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Unformatted text preview: f ( x,y ) ,g ( x,y )) , G ( x,y ) = v ( f ( x,y ) ,g ( x,y )) are also harmonic conjugates. 8. Functions of matrices Problem 1.31 page 159. 9. Critical points and second derivative test Problem 3.19, page 391. 10. Functions on compact sets. Find the global minimum and global maximum of the function f ( x,y,z ) = x 2 + y 2 + z 22 x4 y6 z over the compact set x 2 + y 2 + z 2 ≤ 15 . 1 11. Lagrange multipliers Problem 3.22, page 392. 12. Inverse function theorem Problem 2.30, page 282. 13. Implicit function theorem Problem 3.11(a), page 390. Also calculate the derivative D 1 g r ( r, 0) . 14. Manifolds Problem 3.1, page 389. 15. Tangent spaces Problem 3.4, page 389....
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 Winter '11
 DragosOprea
 Calculus, Topology, Continuity, Derivative, Matrices, Limits, Continuous function, Inverse function, harmonic conjugates

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