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Unformatted text preview: 19.84 b) 12.32 c) 16.16 d) 11.36 e) 11.68 15.9  Reconstructing a Function from its Gradient The gradient of a function ( , ) f x y is ( , ) f x y = So if we have a (gradient) vector in the form ( , ) P x y i + ( , ) Q x y j We can begin reconstruct the function by setting P = / f x and Q = / f y Now when integrating / f x with respect to x , remember that y is a constant! Example: xy 2 i + x 2 y j Note: Sometimes the given vector could not be the gradient of a function. More examples: Popper009 5. Determine whether or not the vector function is the gradient f ( x , y ) of a function everywhere defined. If so, find all the functions with that gradient. a) b) c) d) e) 6. D...
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This note was uploaded on 07/20/2010 for the course MATH 18427 taught by Professor Etgen during the Fall '10 term at University of Houston.
 Fall '10
 Etgen

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