MAT244H1 Study Guide - Midterm Guide: Saddle Point, Phase Portrait, Lagrange Multiplier
11
MAT244H1 Full Course Notes
Verified Note
11 documents
Document Summary
Number of test pages: (including this cover sheet) Page 2 of 7: (6 points) calculus of variations. Find the extremal of the functional y(0) = 1, y(1) = 1. (cid:90) 1. Page 3 of 7: (10 points) lagrange multipliers. I(y) = such that y(0) = 0, y( ) = 1, and (cid:90) (cid:90) . Page 4 of 7: (5 points) matrix exponentials. Page 5 of 7: (7 points) phase portraits. Find the general solution of (cid:18) 1 (cid:19) Page 6 of 7: (10 points) phase portraits. Find the general solution of (cid:18) 1 4 (cid:19) State whether the origin is a node, saddle point, spiral or center. And draw a phase portrait for the system. If the origin is a spiral or center, you don"t need to nd the axes but do nd the direction of rotation (i. e. clockwise or counterclockwise).
