Math 265: 14.1
Supplemental Instruction
IowaStateUniversity
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Trevor
Math 265
Dr. Castillo-Gil
04/08/14
1) Sketch a sample of vectors for the given vector field F
a. 𝐹 (𝑥, 𝑦) = 3𝑥𝑖 + 𝑦𝑗
2) Find ∇f
a. 𝑓(𝑥, 𝑦, 𝑧) = sin(𝑥𝑦𝑧)
b. 𝑓(𝑥, 𝑦, 𝑧) = 𝑦 2 𝑒 −2𝑧
3) Find div F and curl F
a. 𝐹 (𝑥, 𝑦, 𝑧) = 𝑥 2 𝑖 + 𝑦 2 𝑗 + 𝑧 2 𝑘
b. 𝐹 (𝑥, 𝑦, 𝑧) = cos 𝑥 𝑖 + sin 𝑦 𝑗 + 3𝑘
c. 𝐹 (𝑥, 𝑦, 𝑧) = (𝑦 + 𝑧)𝑖 + (𝑥 + 𝑧)𝑗 + (𝑥 + 𝑦)𝑘
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