edits; parameterized surface
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@@ -23,7 +23,6 @@ The `Julia` packages loaded below are all loaded when the `CalculusWithJulia` pa
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A `Julia` package is loaded with the `using` command:
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```{julia}
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using LinearAlgebra
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```
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@@ -455,6 +454,7 @@ This should be contrasted to the case when both `xs` and `ys` are (column) vecto
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```{julia}
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#| error: true
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g.(xs, [4,5])
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```
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@@ -710,10 +710,7 @@ implicit_plot(f)
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### Plotting a parameterized surface $f:R^2 \rightarrow R^3$
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The `pyplot` (and `plotly`) backends allow plotting of parameterized surfaces.
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The low-level `surface(xs,ys,zs)` is used, and can be specified directly as follows:
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The `pyplot` (and `plotly`) backends allow plotting of parameterized surfaces. The low-level `surface(xs,ys,zs)` is used, as illustrated here.
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```{julia}
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@@ -723,7 +720,7 @@ Y(theta, phi) = sin(phi)*sin(theta)
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Z(theta, phi) = cos(phi)
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thetas = range(0, pi/4, length=20)
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phis = range(0, pi, length=20)
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surface(X.(thetas, phis'), Y.(thetas, phis'), Z.(thetas, phis'))
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# surface(X.(thetas, phis'), Y.(thetas, phis'), Z.(thetas, phis'))
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```
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### Plotting a vector field $F:R^2 \rightarrow R^2$.
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