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I have a pre-made slides of mostly text and math formulae, and I want to make a kind of video presentation from it. I need a software that can do the following things:

  1. Smooth difference transition. What I mean by that: if I have two images with only a slight difference in them (say, one added word) I want to apply a transition where this difference fades in or somewhat dynamically pops in without disturbing the rest of the image;
  2. Sliding up/down/left/right with controlled speed and acceleration. To create an effect of a camera sliding over a big sheet of paper.
  3. Shaky camera effect, basically make an image "wiggle" (not very important).

That's pretty much it. So far I've tried only OpenShot and it doesn't seem like a good choice for that, although if you have a tutorial in mind that shows how to do such things please let me know.

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Shotcut

Shotcut might be a bit better then OpenShot. It is free, open-source, and you can do the things you described, just check these tutorials:

Shotcut example project

DaVinci Resolve

If you want a really professional software, go with DaVinci Resolve. It is free and cross platform, but has a bigger learning curve, although the things you described are not that hard:

DaVinci Resolve example project

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Something like this would be done in After-Effects. There is a free trial of the software - I would highly recommend trying this.

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