daviddoji/CalculusWithJuliaNotes.jl
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use quarto, not Pluto to render pages

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jverzani
2022-07-24 16:38:24 -04:00
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CwJ/precalc/plotting.jmd
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@@ -75,10 +75,8 @@ using Plots
```
```julia;echo=false
note("""
`Plots` is a frontend for one of several backends. `Plots` comes with a backend for web-based graphics (call `plotly()` to specify that); a backend for static graphs (call `gr()` for that). If the `PyPlot` package is installed, calling `pyplot()` will set that as a backend. For terminal usage, if the `UnicodePlots` package is installed, calling `unicodeplots()` will enable that usage. There are still other backends.""")
```
!!! note
`Plots` is a frontend for one of several backends. `Plots` comes with a backend for web-based graphics (call `plotly()` to specify that); a backend for static graphs (call `gr()` for that). If the `PyPlot` package is installed, calling `pyplot()` will set that as a backend. For terminal usage, if the `UnicodePlots` package is installed, calling `unicodeplots()` will enable that usage. There are still other backends.
The `plotly` backend is part of the `Plots` package, as is `gr`. Other backends require installation, such as `PyPlot` and `PlotlyJS`.
We use `gr` in these notes, for the most part. (The `plotly` backend is also quite nice for interactive usage, but doesn't work as well with the static HTML pages.)
@@ -112,11 +110,9 @@ Plotting a function is then this simple: `plot(f, xmin, xmax)`.
> style, where the details to execute the action are only exposed as
> needed.
```julia; echo=false
note("""
The time to first plot can feel sluggish, but subsequent plots will be speedy. See the technical note at the end of this section for an explanation.
""")
```
!!! note
The time to first plot can feel sluggish, but subsequent plots will be speedy. See the technical note at the end of this section for an explanation.
Let's see some other graphs.
@@ -165,16 +161,12 @@ plot(x -> mxplusb(x, (m=-1, b=1)), -1, 2)
```
```julia;echo=false
note("""
!!! note
The function object in the general pattern `action(function, args...)`
is commonly specified in one of three ways: by a name, as with `f`; as an
anonymous function; or as the return value of some other action
through composition.
The function object in the general pattern `action(function, args...)`
is commonly specified in one of three ways: by a name, as with `f`; as an
anonymous function; or as the return value of some other action
through composition.
""")
```
Anonymous functions are also created by `Julia's` `do` notation, which is useful when the first argument to function (like `plot`) accepts a function:
@@ -186,11 +178,9 @@ end
The `do` notation can be a bit confusing to read when unfamiliar, though its convenience makes it appealing.
```julia; echo=false
note("""
Some types we will encounter, such as the one for symbolic values or the special polynomial one, have their own `plot` recipes that allow them to be plotted similarly as above, even though they are not functions.
""")
```
!!! note
Some types we will encounter, such as the one for symbolic values or the special polynomial one, have their own `plot` recipes that allow them to be plotted similarly as above, even though they are not functions.
----
@@ -248,22 +238,6 @@ pts_needed(x -> 10x, 0, 10), pts_needed(x -> sin(10x), 0, 10)
(In fact, the `21` is the minimum number of points used for any function; a linear function only needs two.)
##### Example
This demo (which is interactive within a `Pluto` session) shows more points are needed as the function becomes more "curvy." There are the minimum of ``21`` for a straight line, ``37`` for a half period, ``45`` for a full period, etc.
```julia; echo=false
md"""
n = $(@bind 𝐧 Slider(0:20, default=1))
"""
```
```julia; hold=true;
xs,ys = unzip(x -> sin(𝐧*x*pi), 0, 1)
plot(xs, ys, title="n=$(length(xs))")
scatter!(xs, ys)
```
----
For instances where a *specific* set of ``x`` values is desired to be
@@ -495,16 +469,12 @@ The ``3`` main functions used in these notes for adding layers are:
* `annotate!((x,y, label))` to add a label at $(x,y)$
```julia;echo=false
alert("""
!!! warning
Julia has a convention to use functions named with a `!` suffix to
indicate that they mutate some object. In this case, the object is the
current graph, though it is implicit. Both `plot!`, `scatter!`, and
`annotate!` (others too) do this by adding a layer.
Julia has a convention to use functions named with a `!` suffix to
indicate that they mutate some object. In this case, the object is the
current graph, though it is implicit. Both `plot!`, `scatter!`, and
`annotate!` (others too) do this by adding a layer.
""")
```
## Additional arguments
@@ -709,8 +679,8 @@ choices = ["`(-Inf, -1)` and `(0,1)`",
"`(-Inf, -0.577)` and `(0.577, Inf)`",
"`(-1, 0)` and `(1, Inf)`"
];
ans=3;
radioq(choices, ans)
answ=3;
radioq(choices, answ)
```
@@ -737,8 +707,8 @@ choices = ["`(-Inf, -3)` and `(0, 1)`",
"`(-3, 0)` and `(1, Inf)`",
"`(-Inf, -4.1)` and `(1.455, Inf)`"
];
ans=2;
radioq(choices, ans)
answ=2;
radioq(choices, answ)
```
###### Question
@@ -787,15 +757,15 @@ choices = [
"`f(x) = x <= 4 ? 35.0 : 35.0 + 10.0 * (x-4)`",
"`f(x) = x <= 10 ? 35.0 : 35.0 + 4.0 * (x-10)`"
]
ans = 3
radioq(choices, ans)
answ = 3
radioq(choices, answ)
```
Make a plot of the model. Graphically estimate how many bags of trash will cost 55 dollars.
```julia; hold=true;echo=false
ans = 15
numericq(ans, .5)
answ = 15
numericq(answ, .5)
```
###### Question
@@ -829,8 +799,8 @@ What is seen?
choices = [L"It oscillates wildly, as the period is $T=2\pi/(500 \pi)$ so there are 250 oscillations.",
"It should oscillate evenly, but instead doesn't oscillate very much near 0 and 1",
L"Oddly, it looks exactly like the graph of $f(x) = \sin(2\pi x)$."]
ans = 3
radioq(choices, ans)
answ = 3
radioq(choices, answ)
```
The algorithm to plot a function works to avoid aliasing issues. Does the graph generated by `plot(f, 0, 1)` look the same, as the one above?
@@ -840,8 +810,8 @@ choices = ["Yes",
"No, but is still looks pretty bad, as fitting 250 periods into a too small number of pixels is a problem.",
"No, the graph shows clearly all 250 periods."
]
ans = 2
radioq(choices, ans)
answ = 2
radioq(choices, answ)
```
@@ -865,8 +835,8 @@ choices = [
"An ellipse",
"A straight line"
]
ans = 2
radioq(choices, ans)
answ = 2
radioq(choices, answ)
```
@@ -898,8 +868,8 @@ choices = [
"A straight line",
"None of the above"
]
ans = 1
radioq(choices, ans, keep_order=true)
answ = 1
radioq(choices, answ, keep_order=true)
```
@@ -917,8 +887,8 @@ choices = [
"A straight line",
"None of the above"
]
ans = 3
radioq(choices, ans,keep_order=true)
answ = 3
radioq(choices, answ,keep_order=true)
```
@@ -936,8 +906,8 @@ choices = [
"A straight line",
"None of the above"
]
ans = 2
radioq(choices, ans, keep_order=true)
answ = 2
radioq(choices, answ, keep_order=true)
```
@@ -956,8 +926,8 @@ choices = [
"A straight line",
"None of the above"
]
ans = 5
radioq(choices, ans, keep_order=true)
answ = 5
radioq(choices, answ, keep_order=true)
```
----