1 00:00:08,000 --> 00:00:14,999 MATH GIRL by Dr. Veselin Jungic http://www.math.sfu.ca/~vjungic/ 2 00:00:17,000 --> 00:00:21,000 Hi I'm MathGirl, a protector of calculopolis. 3 00:00:22,000 --> 00:00:27,999 I help calculopolates who need to find the instantanious rate of change 4 00:00:28,000 --> 00:00:32,049 or who need to perform approximations of some of those nasty functions. 5 00:00:33,700 --> 00:00:38,089 but some people don't understand me and mistake me for a villain. 6 00:00:38,900 --> 00:00:47,899 These are the two fathers of calculus Newton and Leibniz, but that's a long story. 7 00:00:48,000 --> 00:00:51,999 I'd rather tell you how I use calculus to save my friend Pat. 8 00:00:52,250 --> 00:00:59,249 This is my linear approximator or you can think of it as a segment of a straight line. 9 00:01:01,250 --> 00:01:08,249 It's very fun to use because you only need multiplication addition and a little bit of calculus, 10 00:01:08,250 --> 00:01:16,250 to get you to weird places, you don't always get to exactly where you wish but sometime close enough is good enough. 11 00:01:16,999 --> 00:01:22,998 Once upon a time, I was here in my problem solving room when 12 00:01:25,500 --> 00:01:33,499 That sounds like Pat Thagoras, he's stuck on square root axe mountain ! 13 00:01:35,029 --> 00:01:40,109 Those non-square numbers can make some places on square root axe mountain very difficult to get you. 14 00:01:41,000 --> 00:01:43,999 I'll use my linear approximator. 15 00:01:45,000 --> 00:01:48,999 I summon the power of Descartes 16 00:01:50,500 --> 00:01:54,000 creator of XY-coordinates ! 17 00:01:54,200 --> 00:01:56,199 Hurry I'm falling ! 18 00:01:56,200 --> 00:01:59,199 Look Pat's x-coordinate is 37. 19 00:02:01,299 --> 00:02:10,098 Since the first derivative of y=sqrt(x) is y'=1/(2sqrt(x)), 20 00:02:10,299 --> 00:02:12,298 my linear approximator 21 00:02:13,500 --> 00:02:18,499 easily jumps from perfect square to perfect square. 22 00:02:19,300 --> 00:02:24,299 36 is the closest to Pat's coordinates. Is it close enough to save him ? 23 00:02:24,500 --> 00:02:25,700 Let's see ! 24 00:02:26,000 --> 00:02:27,999 Hurry I'm falling ! 25 00:02:28,100 --> 00:02:32,599 Almost there Pat, let's take a closer look ! 26 00:02:34,000 --> 00:02:41,999 Now if my linear approximator is at the point (36,sqrt(36))=(36,6) 27 00:02:42,000 --> 00:02:46,999 it will coincide with the tangent line of the function y=sqrt(x) at that point. 28 00:02:47,199 --> 00:02:52,449 The distance between us will be very small, close to the differantial 29 00:03:03,000 --> 00:03:04,999 My arm is long enough. 30 00:03:05,829 --> 00:03:09,828 I'll save you Pat ! Grab my hand ! 31 00:03:13,500 --> 00:03:17,499 Thanks MATHGIRL ! My math teacher was right math is useful ! 32 00:03:18,100 --> 00:03:21,799 I think I should wake up and pay more attention in math class. 33 00:03:22,730 --> 00:03:25,730 See close enough was good enough ! 34 00:03:26,300 --> 00:03:31,299 Ahh Y.. you wanna go get something to eat ? 35 00:03:40,000 --> 00:03:42,999 Synchro & Transcript by KBIDA Abdellatif special thanks Hausermann Christophe and Schultz Hannah.