Calculus Sentence in English in textbook "Calculus", by Robert A. Adams

AI Thread Summary
The discussion revolves around a translation issue in the sixth edition of "Calculus" by Robert A. Adams, specifically in the second chapter on differentiation. The participant seeks clarification on the title of a section, suggesting it might be "Velocity and Acceleration," and requests the English version of a specific sentence from Example 2 regarding velocity continuity. There is confusion between the Mean Value Theorem and the Intermediate Value Theorem, with one participant noting that the terms can be easily mixed up due to their similar names. They explain that while the Mean Value Theorem deals with average values, the Intermediate Value Theorem pertains to the continuity of functions, emphasizing that every derivative has the intermediate value property. The conversation highlights the nuances in mathematical terminology and the importance of precise definitions in calculus.
mcastillo356
Gold Member
Messages
634
Reaction score
342
Hi, PF

I've got a translation into spanish of the sixth edition of "Calculus", by Robert A. Adams. At the second chapter, "Differentiation", eleventh section, I would like to know: the title of the section (Could it be "Velocity and Acceleration"?); and a sentence of the Example 2 ("A point P moves along the x axis..."): at the solution of the question (d), I have something like "Velocity is continuous for all t, so, according to the Mean value theorem...". Wich would be the sentence in English?

Thanks!
 
Physics news on Phys.org
The velocity is continuous for all t so, by the Intermediate-Value Theorem, has a constant sign on the intervals between the points where it is 0.
 
  • Love
Likes mcastillo356
In my edition, it mentioned Mean Value Theorem, and it didn't make sense.

Greetings!
 
Yeah, it's probably easy to mix up 'Teorema del valor medio' and 'Teorema del valor intermedio'.
 
  • Like
Likes PeroK and mcastillo356
The English word "mean" refers to an average, so the mean value theorem talks about the average value.
 
  • Informative
Likes mcastillo356
actually every derivative, continuous or not, has the intermediate value property, and the proof uses the mean value theorem, or at least its equivalent version, rolle's theorem. ( a function that goes up and then down, must take the same value twice and hence must level off somewhere in between.) so many interpretations are possible.
 
  • Informative
Likes mcastillo356
For the following four books, has anyone used them in a course or for self study? Compiler Construction Principles and Practice 1st Edition by Kenneth C Louden Programming Languages Principles and Practices 3rd Edition by Kenneth C Louden, and Kenneth A Lambert Programming Languages 2nd Edition by Allen B Tucker, Robert E Noonan Concepts of Programming Languages 9th Edition by Robert W Sebesta If yes to either, can you share your opinions about your personal experience using them. I...
Hi, I have notice that Ashcroft, Mermin and Wei worked at a revised edition of the original solid state physics book (here). The book, however, seems to be never available. I have also read that the reason is related to some disputes related to copyright. Do you have any further information about it? Did you have the opportunity to get your hands on this revised edition? I am really curious about it, also considering that I am planning to buy the book in the near future... Thanks!
I’ve heard that in some countries (for example, Argentina), the curriculum is structured differently from the typical American program. In the U.S., students usually take a general physics course first, then move on to a textbook like Griffiths, and only encounter Jackson at the graduate level. In contrast, in those countries students go through a general physics course (such as Resnick-Halliday) and then proceed directly to Jackson. If the slower, more gradual approach is considered...

Similar threads

Replies
5
Views
484
Replies
2
Views
962
Replies
2
Views
2K
Replies
9
Views
2K
Replies
12
Views
4K
Back
Top