Section 1.10

Main Points: The main points of section 1.10 basically explain what a periodic function is, what characteristics make it periodic, and defines certain aspects of this type of function. A periodic function is one that has values repeating at regular intervals. The book also explains that in the function of y=Asin (Bt), A and B are parameters called amplitude and period. Amplitude is half the difference between the functions max and min values on the graph. The period is the time it takes the function to go through one complete cycle. Finally, a function in the form of y=Asin(Bt) + C or y=Acos(Bt) + C is periodic as long as Amplitude = A, period= 2pi/B, and vertical shift = C.

Challenges: My Calc teacher focused on periodic functions for a very long time, so I understood 99% of the reading. However, for someone who hasn't had as much emphasis on this type of function, he or she may have had difficulty understanding that when the period of a function (ie y=sinx) is increased (y=sin2x), the graph becomes narrower and when it is decreased (y=sin(1/2)x, the graph becomes wider. When I first learned this I was super confused.

Reflections: I really liked the sample problems the book gave for this unit because it actually showed how periodic functions relate to the world. In my past calculus class, we just did problems about finding the amplitude, etc., but the sample problem about high and low tide actually applied math to real life. Good deal!