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
parent 93c993206a
commit 7b37ca828c
879 changed files with 793311 additions and 2678 deletions
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CwJ/precalc/vectors.jmd
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@@ -8,7 +8,8 @@ using Plots
using Measures
using LaTeXStrings
fig_size = (400, 300)
#fig_size = (400, 300)
fig_size = (800, 600)
const frontmatter = (
title = "Vectors",
@@ -463,23 +464,13 @@ component. However, the special keyword `end` will do so as well, when
put into the context of indexing. So `v[end]` is more idiomatic. (Similarly, there is a `begin` keyword that is useful when the vector is not ``1``-based, as is typical but not mandatory.)
```julia; echo=false;
note("""
There is [much more](http://julia.readthedocs.org/en/latest/manual/arrays/#indexing)
to indexing than just indexing by a single integer value. For example, the following can be used for indexing:
* a scalar integer (as seen)
* a range
* a vector of integers
* a boolean vector
Some add-on packages extend this further.
""",
title="More on indexing", label="More on indexing")
```
!!! note "More on indexing"
There is [much more](http://julia.readthedocs.org/en/latest/manual/arrays/#indexing) to indexing than just indexing by a single integer value. For example, the following can be used for indexing:
* a scalar integer (as seen)
* a range
* a vector of integers
* a boolean vector
Some add-on packages extend this further.
### Assignment and indexing
@@ -668,10 +659,9 @@ performant `abs2` function which, in general, efficiently finds $|x|^2$
for various number types. The `.-` uses broadcasting to subtract a scalar (`mean(xs)`) from a vector (`xs`). Without the `.`, this would error.
```julia; echo=false;
note("""The `map` function is very much related to broadcasting and similarly named functions are found in many different programming languages. (The "dot" broadcast is mostly limited to `Julia` and mirrors on a similar usage of a dot in `MATLAB`.) For those familiar with other programming languages, using `map` may seem more natural. Its syntax is `map(f, xs)`.
""")
```
!!! note
The `map` function is very much related to broadcasting and similarly named functions are found in many different programming languages. (The "dot" broadcast is mostly limited to `Julia` and mirrors on a similar usage of a dot in `MATLAB`.) For those familiar with other programming languages, using `map` may seem more natural. Its syntax is `map(f, xs)`.
### Comprehensions
@@ -763,15 +753,9 @@ In the sequel, we will typically use broadcasting for this task using two
steps: one to define a function the second to broadcast it.
```julia; echo=false;
note(L"""
!!! note
The style generally employed here is to use plural variable names for a collection of values, such as the vector of $y$ values and singular names when a single value is being referred to, leading to expressions like "`x in xs`".
The style generally employed here is to use plural variable names for a collection
of values, such as the vector of $y$ values and singular names when a
single value is being referred to, leading to expressions like "`x in xs`".
""")
```
## Other container types
@@ -805,8 +789,8 @@ q"v = {4, 3}",
q"v = '4, 3'",
q"v = (4,3)",
q"v = <4,3>"]
ans = 1
radioq(choices, ans)
answ = 1
radioq(choices, answ)
```
###### Question
@@ -815,8 +799,8 @@ Which command will create the vector with components "4,3,2,1"?
```julia; hold=true; echo=false;
choices = [q"v = [4,3,2,1]", q"v = (4,3,2,1)", q"v = {4,3,2,1}", q"v = '4, 3, 2, 1'", q"v = <4,3,2,1>"]
ans = 1
radioq(choices, ans)
answ = 1
radioq(choices, answ)
```
@@ -840,8 +824,8 @@ Which of the following is the unit vector in the direction of $\vec{v} = \langle
```julia; hold=true; echo=false;
choices = [q"[3, 4]", q"[0.6, 0.8]", q"[1.0, 1.33333]", q"[1, 1]"]
ans = 2
radioq(choices, ans)
answ = 2
radioq(choices, answ)
```
@@ -851,8 +835,8 @@ What vector is in the same direction as $\vec{v} = \langle 3,~ 4 \rangle$ but is
```julia; hold=true; echo=false;
choices = [q"[3, 4]", q"[30, 40]", q"[9.48683, 12.6491 ]", q"[10, 10]"]
ans = 2
radioq(choices, ans)
answ = 2
radioq(choices, answ)
```
###### Question
@@ -861,8 +845,8 @@ If $\vec{v} = \langle 3,~ 4 \rangle$ and $\vec{w} = \langle 1,~ 2 \rangle$ find
```julia; hold=true; echo=false;
choices = [q"[4, 6]", q"[6, 8]", q"[11, 18]", q"[5, 10]"]
ans = 3
radioq(choices, ans)
answ = 3
radioq(choices, answ)
```
###### Question
@@ -939,24 +923,24 @@ Express vector **c** in terms of **a** and **b**:
```julia; hold=true; echo=false;
choices = ["3a", "3b", "a + b", "a - b", "b-a"]
ans = 1
radioq(choices, ans)
answ = 1
radioq(choices, answ)
```
Express vector **d** in terms of **a** and **b**:
```julia; hold=true; echo=false;
choices = ["3a", "3b", "a + b", "a - b", "b-a"]
ans = 3
radioq(choices, ans)
answ = 3
radioq(choices, answ)
```
Express vector **e** in terms of **a** and **b**:
```julia; hold=true; echo=false;
choices = ["3a", "3b", "a + b", "a - b", "b-a"]
ans = 4
radioq(choices, ans)
answ = 4
radioq(choices, answ)
```
@@ -966,8 +950,8 @@ If `xs=[1, 2, 3, 4]` and `f(x) = x^2` which of these will not produce the vector
```julia; hold=true; echo=false;
choices = [q"f.(xs)", q"map(f, xs)", q"[f(x) for x in xs]", "All three of them work"]
ans = 4
radioq(choices, ans, keep_order=true)
answ = 4
radioq(choices, answ, keep_order=true)
```
###### Question
@@ -982,8 +966,8 @@ What construct will give the function values of $f$ at the zeros of $g$?
```julia;hold=true; echo=false;
choices = [q"sin(zs)", q"sin.(zs)", q"sin(.zs)", q".sin(zs)"]
ans = 2
radioq(choices, ans, keep_order=true)
answ = 2
radioq(choices, answ, keep_order=true)
```
###### Question
@@ -997,6 +981,6 @@ q"sqrt.(zs)",
q"zs^(1/2)",
q"zs^(1./2)"
]
ans = 2
radioq(choices, ans, keep_order=true)
answ = 2
radioq(choices, answ, keep_order=true)
```