If someone says something about a fourth-order approximation, does that mean ?

Thread starter AxiomOfChoice
Start date Jun 29, 2009
Tags

Approximation Mean

AI Thread Summary

A fourth-order approximation refers to retaining terms up to order κ^4 in a Taylor series expansion. This means that when approximating a function using a small parameter κ, only the first few terms, including those up to the fourth power, are considered. This method provides a balance between accuracy and complexity in mathematical modeling. The discussion confirms that the term specifically denotes the truncation of the series at the fourth-order term. Understanding this concept is crucial for effective application in various mathematical and engineering contexts.

Jun 29, 2009

AxiomOfChoice

If someone says something about a "fourth-order approximation," does that mean...?

...that, say, if something is being approximated by a Taylor series expansion in which only the first few terms are retained, and the expansion is in a small parameter \kappa, we only keep the terms up to order \kappa^4?

Physics news on Phys.org

Jun 29, 2009

Monocles

You got it.

Thread 'Need help understanding particle physics and quantum physics'

So I know that electrons are fundamental, there's no 'material' that makes them up, it's like talking about a colour itself rather than a car or a flower. Now protons and neutrons and quarks and whatever other stuff is there fundamentally, I want someone to kind of teach me these, I have a lot of questions that books might not give the answer in the way I understand. Thanks

View full post »

Thread 'Linear generator prototype'

i want to just test a linear generator with galvanometer , the magnet is N28 and the wire (Cu) is of 0.6mm thikness and 10m long , but galvanometer dont show anthing , The core is PLA material (3d printed) The magnet size if 28mm * 10mm * 5mm

View full post »

Thread 'Fundamental Probability'

If the universe is fundamentally probabilistic, and all possible outcomes are realized in some branch of the multiverse, does that invalidate the concept of scientific inquiry? If knowledge is merely a description of one particular branch of reality, does it have any inherent value?

View full post »