Definition of piecewise continuous/piecewise smooth

  • Context: Undergrad 
  • Thread starter Thread starter AlonsoMcLaren
  • Start date Start date
  • Tags Tags
    Definition Smooth
Click For Summary
SUMMARY

Piecewise continuous and piecewise smooth functions are traditionally defined on closed intervals [a,b]. However, the discussion confirms that these definitions can also be applied to open intervals (a,b) without any inherent contradictions. This flexibility allows for broader applications in mathematical analysis and function theory. The consensus among participants emphasizes the importance of context when defining these concepts.

PREREQUISITES
  • Understanding of mathematical analysis concepts
  • Familiarity with function continuity definitions
  • Knowledge of interval notation in mathematics
  • Basic principles of piecewise functions
NEXT STEPS
  • Research the properties of piecewise continuous functions
  • Explore applications of piecewise smooth functions in calculus
  • Study the implications of defining functions on open vs. closed intervals
  • Investigate the role of piecewise functions in real-world modeling scenarios
USEFUL FOR

Mathematicians, students of advanced calculus, and anyone interested in the theoretical foundations of function analysis.

AlonsoMcLaren
Messages
89
Reaction score
2
In my textbook, piecewise continous/piecewise smooth is always defined on interval[a,b]. Can they be defined on open interval (a.b)?
 
Physics news on Phys.org
Sure, I see no reason why not...
 

Similar threads

Graduate Integrating over piecewise functions
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Give me a function that is piecewise continuous but not piecewise smooth
  • · Replies 5 ·
Replies
5
Views
6K
I have troubles finding the limit of this piecewise function
  • · Replies 9 ·
Replies
9
Views
3K
MHB Piecewise Continuous and piecewise smooth functions
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Fourier Transform of Piecewise linear spline wavelet
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Proving Continuous Functions in Smooth Infinitesimal Analysis
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Piecewise Functions in the Einstein Field Equations
  • · Replies 57 ·
2
Replies
57
Views
4K
Undergrad Open interval or Closed interval in defining convex function
  • · Replies 4 ·
Replies
4
Views
3K
Finding a Piecewise Smooth Parametric Curve for the Astroid
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Continuity of Hamiltonian at separatrix in action-angle variables
  • · Replies 1 ·
Replies
1
Views
1K