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SOLUTIONS
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Vector Analysis
Building on Mathematica's powerful capabilities in calculus and algebra, Mathematica 9 introduces support for vector analysis. Vectors in any dimension are supported in common coordinate systems. By exploiting Mathematica's efficient representation of arrays, operations can be performed on scalars, vectors, and higher-rank tensors in a uniform manner.
Featured ExamplesFeatured Examples |
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3D Laplacians
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Automatically Place Streamlines
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Control the Location of Streamlines
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Curve in Spherical Coordinates
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Do High-Resolution Vector Visualization
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Electric Potential and Field of a Dipole
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Normals to Contours
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Plot Field Vectors at Random Positions
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Plot Field Vectors in 3D
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Plot Field Vectors in a Spherical Shell
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Plot Field Vectors on a Regular Grid
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Plot Streamlines on Any Region
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Plot Streamlines with a Density Background
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Plot the Density and Mesh and Overlay Streamlines
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Seed Streamlines on a Regular Grid
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Show the Divergence as a Background Density
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Specify Location and Length of Streamlines
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Use Any Graphic for Line Integral Convolutions
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Use Simulated Lighting for the Background Density
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Vector Laplacian Identity
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Visualize Vector Fields Using Line Integral Convolutions
ReferenceReference
Vector Calculus
Grad — gradient
Div — divergence
Curl — curl in any dimension
Laplacian — Laplacian
Coordinate Systems
CoordinateChartData — properties of coordinate systems
CoordinateTransformData — relationships between coordinate systems
TransformedField — transform a scalar, vector, or tensor field between coordinate systems
CoordinateTransform — re-express a point in a new coordinate system
Visualization
StreamPlot ▪ VectorPlot ▪ ListVectorPlot ▪ VectorPlot3D ▪ ...
