Time Complexity

I still do not quite understand time complexity stuff in Friday's lecture, especially the slides below. I will try to figure out as soon as possible on weekdays.

Now I understand all those stuffs after finishing Assignment 2. First, n stands for the input size, and we need to use divide-and-conquer method to find the time complexity of this algorithm. For simplicity, we assume n = 2^k,and we can easily get the time complexity for that certain input. The calculation for n != 2^k needs more work and we must use other tricks (like sandwich theorem) to figure it out.