Warm-ups
Buzzing with the mouthpiece is a good way to start the day. Here's a few examples, feel free to make up more yourself. If available, use a piano to stay in pitch. If not, take the first note of each phrase from the trumpet.
Sound example: mouthpiece warm-up 1, c1, Tempo=60
Mouthpiece warm-up 1

created by jjs
Sound example: mouthpiece warm-up 1, c, Tempo=60

created by jjs
Sound example: mouthpiece warm-up 1, c2, Tempo=60
Sound example: Mouthpiece warm-up 2, Tempo=60
Mouthpiece warm-up 2

created by jjs
Further studies:

Stamp, James: Warm-Ups + Studies