ZTest_Belinda's copy of Harry's copy of Find the curl of a vector field

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Belinda Schwerin

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Belinda Schwerin 7 years ago

Created this as a copy of Harry's copy of Find the curl of a vector field.

Name	Status	Author	Last Modified
Find the curl of a vector field	Has some problems	Newcastle University Mathematics and Statistics	20/11/2019 14:51
Harry's copy of Find the curl of a vector field	draft	Harry Flynn	14/03/2018 14:48
ZTest_Belinda's copy of Harry's copy of Find the curl of a vector field	draft	Belinda Schwerin	03/03/2019 03:20

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Question statement

Find the curl $\boldsymbol{\nabla}\times\boldsymbol{u}$ of the vector field $\boldsymbol{u}=(\simplify{{a1}*x^{p1}*y^{p2}*z^{p3}})i + (\simplify{{b1}*x^{p4}*y^{p5}*z^{p6}}) j + (\simplify{{c1}*x^{p7}*y^{p8}*z^{p9}}) k$ .

Note on entering solution: For example: input $xyz$ as $x$ * $y$ * $z$

Give any introductory information the student needs.

			Name	Type	Generated Value

p2	integer	4
p3	integer	2
p1	integer	0
p6	integer	3
p7	integer	4
p4	integer	0
p5	integer	2
p8	integer	0
p9	integer	4
a1	number	-6
b1	number	-7
c1	number	-4

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Generated value: `integer`

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Parts

Gap-fill

Gap-fill

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$\boldsymbol{\nabla}\times\boldsymbol{u}=$ Gap 0. $i$ + Gap 1. $j$ + Gap 2. $k$

Advice

The curl of a vector field $\boldsymbol{u}=\pmatrix{u_x,u_y,u_z}$ is given by

$\boldsymbol{\nabla}\times\boldsymbol{u}=\pmatrix{\frac{\partial u_z}{\partial y}-\frac{\partial u_y}{\partial z},\frac{\partial u_x}{\partial z}-\frac{\partial u_z}{\partial x},\frac{\partial u_y}{\partial x}-\frac{\partial u_x}{\partial y}}.$

Hence, in this example, after straight forward partial differentiation

$\boldsymbol{\nabla}\times\boldsymbol{u}=\pmatrix{\simplify{{c1*p8}*x^{p7}*y^{p8-1}*z^{p9}-{b1*p6}*x^{p4}*y^{p5}*z^{p6-1}},\simplify{{a1*p3}*x^{p1}*y^{p2}*z^{p3-1}-{c1*p7}*x^{p7-1}*y^{p8}*z^{p9}},\simplify{{b1*p4}*x^{p4-1}*y^{p5}*z^{p6}-{a1*p2}*x^{p1}*y^{p2-1}*z^{p3}}}.$

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ZTest_Belinda's copy of Harry's copy of Find the curl of a vector field

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Taxonomy: mathcentre

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History

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Checkpoint description

Belinda Schwerin 7 years ago

Note on entering solution: For example: input $xyz$ as $x$ * $y$ * $z$

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Loading...

Error

ZTest_Belinda's copy of Harry's copy of Find the curl of a vector field

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Belinda Schwerin 7 years ago

Note on entering solution: For example: input xyzxyz as xx*yy*zz

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Note on entering solution: For example: input $xyz$ as $x$ * $y$ * $z$

Generated value: `integer`