
Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community for help and clear up your study doubts
Discover the best universities in your country according to Docsity users
Free resources
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
Material Type: Exam; Class: Multivariable Calculus; Subject: mathematics; University: Boston College; Term: Unknown 1989;
Typology: Exams
1 / 1
This page cannot be seen from the preview
Don't miss anything!
Topics we have covered and you should know:
functions of several variables
continuity of f(x,y) or f(x,y,z) at a point or in a region, partial derivatives of a function of two or three variables, higher order derivatives, differentiable vs continuous (example p. 167), finding partial derivative “by definition” (same example), chain rule(s), gradient (compute, interpret: direction of maximum/minimum increase), directional derivatives in direction of unit and non-unit vectors, gradient of f is orthogonal to level curve of f, finding normal line or tangent plane to a surface F(x,y,z)=c at a point on it, finding normal line or tangent plane to graph of f(x,y) at a point, max-min problems, critical points, local max/min, saddle points, second derivative test for f(x,y) at a critical point, global max/min, applied max-min problems, Lagrange multipliers.
multiple integrals
double integral of f(x,y) over a rectangular region or horizontally or vertically simple region, switching the order of integration.