Hey everyone. I have a 2004 Corolla S stick-shift and I'm concerned about a vibration I'm feeling in my clutch pedal. Everything seems normal when the car is cold but once it warms up and I have been driving it for a little while, starting from a stop, especially on an incline, usually causes a profound vibration in the pedal (as I engage the clutch) and a sputtering noise from the engine. It's usually not too bad until I get to my driveway which is at a relatively steep incline. I have to come to a complete stop before pulling my car up, so I put it into first and as I engage the clutch, the vibration and sputtering return with a vengeance.
I've tried various things like giving it more gas or letting off the clutch a bit slower. As it is, I never drive up the driveway with the clutch fully engaged to prevent stalling and because it's not that long. When I do give it more gas (about 2000-2500rpm), this tends to burn the clutch. I've also never stalled out while this has happened (except while I was learning to drive stick

)
Any ideas as to what is going on here? Perhaps this is normal and I'm just paranoid? When I bought the car used back in January, I had a local mechanic inspect it and he said that everything was fine. I can't imagine I've caused any major damage to the car since the majority of my driving is to and from school!
Thanks for any and all help!