MATH 2043 Lecture Notes - Lecture 1: The Contours, Talking Lifestyle 1278
Document Summary
Math 2043, fall 2017: match the contours to the graphs (section 14. 1): The rightmost picture shows the intersection of the graph of the function with several horizontal planes (z = constant). Xy plane of these intersections: for the given function, compute. Y (section 14. 3): f (x, y) = x2 + 2xy, f (x, y) = x3. 3xy2: f (x, y) = x y cos(2xy), f (x, y) = xexy, for the given function, compute. Y (x, y): let h be the function in problem 6. Y2 : a function h of the variables (x, y) is called harmonic if it satis es. Y2 = 0 (in the case of a function of more than two variables we keep adding second order derivatives). Determine which of the following functions is harmonic. 6x2y2 + y4: x3, x4, sin(xyz, xex cos(y) yex sin(y, yex cos(y) + xex sin(y, 3xz2 + 3xy2, x2 + y2 + z2 + 2xy + 2xz + 2yz.
