Power supply capacitors

[MrDEB]

Need to build a LDO power supply using the LM2937 5v regulator powered from an automotive electrical system.
In the data sheet it shows some pretty small filter capacitors and they are not electrolytic type.
Not real savy on power supply design but seems like the caps should be larger and more?
But going by data sheet?

 

[MikeMl]

The manufacturer of the IC has determined the minimum capacitance which will prevent the regulator from oscillating due to distributed resistance and inductance of the wires between the battery and the regulator.

Any capacitor that you put there will not "filter" the automobiles' 12V bus. It would take Farads to capacitance to reduce any transients and alternator ripple that might be there. The input voltage may sag as low as 8V during starting, but that is still plenty of headroom for an LDO 5V regulator.