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Unformatted text preview: Checklist for Quiz 2 Andrei Jorza October 15, 2009 The purpose of this checklist is to give you a brief overview of what happened in class since the first quiz and what kinds of things you might expect for the second take-home quiz. 1 Derivatives 1. Make sure you understand what type of object the derivative is. (Matrix, know dimensions.) 2. Basic properties, e.g., D ( f + g ) , D ( fg ) , D (1 /f ). 3. Chain rule D ( f ◦ g ) = ( Df )( g ) Dg with matrix multiplication. Make sure you know this. 4. Directional derivatives using the gradient. The direction need not be of length one. Measures rate of change in that direction. 5. Gradient as direction of fastest increase. 6. Gradient is normal to level sets. 7. Equations of tangent planes to level surfaces (given by normal to gradient). 8. Equations of tangent planes to graphs of functions by exhibiting the function definition as a level set for a function of one more variable. (E.g., for f ( x, y ) = radicalbig x 2 + y 2 with graph z = f...
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This note was uploaded on 11/05/2011 for the course MAT 203 at Princeton.