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Homework2 - 1 Mathematics 1c: Homework Set 2 Due: Monday,...

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1 Mathematics 1c: Homework Set 2 Due: Monday, April 12th by 10am. 1. (10 Points) Section 2.5, Exercise 8 Suppose that a function is given in terms of rectangular coordinates by u = f ( x,y,z ) . If x = ρ cos θ sin φ,y = ρ sin θ sin φ,z = ρ cos φ, express the partial derivatives ∂u/∂ρ,∂u/∂θ, and ∂u/∂φ in terms of ∂u/∂x,∂u/∂y , and ∂u/∂z . 2. (10 Points) Section 2.5, Exercise 12 Suppose that the temperature at the point ( x,y,z ) in space is T ( x,y,z ) = x 2 + y 2 + z 2 . Let a particle follow the right circular helix σ ( t ) = (cos t, sin t,t ) and let T ( t ) be its temperature at time t . (a) What is T 0 ( t ) ? (b) Find an approximate value for the temperature at t = ( π/ 2) + 0 . 01 . 3. (10 Points) Section 2.6, Exercise 3(c) Compute the directional derivative of the function f ( x,y,z ) = xyz at the point ( x 0 ,y 0 ,z 0 ) = (1 , 0 , 1) in the direction of the unit vector parallel to the vector d = (1 , 0 , - 1) . 4. (20 Points)
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This note was uploaded on 07/19/2010 for the course MA 1C taught by Professor Ramakrishnan during the Spring '08 term at Caltech.

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Homework2 - 1 Mathematics 1c: Homework Set 2 Due: Monday,...

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