MATH 14 Lecture Notes - Lecture 12: Polar Coordinate System, Central Limit Theorem

• School: Santa Clara University
• Department: Mathematics and Computer Science
• Course: MATH 14
• Professor: Daniel Ostrov

Document Summary

2/8/19: change of coordinates in 1-d (method of substitution from. Math 12) x = 4 x = 0 (x)dx f. A: substitution: x = 2u u = 2 dx du = 2. The jacobian, j(u), represents the local shrinking/stretching of the coordinates. Here, we uniformly are shrinking by a factor of. 2, so j(u) = 2: general substitution: x = g(u) where g is strictly increasing (x) exists. 2 out of 8 or strictly decreasing, so g 1 u = g (u) Where f (g(u)) du dx du dx du = j (u) 0 u x = 2 v y = 3. r u = 1 u = 0 (2u, 3v)(2. Note: book uses g instead of v = 1 v = 0. = j(u, v) (shrink area uniformly by a factor of 6) )du dv: general case x = g y = h (u, v) (u, v)