MAT237Y1 Study Guide - Final Guide: Hessian Matrix, Multivariable Calculus, Saddle Point
Document Summary
This set of notes discusses material covered in weeks 7 - 9 of the lectures. (that is, most of the lectures will nish this material during the week of november 13. ) 1. 1. topics: critical points (folland"s advanced calclulus, section 2. 8), extreme value problems (folland"s advanced calclulus, section 2. 9). Important points include point: de nitions of critical point, hessian matrix, local minimum, local maximum, saddle, theorems 2. 81 and 2. 82 in folland"s advanced calculus. For this material, we are sticking pretty close to the discussion in folland"s book. Here h(a) denotes the hessian matrix of f , evaluated at the point a. all eigenvalues of h(a) 0. 2: if f is c 2, then if if (cid:26) (cid:26) F (a) = 0 and all eigenvalues of h(a) < 0, F (a) = 0 and all eigenvalues of h(a) > 0, then a is a local max for f then a is a local min for f.
