MATH 234 Lecture 18: 36345- Lecture #18- Math 234

• School: UW-Madison
• Department: Mathematics
• Course: MATH 234
• Professor: Betsy Stovall

Document Summary

Let d be a plane domain and f is a function on d (cid:573)x+(cid:574)y+ = 0 x(cid:3410)(cid:882) y(cid:3410)(cid:882) (cid:573)x+(cid:574)y+ (cid:3409)(cid:882) f(x, y) = 5x y + 10 on the domain d. Def: the function of f on a domain d has a local max at the point (a, b) if there is r > 0. The definition of the global al local min is the same, but we replace (cid:3409) with (cid:3410) For all the poi(cid:374)ts (cid:894)(cid:454), (cid:455)(cid:895) i(cid:374) d (cid:449)hich also lie i(cid:374) the disc of radius (cid:862)r(cid:863) ce(cid:374)tered at (a, b) For any plane domain d, we have (1) interior point (2) boundary. Def a domain d is called bounded if there is a disk containing d. Def a domain d is called closed if it contains all its boundary points. Ex d = {(x, y) ir2 {(cid:882)(cid:3409)x(cid:3409)a (cid:882)(cid:3409)y(cid:3409)b } D = {(x, y) |r2| {(cid:882)(cid:3409)x(cid:3409)a (cid:882)(cid:3409)y(cid:3409)b }