MA 3065 Study Guide - Final Guide: Leibniz Integral Rule, Unit Disk, Unit Square

• School: Minneapolis College of Art and Design
• Department: Filmmaking-Sound
• Course: MA 3065
• Professor: p

Document Summary

Math 5588 homework 9 (due thursday april 6: prove the leibniz integral rule d dx z b(x) a(x) f (x, t) dt! = f (x, b(x))b (x) f (x, a(x))a (x) +z b(x) a(x) [hint: for a, b, x r de ne and apply the multivariate chain rule. F (a, b, x) =z b a f (x, t) dt, d dx. Fix x0 rn, t0 > 0, and de ne the backwards wave cone. K(x0, t0) :=n(x, t) : 0 t t0 and |x x0| t0 to. Prove that if f g 0 in b(x0, t0) {t = 0}, then u 0 in the cone k(x0, t0). Mimic the proof from class, in particular use the same energy. : repeat problem 3 for the nonlinear wave equation utt u + u3 = 0.