The temperature of points in space given by a scalar field is T(x, y, z) = x² + y² − z a. Find the temperature, T, at the point (-1, 0, 5). b. Evaluate the directional derivative of the scalar function T(x, y, z) at the point (1, 3,-1) in the direction of (2, 1,2). c. An isothermal is a surface upon which the temperature of the surface is constant i. find the equation of the isothermal (i.e. the surface) through the point (1,1,2) by making z the subject ii. in Matlab plot the equation of the isothermal contours in the x - y plane s.t. -5 ≤ x ≤ 5 and −5 ≤ y ≤ 5 (include screenshot)
The temperature of points in space given by a scalar field is T(x, y, z) = x² + y² − z a. Find the temperature, T, at the point (-1, 0, 5). b. Evaluate the directional derivative of the scalar function T(x, y, z) at the point (1, 3,-1) in the direction of (2, 1,2). c. An isothermal is a surface upon which the temperature of the surface is constant i. find the equation of the isothermal (i.e. the surface) through the point (1,1,2) by making z the subject ii. in Matlab plot the equation of the isothermal contours in the x - y plane s.t. -5 ≤ x ≤ 5 and −5 ≤ y ≤ 5 (include screenshot)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:3. The temperature of points in space given by a scalar field is
T(x, y, z) = x² + y² − z
a. Find the temperature, T, at the point (-1, 0, 5).
b. Evaluate the directional derivative of the scalar function T(x, y, z) at the point (1,
3, -1) in the direction of (2, 1,2).
c. An isothermal is a surface upon which the temperature of the surface is constant
i. find the equation of the isothermal (i.e. the surface) through the point (1,1,2)
by making z the subject
ii.
in Matlab plot the equation of the isothermal contours in the x - y plane s.t.
-5 ≤ x ≤ 5 and -5 ≤ y ≤ 5 (include screenshot)
d. A mosquito is located at the point (1,1,2), and desires to fly in such a direction that
it will get cool as soon as possible. In what direction should it move and why?
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