." That's the first erratum. He's wrong. It is accurate to one significant digit. That's the second erratum.
 
  • #12
What's pedantry? All I'm saying is the author's statement that 2 is not accurate to one decimal place of the square root of 3 is perfectly correct, I'm not debating its context. And the statement also doesn't hinge on the fact that the square root of 3 starts with a 1 instead of a 2 (well, in this particular case it does, but only indirectly, as the first decimal is 7).
 
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  • #13
Jimmy Snyder said:
The author means "not even accurate to one significant digit." That's the first erratum. He's wrong. It is accurate to one significant digit. That's the second erratum.
How do you know he means that it's accurate to one significant digit. In this case, he would indeed be wrong, but if he meant one decimal place, then he is right.
 
  • #14
Ryker said:
How do you know he means that it's accurate to one significant digit. In this case, he would indeed be wrong, but if he meant one decimal place, then he is right.
Because it makes no sense to focus on the digits to the right of the decimal place when there is a discrepency on the left.
 
  • #15
Of course it makes sense. 2 in regards to 1.96 is accurate to one decimal place, even though 1.96 starts with 1. 2 in regards to 1.73 isn't, but the fact that 1.73 starts with 1 alone isn't the reason for this. I think you're not getting the concept of accuracy to one decimal place.
 
  • #16
OK, I see what you are saying. However the book is still wrong. The number of accurate decimals places is not an issue when it comes to accuracy. You pointed out yourself that 2000 as an approximation 2001 is not accurate to a single decimal place. So the author may well have meant decimal places, but he shouldn't have. Accuracy is always a matter of significant digits, not necessarily of places to the right of the decimal point.
 
  • #17
No, the author is still right. In this specific case, you're comparing to the square root of 3, so accurate to one decimal place just means accurate to two significant digits.
 
  • #18
Ryker said:
No, the author is still right. In this specific case, you're comparing to the square root of 3, so accurate to one decimal place just means accurate to two significant digits.
I'd like to see him say that 299,792,000 m/s is no more accurate as an estimate of the speed of light than 400,000,000 m/s, neither have any decimal places of accuracy. What I'm saying is that accuracy isn't measured in terms of decimal places of accuracy, it's measured in terms of significant digits of accuracy. He might measure distance in terms of quarts and get the right number, but he'd still be wrong.
 
  • #19
Look, I don't know how to explain this further, but he is measuring accuracy in terms of significant digits, he just uses the term "to one decimal place". But that's the same thing, it's just that when you relate accuracy to decimal places, the number of significant digits depends upon each specific case of a number being compared to!

And I don't get what you're getting at with those two numbers compared to the speed of light, because they don't have anything to do with what I was saying. Of course he wouldn't say 400,000,000 m/s is more accurate than 299,792,000 m/s, and I wouldn't either. But those two numbers do have decimal places, because when you take an exact number 400,000,000 m/s is actually taken to be 400,000,000.0000000000000000000... m/s, you just don't expressly write out all the zeroes. So you could have just as easily asked for an accuracy to one decimal place comparison, and in this particular case, none of them would satisfy it when compared to the speed of light.

Again, accuracy to one decimal place just means two numbers are the same when you round them up to one decimal place. The square root of 3 rounded to one decimal place is 1.7, 2 rounded to one decimal place is 2.0. Clearly 1.7 is not 2.0, hence, they are not accurate to one decimal place, ie. two significant digits. He hasn't said anything wrong.
 
  • #20
I understand that his numbers are correct. I dispute that decimal points of accuracy is a measure of accuracy even if from time to time it gets the right answer. It gets the wrong answer when there are two or more decimal places to the left as in the speed of light example. It gets the wrong answer when there are 1 or more zeros directly to the right of the decimal point. It is an unreliable measure of accuracy that sometime works. The correct measure of accuracy is significant digits. It always works.
 
  • #21
No, it always works, and it doesn't get you the wrong answer in the speed of light example. Show me how you think it does.
 
  • #22
Putting this in context:
Thomas Calculus 11th edition said:
"Look at how accurate the approximation [itex] \sqrt{1 \ + \ x} \ \simeq \ (1 \ + \ ( \frac{x}{2})) [/itex] from example 1 is for values of x near zero.
As we move away from zero, we lose accuracy. For example, for x = 2, the linearization
gives 2 as the approximation for [itex]\sqrt{3}[/itex] which is not even accurate to
on decimal place".

All he means is that since [itex]\sqrt{3} \ \simeq \ 1.73205...[/itex] the linearization
value of 2 is not even accurate to one decimal place, i.e. between 1.7 & 1.8. All he's
trying to point out is that the linearization has a small scope of influence before the
value diverges too far.

as if I need to do this but: said:
"Accurate to N decimal places" means the number of digits to the right of the decimal point
that you can trust is N."Accurate to N decimal places" means the number of digits to the
right of the decimal point that you can trust is N. For example, if I measure a length with
a ruler that shows millimeters, the measurement will be accurate to one millimeter, or 3
decimal places if I write it in meters (0.001 m). If I claimed to have measured it as
1.1293 m, you'd know I was guessing about the 3, and would round it off to the nearest
thousandth: 1.129.
http://mathforum.org/library/drmath/view/59014.html

Jimmy Snyder said:
On page 179 at the bottom right hand corner there is what purports to be a multiflash photograph of falling balls. This cannot be a photograph but perhaps is an artist's rendition.

It may be an artists rendition of a photograph as opposed to an actual photograph but I
mean if you're going to call that an error I don't know what to say other than this kind of
pedantic slavery over language will annoy you to no end if you continue reading math
books :tongue2: I think it's quite clear what he means.

Jimmy Snyder said:
Near the top of the figure, the later images of the falling balls appear beneath the earlier ones.

Erm, "the later images of the falling balls appear beneath the earlier ones" is how
things look once they are dropped downwards. If you drop something it will appear
below the point you dropped it from (:rofl:) Surely you meant something less
tautological and more error prone but I can't figure out what you meant, in any case the
picture does not look like it has any error to me other than purporting to be a real photo
as opposed to an artists rendition (despite the fact it's obvious what he meant).
 
  • #23
Behind.
 
  • #24
1.000 km vs 1.001 km, accurate to 2 decimal places.
1000 m vs 1001 m, accurate to 0 decimal places.
In spite of the difference in decimal place accuracy (2 vs 0), these two are exactly the same thing. Both are accurate to 3 significant digits.

9999 vs 9998 accurate to 0 decimal places
9999999 vs 9999998 accurate to 0 decimal places.
There is no difference in decimal place accuracy (0 vs 0), but the first is accurate to 3 significant digits and the second is accurate to 6 significant digits.

.0123 vs .0124, accurate to 3 decimal places
.0000004 vs .0000001, accurate to 6 decimal places
The first is half as acccurate as the second according to counting decimal places, but is off by less than 1%. The second is off by nearly an order of magnitude.

2.0 vs 1.7, accurate to 0 decimal places and 1 significant digit. Spot on.

My point is that counting decimal places of accuracy gives a false report in too many cases and that makes it useless as a measure of accuracy. Counting significant digits doesn't have this problem.
 
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  • #25
Yup. None of what you wrote is relevant in showing whether the thing you mentioned is an error or not, though.
 
  • #26
Ryker said:
Yup. None of what you wrote is relevant in showing whether the thing you mentioned is an error or not, though.
You're right about the OP. The only problem is in the author's use of decimal place accuracy as an absolute measure of accuracy.
 
  • #27
sponsoredwalk, can you verify that the images of the balls taken later are layered behind the images taken earlier and not in front as they would be in an actual multiflash photograph?
 
  • #28
Here is the photo:

attachment.php?attachmentid=35557&stc=1&d=1305396158.png


Here is another multiflash photo:

[PLAIN]http://www.math.jhu.edu/~mathclub/book_covers/spivak_calculus.jpg [Broken]

I think you can see that it's not so clear as to whether an image of something falling will
unambiguously appear on top regardless of where it is temporally. In fact you can see in
Spivak's book cover the author manipulated the coin aty different points for clarity (just
as most pictures of this kind are manipulated). Furthermore it's a drawing so I mean they
can hardly draw things perfectly & I honestly think it would be less clearer if he didn't draw
the picture at the top the way it's done, if I were an artist doing that I'd want to make the
top look clear to indicate what's going on.
 

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  • #29
sponsoredwalk said:
Furthermore it's a drawing ...
That was my whole point. The text says it's a photo.
 
  • #30
Here's another erratum, a little more serious, but still not too bad.

On page 297 in the solution to Example 8 it has

[tex]f'(x) = e^{2/x}(-\frac{2}{x^2}) = -\frac{2e^{2/x}}{x^2}[/tex]

[tex]f''(x) = \frac{x^2(2e^{2/x})(-2/x^2) - 2e^{2/x}(2x)}{x^4} = \frac{4e^{2/x}(1 + x)}{x^4}[/tex]

It seems that a minus sign went missing in the middle term on the second line and then reappeared in the last term. It should be:

[tex]f''(x) = -\frac{x^2(2e^{2/x})(-2/x^2) - 2e^{2/x}(2x)}{x^4} = \frac{4e^{2/x}(1 + x)}{x^4}[/tex]
 
  • #31
I can't find that example in the book, what section is it in? In any case yeah a (ghost) minus
sign is factored out in front & put back in in the end, if you tell me the section I can check if
my version also forgot the minus sign.
 
  • #32
Page 297, section 4.4 Concavity and Curve Sketching, Example 8. I would appreciate confirmation. Even better would be if someone has the 12th edition to see if it is fixed.
 
  • #33
In my book they only go up to example 7 in that section, wonder why? :tongue2:
 
  • #34
Here's another minor erratum. On page 306 in the solution to example 4, the 6th line on the page it refers to Figure 4.37. It should say Figure 4.39.
 
  • #35
I note that on page 327 in the table in the middle of the page, that 'Number of correct digits' is used as a measure of accuracy. This is in an approximation to the value of [itex]\sqrt{2}[/itex].
 
<h2>1. What are errata in Thomas' Calculus 11th Edition?</h2><p>Errata are mistakes or errors found in the 11th edition of Thomas' Calculus textbook. These can include typos, incorrect equations or figures, or other errors that may affect the accuracy or clarity of the content.</p><h2>2. How do I know if I have the 11th edition with errata?</h2><p>You can check the version of your textbook by looking at the title page or copyright page. If it says "11th edition" and was published in 2017 or later, it likely contains errata. You can also check the publisher's website for a list of known errata for the 11th edition.</p><h2>3. Why are errata important to be aware of?</h2><p>Errata can impact your understanding of the material and may lead to incorrect solutions or confusion. It is important to be aware of any known errata so that you can correct them in your notes or when working on problems.</p><h2>4. How can I find the errata for the 11th edition of Thomas' Calculus?</h2><p>The publisher's website typically has a list of known errata for their textbooks. You can also search online for "Thomas' Calculus 11th edition errata" to find any unofficial lists or forums discussing the errors in the textbook.</p><h2>5. Can I get a corrected version of the 11th edition without errata?</h2><p>Unfortunately, there is no way to get a completely corrected version of the 11th edition. However, you can check for any updates or revisions on the publisher's website and make note of any corrections in your own textbook. Alternatively, you can purchase a newer edition of the textbook that may have corrected the errata.</p>

1. What are errata in Thomas' Calculus 11th Edition?

Errata are mistakes or errors found in the 11th edition of Thomas' Calculus textbook. These can include typos, incorrect equations or figures, or other errors that may affect the accuracy or clarity of the content.

2. How do I know if I have the 11th edition with errata?

You can check the version of your textbook by looking at the title page or copyright page. If it says "11th edition" and was published in 2017 or later, it likely contains errata. You can also check the publisher's website for a list of known errata for the 11th edition.

3. Why are errata important to be aware of?

Errata can impact your understanding of the material and may lead to incorrect solutions or confusion. It is important to be aware of any known errata so that you can correct them in your notes or when working on problems.

4. How can I find the errata for the 11th edition of Thomas' Calculus?

The publisher's website typically has a list of known errata for their textbooks. You can also search online for "Thomas' Calculus 11th edition errata" to find any unofficial lists or forums discussing the errors in the textbook.

5. Can I get a corrected version of the 11th edition without errata?

Unfortunately, there is no way to get a completely corrected version of the 11th edition. However, you can check for any updates or revisions on the publisher's website and make note of any corrections in your own textbook. Alternatively, you can purchase a newer edition of the textbook that may have corrected the errata.

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