- #1
quicksilver123
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What do the stars mean? I can't find a reference or definition elsewhere in my textbook...
Question about area between curves (integral calc textbook q
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Discussion Overview
The discussion revolves around the meaning of asterisks used in a calculus textbook, specifically in the context of denoting sampled points in relation to area between curves and integrals. Participants seek clarification on whether this notation is conventional or specific to the textbook in question.
Discussion Character
- Conceptual clarification, Debate/contested
Main Points Raised
- Some participants suggest that the asterisks denote sampled points, as indicated by the text.
- Others express uncertainty about the use of asterisks, noting that they are more accustomed to seeing different letters (a, b, c) used for constants.
- A participant mentions that the use of an asterisk may depend on context, referencing its common use in complex number notation for complex conjugation.
- Another participant recommends reviewing the definition of the integral via limits of Riemann sums for further clarification.
- One participant inquires whether the textbook defines a Net on an interval and the concept of the Mesh of a Net, suggesting this may relate to the notation.
Areas of Agreement / Disagreement
Participants generally agree that the asterisks are used to denote sampled points, but there is no consensus on whether this is a conventional notation or specific to the textbook. Some participants express differing views on the use of asterisks in mathematical contexts.
Contextual Notes
There is a lack of clarity regarding the specific definitions and conventions used in the textbook, as well as the potential for varying interpretations based on context.
What do the stars mean? I can't find a reference or definition elsewhere in my textbook...
- #2
blue_leaf77
Science Advisor
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Just for denoting the sampled points, as the text says.
- #3
quicksilver123
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Oh I see so this is not some convention, but merely indicating the points on the graph?
I've just never seen an asterisk used before, they usually use a different letter value (a, b, c) to designate constants.
Can anyone confirm the previous poster?
I've just never seen an asterisk used before, they usually use a different letter value (a, b, c) to designate constants.
Can anyone confirm the previous poster?
- #4
elements
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Yeah, it's just for sampling the points. My textbooks do it as well
- #5
blue_leaf77
Science Advisor
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Of course it depends on the context. When you start learning complex number you will see that an asterisk is often understood to represent the so-called complex conjugation of a complex number. At least that's the tradition in physics textbooks, among mathematicians as far as I know they use an overbar to represent a complex conjugation instead of an asterisk.quicksilver123 said:
- #6
mathwonk
Science Advisor
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the best way to confirm this is to go back and read closely the definition of the integral via limits of Riemann sums, possibly in chapter 5. Almost certainly this was explained in the book.
- #7
MidgetDwarf
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I believe, the asterix is used to denote sample points in your book. Does your book define a Net on an interval? The Mesh of a Net?
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