MAT 21C Lecture Notes - Lecture 25: Unit Vector, Dot Product, Directional Derivative
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MAT 21C Full Course Notes
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Announcements: m 11/28 from 3:10-4pm 204 art, w 11/30 6:10-8pm 6 olson, r 12/1 for 4:10-5pm 6 wellman. Important concepts: limits, convergence, intervals of convergence. 12 vectors and the geometry of space: 12. 1-12. 5. ~v v1(x x0) + v2(y y0) + v3(z z0) = 0: the distance from a point s to a line through p parallel to ~v is d = | ~v : the distance from a point s to a plane through p with normal ~v is d = (cid:12)(cid:12)(cid:12)(cid:12) 13 vector-valued functions and motion in space: 13. 1-13. 2. Di erentiation rules is the particle"s velocity vector and ~a (t) = d ~v dt. , when it exists, is the particle"s: product rule: d dt. [ ~u (t) ~v (t)] = ~u (t) ~v (t) + ~u (t) ~v (t: chain rule: d dt. [ ~u (f (t))] = f (t) ~u (f (t): when | ~r (t)| = c is constant, ~r ~r = 0.
