My Math Forum Spatial and temporal periods and periodic functions

 Algebra Pre-Algebra and Basic Algebra Math Forum

 April 20th, 2014, 10:55 PM #1 Senior Member   Joined: Nov 2013 Posts: 137 Thanks: 1 Spatial and temporal periods and periodic functions A periodic function is one that $f(\theta)= f(\theta + nT)$, by definition. However, the argument $\theta$ can be function of space and time ( $\theta(x, t)$ ), so exist 2 lines of development, one spatial and other temporal: $f(\theta)= f(kx + \varphi) = f(2 \pi \xi x + \varphi) = f\left(\frac{2 \pi x}{\lambda} + \varphi \right)$ $f(\theta)= f(\omega t + \varphi) = f(2 \pi \nu t + \varphi) = f\left(\frac{2 \pi t}{T} + \varphi \right)$ or the both together: $f(\theta)= f(kx + \omega t + \varphi) = f(2 \pi \xi x + 2 \pi \nu t + \varphi) = f\left(\frac{2 \pi x}{\lambda} + \frac{2 \pi t}{T} + \varphi \right)$ so, becomes obvius that $\lambda$ is the analogus of $T$, thus the correct wound't be say that a periodic function is one that $f(\theta)= f(\theta + nT + m\lambda)$ ?
 April 21st, 2014, 09:09 AM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,600 Thanks: 2588 Math Focus: Mainly analysis and algebra I suspect that your confusion arises because the notation $nT$ suggests time. In reality a periodic function is one that repeats regularly repeats its values as the free parameter increases, whatever that parameter represents.

 Tags functions, periodic, periods, spatial, temporal

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post hoyy1kolko Algebra 2 January 10th, 2011 02:28 PM Sarah112 Algebra 1 November 13th, 2010 01:56 PM roncarlston Algebra 2 September 26th, 2010 11:33 AM conradtsmith Calculus 1 August 20th, 2009 05:36 AM Sarah112 Real Analysis 0 December 31st, 1969 04:00 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top