What does C^r mean for a function of several variables?

Context: Graduate
Thread starter quasar987
Start date Jul 23, 2006
Tags

Function Mean Variables

Join the discussion

Ask a follow-up here, or get your own question answered by working scientists, mathematicians and engineers — people, not an autocomplete.

Real named experts · corrections over time · the nuance an AI answer skips

1 reply · 3K views

quasar987

Science Advisor

Homework Helper

Gold Member

Thread starter
Jul 23, 2006

Wiki and mathworld only talk about C^r for functions of one variables, saying C^r is the space of function with and rth derivative that is continuous. But for a function of several variables to be C^r means that all its partial derivatives (mixed and not mixed) of order r are continuous, correct?

Physics news on Phys.org

Materials surrounding a fusion reaction can dramatically increase how often it occurs
Chocolate syrup-like fluid stores multiple interacting memories
Engineers observe quantum heat waves at room temperature

DeadWolfe

Jul 23, 2006

Yes. Tht is correct.

What does C^r mean for a function of several variables?

Graduate A nice YouTube channel about all things Riemann Zeta

Undergrad What is "x" in this definition of a basis?

Graduate Knots In 4D

Graduate Zeros of functions analytic in 2 variables

Graduate Another similar notion to compactness

Graduate Nonautonomous Lie derivative

Graduate Shauder basis for Hilbert spaces

Graduate On covariance of the Lagrange equations

Insights Revisiting the Velocity-Time Function

Insights Remote Operated Gate Control System

Insights AI Enriched Problem Solving

Insights Thinking Outside The Box Versus Knowing What’s In The Box

Insights Why Entangled Photon-Polarization Qubits Violate Bell’s Inequality

Insights Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect

What does C^r mean for a function of several variables?

Similar threads