My Math Forum Spatial and temporal periods and periodic functions

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 April 20th, 2014, 09:55 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, 08:09 AM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,386 Thanks: 2476 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.

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