align fix; theorem style; condition number

quarto/precalc/plotting.qmd

@@ -30,7 +30,7 @@ A scalar, univariate function, such as $f(x) = 1 - x^2/2$, can be thought of in
 
   * It can be represented through a rule of what it does to $x$, as above. This is useful for computing numeric values.
   * it can be interpreted verbally, as in *square* $x$, take half then *subtract* from one. This can give clarity to what the function does.
-  * It can be thought of in terms of its properties: a polynomial, continuous, $U$-shaped, an approximation for $\cos(x)$ near $0$, $\dots$
+  * It can be thought of in terms of its properties: a polynomial, continuous, upside down $U$-shaped, an approximation for $\cos(x)$ near $0$, $\dots$
   * it can be visualized graphically. This is useful for seeing the qualitative behavior of a function.
 
 
@@ -243,15 +243,15 @@ For instances where a *specific* set of $x$ values is desired to be used, the `r
 
 
 ```{julia}
-𝒙s = range(0, 2pi, length=10)
-𝒚s = sin.(𝒙s)
+xs = range(0, 2pi, length=10)
+ys = sin.(xs)
 ```
 
 Finally, to plot the set of points and connect with lines, the $x$ and $y$ values are passed along as vectors:
 
 
 ```{julia}
-plot(𝒙s, 𝒚s)
+plot(xs, ys)
 ```
 
 This plots the points as pairs and then connects them in order using straight lines. Basically, it creates a dot-to-dot graph. The above graph looks primitive, as it doesn't utilize enough points.
@@ -490,7 +490,7 @@ For plotting points with `scatter`, or `scatter!` the markers can be adjusted vi
   * `scatter(..., marker=:square)`: change the marker (uses a symbol, not a string to specify)
 
 
-Of course, zero, one, or more of these can be used on any given call to `plot`, `plot!`, `scatter` or `scatter!`.
+Of course, zero, one, or more of these can be used on any given call to `plot`, `plot!`, `scatter`, or `scatter!`.
 
 #### Example: Bresenham's algorithm
 
@@ -575,9 +575,9 @@ The most "famous" parametric graph is one that is likely already familiar, as it
 
 
 ```{julia}
-𝒇(x) = cos(x); 𝒈(x) = sin(x)
-𝒕s = range(0, 2pi, length=100)
-plot(𝒇.(𝒕s), 𝒈.(𝒕s), aspect_ratio=:equal)   # make equal axes
+f(x) = cos(x); g(x) = sin(x)
+ts = range(0, 2pi, length=100)
+plot(f.(ts), g.(ts), aspect_ratio=:equal)   # make equal axes
 ```
 
 Any point $(a,b)$ on this graph is represented by $(\cos(t), \sin(t))$ for some value of $t$, and in fact multiple values of $t$, since $t + 2k\pi$ will produce the same $(a,b)$ value as $t$ will.
@@ -599,8 +599,8 @@ DataFrame(θ=θs, x=cos.(θs), y=sin.(θs))
 ```{julia}
 #| hold: true
 θs =[0, pi/6, pi/4, pi/3, pi/2, 2pi/3, 3pi/4, 5pi/6, pi]
-plot(𝒇.(θs), 𝒈.(θs), legend=false, aspect_ratio=:equal)
-scatter!(𝒇.(θs), 𝒈.(θs))
+plot(f.(θs), g.(θs), legend=false, aspect_ratio=:equal)
+scatter!(f.(θs), g.(θs))
 ```
 
 ---
@@ -610,7 +610,7 @@ As with the plot of a univariate function, there is a convenience interface for
 
 
 ```{julia}
-plot(𝒇, 𝒈, 0, 2pi, aspect_ratio=:equal)
+plot(f, g, 0, 2pi, aspect_ratio=:equal)
 ```
 
 ##### Example
@@ -876,6 +876,24 @@ answ = 2
 radioq(choices, answ)
 ```
 
+###### Question
+
+The `plot` function can have its data specified through a vector of points. Such data can be generated through a comprehension. Does this command plot the given expression avoiding the need to define a function?
+
+```{julia}
+#| eval: false
+plot([(x, sin(x^2)-sin(x)) for x in range(-pi, pi, 100)])
+```
+
+```{julia}
+#| echo: false
+explanation = """
+Yes, it does. Whether this is more convenient than say `plot(x -> sin(x^2) - sin(x), -pi, pi)` is a different question.
+"""
+buttonq(["Yes", "No"], 1; explanation)
+```
+
+
 ###### Question