HW-1 EMA 4125- 2011

HW-1 EMA 4125- 2011 - βˆ βˆ’ = ΞΎ Ο€ d e x erf 2 2...

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EMA 4125 Homework 1 Due Wednesday 09/ 08/11 1. Suppose the temperature T at (x, y, z) is given by in which direction is the temperature increasing most rapidly at the point (-1, 2, 3) and what is the rate? ; 273 2 2 + + = xyz y x T 2. Show 2 2 2 2 2 2 2 . z y x + + = = φφ φ where is a scalar function. 3. Solve x e y D D = + ) 2 )( 1 ( 4. For the error function defined by
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Unformatted text preview: ∫ βˆ’ = ΞΎ Ο€ d e x erf 2 2 ) ( , calculate: ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ βŽ› βˆ‚ βˆ‚ t y erf t Ξ± 2 and simplify as much as possible. 5. Show that Dt x e t a C 4 / 2 βˆ’ = is a solution to the partial differential equation . 2 2 x C D t C βˆ‚ βˆ‚ = βˆ‚ βˆ‚...
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This note was uploaded on 11/16/2011 for the course MSE 4125 taught by Professor Bourne during the Fall '11 term at University of Florida.

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