Hints for Lesson VC.06

• General Hint: Many times in this lesson, you see some big divField's denominator compared to something like (x-a)²+(y-b)². One purpose of this comparison is so that you can see the what values of x and y make it zero. That helps you find singularities. Another thing this tells you is that the denominator is always positive (or zero) because the square of a number (like (x-a)²) has to be positive, and adding two positives stays positive. You can use this to tell that the divField[x,y] = -7 / ( (x-a)² + (y-b)² ) is always going to be negative (except at the singularity) --- because the top is negative and the bottom is positive --- so every point except (a,b) is a sink.
• Remember: To tell what happens at a singularity, you must use the path integral. The rotField or divField can't tell you anything about what's going on.