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Assignment Problems Notice
Please do not email me to get solutions and/or answers to these problems. I will not give them out under any circumstances nor will I respond to any requests to do so. The intent of these problems is for instructors to use them for assignments and having solutions/answers easily available defeats that purpose.
If you are looking for some problems with solutions you can find some by clicking on the "Practice Problems" link above.
If you are looking for some problems with solutions you can find some by clicking on the "Practice Problems" link above.
Section 16.1 : Vector Fields
- Sketch the vector field for \(\vec F = - {y^2}\,\vec i + x\,\vec j\).
- Sketch the vector field for \(\vec F = \,\vec i + xy\,\vec j\).
- Sketch the vector field for \(\vec F = \,4y\,\vec i + \left( {x + 2} \right)\vec j\).
- Compute the gradient vector field for \(f\left( {x,y} \right) = 6{x^2} - 9y + {x^3}\,\sqrt y \).
- Compute the gradient vector field for \(f\left( {x,y} \right) = \sin \left( {2x} \right)\cos \left( {3x} \right)\).
- Compute the gradient vector field for \(f\left( {x,y,z} \right) = z\,{{\bf{e}}^{x\,y}} + {y^3}\tan \left( {4x} \right)\).
- Compute the gradient vector field for \(f\left( {x,y,z} \right) = x\,{y^2}{z^3} + 4x{{\bf{e}}^{{y^{\,2}}}} - \ln \left( {x - z} \right)\).