Chapter 9: Vector Calculus
Section 9.3: Differential Operators
Example 9.3.2
If r and θ are polar coordinates, obtain ∇f for fr,θ=lnr tanθ.
Solution
Mathematical Solution
In polar coordinates, ∇f=frfθr. Applying this to the given f results in 1rtan(θ)ln(r)sec2(θ).
Note that Maple differentiates tanx to 1+tan2x on the grounds that having a new function name (i.e., sec) appear is somehow less simple than sticking with the name "tan".
Maple Solution - Interactive
Initialize
Tools≻Load Package: Student Vector Calculus
Loading Student:-VectorCalculus
Tools≻Tasks≻Browse: Calculus - Vector≻Vector Algebra and Settings≻Display Format for Vectors
Press the Access Settings button and select "Display as Column Vector"
Display Format for Vectors
Obtain the gradient
Control-drag f.
Context Panel: Student Vector Calculus≻Differentiate≻Gradient (Complete the resulting dialog as shown below, and click OK.)
lnrtanθ→gradient
Maple Solution - Coded
Load the Student VectorCalculus package and execute the BasisFormat command.
withStudent:-VectorCalculus:BasisFormatfalse:
Obtain the gradient of f
Apply the Gradient command, including the name of the coordinate system.
Gradientlnrtanθ,polar
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