I understand the majority of this circuit, but could anyone explain to me why there is +2.5V connected to the non-inverting terminal on the first and last op-amps? In my classes, we've always connected this to ground when using an inverting configuration.

 

There wanting the heart beat to swing like a sine wave doing so with half the power supply voltage.

 

This article might clear things up for you.

 

In my classes, we've always connected this to ground when using an inverting configuration.

That applies if your opamp has dual polarity supplies, e.g.+5V and -5V. If the opamp has ony a single polarity supply, say +5V, then it is common practice to provide a 'virtual ground' at half the supply voltage, i.e +2.5V.