Supplementary Notes pp 4-8

Main Points: The idea of a gradient is introduced. A gradient is a vector that consists of partial derivatives and is denoted as grad(f). A directional derivative tells the rate of change in any direction on the xy plane where as a partial derivative tells the rate of change in either the x direction or the y direction. Directional derivative can be justified in the exactly the same way a regular derivative can be justified. The properties of a gradient are as follows. It always points in the direction of the greatest increase. Similarly, the direction opposite the direction of the gradient shows the greatest decrease. The length of the gradient directly corresponds to the steepness of the slope. Thus, larger slopes mean larger gradients. A gradient is always perpendicular to the level curve at which it is rooted.

Challenges: The idea of gradients is a bit hard to grasp. I'm a bit confused as to their importance and how exactly they are calculated. I don't have a specific question to ask about gradients - I'm just confused about everything!

Reflections: Gradients are totally new to me and I'm still a little puzzled as to how to go about solving problems in this area. However, I think that once you explain it in class I will be able to grasp the concept a lot better!