I'm getting a bit lost here with the mathematical notation. I understand the first two equations, but can someone explain the bottom two? I understand the left hand sides are first and second derivatives at times (time + time interval), and the values within the parentheses also make sense, but I'm not sure what the outside "V" and "A" are implying. Is this "V" a logic symbol like an "or"?
No, I think V just stands for "Velocity" and A for "Acceleration". I think this slide is super general, and is just saying that we calculate xdot and xdotdot using more general functions V and A, which depend on the future time step delta t. What the functions look like exactly haven't been specified yet.