What is the meaning of c = min {a, b/M} in IVP proofs?

  • Context: Undergrad 
  • Thread starter Thread starter hawkingfan
  • Start date Start date
  • Tags Tags
    Mean Notation
Click For Summary
SUMMARY

The notation c = min {a, b/M} in initial value problem (IVP) proofs indicates that c represents the minimum value between a and the quotient b/M. In this context, a is related to the x-axis and b/M to the y-axis, as illustrated in the accompanying graph. The general definition of min {y1, y2, ..., yn} is to select the smallest element from the set, which is crucial for understanding the behavior of solutions in differential equations.

PREREQUISITES
  • Understanding of initial value problems (IVPs)
  • Familiarity with basic calculus concepts
  • Knowledge of real analysis fundamentals
  • Graph interpretation skills
NEXT STEPS
  • Study the properties of minimum functions in mathematical analysis
  • Explore the implications of IVPs in differential equations
  • Learn about the graphical representation of functions and their minima
  • Investigate the definitions and applications of ordered sets in mathematics
USEFUL FOR

Students studying real analysis, mathematicians focusing on differential equations, and educators teaching IVP concepts will benefit from this discussion.

hawkingfan
Messages
24
Reaction score
0
Hey dudes, I'm trying to understand the proofs about IVPs in the appendix of my differential equations book but I can't understand this notation that says c = min {a, b/M}.

What is that notation supposed to mean? I'm guessing that it stands for minimum value between a and b/m. (a is associated with the x-axis and b/M is associated with the y-axis based on the picture of the graph in the book) I'm just beginning to study real analysis so I haven't seen this notation yet.
 
Physics news on Phys.org
Yes it just means to take the minimum value between a and b/M.

In general x = min{y1,y2,y3,...,yn} means to take the minimum value from the set {y1,y2,y3,...,yn}.
 
"min S" is the element of S that is less than every other element -- it's minimum.

(the domain of "min" consists only of those ordered sets with a minimum. In other words, if S doesn't have a minimum, then "min S" is undefined)
 

Similar threads

Undergrad Understanding a proof of inexistence of max nor min
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Confusing max(min(f(x,y)) notation?
  • · Replies 4 ·
Replies
4
Views
3K
MHB -b.2.2.26 IVP min value y'=2(1+x)(1+y^2); y(0)=0
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Some questions on l'Hôpital rules
  • · Replies 9 ·
Replies
9
Views
3K
Undergrad Lipschitz continuity of vector-valued function
  • · Replies 3 ·
Replies
3
Views
4K
Prove ##(a+b)\cdot c=a\cdot c+b\cdot c## using Peano postulates
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Attempting to find an intuitive proof of the substitution formula
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Mean values of observables
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad What does a delta symbol mean in mathematics?
  • · Replies 2 ·
Replies
2
Views
5K
High School What is the meaning of g: [a, b] → R in set notation?
  • · Replies 2 ·
Replies
2
Views
1K