Undergrad Question about area between curves (integral calc textbook q

Click For Summary
SUMMARY

The discussion centers on the use of asterisks in integral calculus textbooks to denote sampled points on graphs. Participants confirm that this notation is not a standard convention but rather a specific choice made by the textbook author. The conversation also touches on the distinction between using asterisks and other symbols, such as letters or overbars, particularly in the context of complex numbers and their conjugates. For a deeper understanding, readers are encouraged to refer back to the definitions provided in their textbooks, particularly in relation to Riemann sums.

PREREQUISITES
  • Understanding of integral calculus concepts, particularly Riemann sums
  • Familiarity with complex numbers and their representations
  • Knowledge of mathematical notation and conventions
  • Access to a calculus textbook that discusses sampling points
NEXT STEPS
  • Review the definition of Riemann sums in your calculus textbook
  • Study the representation of complex conjugates in mathematics
  • Explore different notational conventions used in various calculus textbooks
  • Investigate the concept of nets and mesh in the context of integrals
USEFUL FOR

Students of calculus, educators teaching integral calculus, and anyone interested in understanding mathematical notation and conventions in textbooks.

quicksilver123
Messages
173
Reaction score
0
IMG_2104.jpg
hi please refer to the inline image:
What do the stars mean? I can't find a reference or definition elsewhere in my textbook...
 
Physics news on Phys.org
Just for denoting the sampled points, as the text says.
 
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?
 
Yeah, it's just for sampling the points. My textbooks do it as well
 
quicksilver123 said:
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?
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.
 
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.
 
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?
 

Similar threads

Undergrad What would a calculus author have to say on ##\int r^2dm##?
  • · Replies 11 ·
Replies
11
Views
3K
High School Question about units for "area under curve"
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Calculus- Area between two curves (minimize it)
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad How to evaluate the enclosed area of this implicit curve?
  • · Replies 2 ·
Replies
2
Views
3K
High School Calculating shaded area: I'm getting discrepancies between methods
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Question about Integrals to Determine Volume vs Surface Area
  • · Replies 5 ·
Replies
5
Views
3K
High School Explain Integration to me, please
  • · Replies 5 ·
Replies
5
Views
3K
Insights An Overview of Complex Differentiation and Integration
  • · Replies 1 ·
Replies
1
Views
4K
High School Area Under Curve: Calculus Senior Year | Uses, Benefits
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Find the area enclosed by the curve y = x csch(x+y)
  • · Replies 3 ·
Replies
3
Views
2K