I have a follow on question - I would like to delete or possibly edit the AppearanceElements of the Manipulators (the sliders) that David's examples produce. Here is a simple example as above:

Manipulate[u, {u, 0, 1},  AppearanceElements -> None]

deletes the + button symbol at the top right of the Manipulate but does not affect the +button at the right hand end of the Manipulator slider. In fact with Mathematica Version 10.3.1.0 running on OS X 10 11.3, some odd symbols appear at the end of the line of Appearance Elements as shown in this screen capture, where I have clicked the +button to expand it into the line below:

I would like to get rid of those weird characters, and all the Appearance Elements except the InputField, but have not found a method, other than assembling a home made Manipulate from components. By the way these weird characters appear in all the Wolfram Documentation that use Manipulators, so in the immortal words of Homer Simpson, "It was like that when I got here".

Thanks very much for this. I did not know you could put Options into the Manipulate variables. This let me simplify my interface as I had hoped, but had no effect on the weird characters which still appear, as this image shows. This is using the latest OS X and reasonably current Mathematica.