Chapter 9: Vector Calculus
Section 9.3: Differential Operators
Example 9.3.8
Compute the curl of the Cartesian vector field F=x y i−y z j−x z k.
Solution
Mathematical Solution
Using the notation ∂x to represent the partial-differentiation operator ∂∂x, etc., the curl of F is given by
∇×F=ijk∂x∂y∂zx y−y z−x z = ∂y(−x z)−∂z(−y z)−(∂x(−x z)−∂z(x y))∂x(−y z)−∂y(x y) = yz−x
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
Define the vector field F
Enter a free vector with the components of F. Context Panel: Evaluate and Display Inline
Context Panel: Student Vector Calculus≻Conversions≻To Vector Field
Context Panel: Assign to a Name≻F
x y,−y z,−x z = →to Vector Field →assign to a nameF
Obtain the curl of F
Common Symbols palette: Del and cross-product operators.
Context Panel: Evaluate and Display Inline
∇×F =
Alternate approach to the curl of F
Write the name F. Context Panel: Evaluate and Display Inline
Context Panel: Student Vector Calculus≻Curl
F = →curl
Maple Solution - Coded
Load the Student VectorCalculus package and execute the BasisFormat command.
withStudent:-VectorCalculus:BasisFormatfalse:
Invoke the VectorField command.
F≔VectorFieldx y,−y z,−x z:
Apply the Curl command.
CurlF =
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