Math Problem Solver

Consider the temperature distribution function 𝑇(𝑥, 𝑦) = 2 − 𝑥

2 − 𝑦

2 on a thin metallic

plate that extends over 0 ≤ 𝑥 ≤ 1, 0 ≤ 𝑦 ≤ 1 in 𝑥𝑦 −plane. Plot graphically the isotherms

(level curves) described by 𝑇(𝑥, 𝑦) = 𝑐 for 𝑐 =

7

4

and 𝑐 = 1 respectively.

2. Determine the gradient vector (∇𝑇)𝑃 at the point 𝑃(1,1) on the plate for the temperature

distribution function 𝑇(𝑥, 𝑦) defined in Problem 1. Represent the vector (∇𝑇)𝑃

graphically, clearly highlighting the angles it makes with the plotted isotherms.