more writing

intro/intro.jl

@@ -1,5 +1,5 @@
 ### A Pluto.jl notebook ###
-# v0.14.7
+# v0.14.8
 
 using Markdown
 using InteractiveUtils
@@ -25,6 +25,12 @@ begin
 	using LaTeXStrings
 end
 
+# ╔═╡ 3228a21e-cab8-4738-bdc5-a6827c764c06
+using Unitful
+
+# ╔═╡ 2df0563d-054a-4ad0-97af-6e06b31a7b1d
+using LinearAlgebra
+
 # ╔═╡ bb461e00-c0aa-11eb-2c7d-1bd1591779c6
 md"""
 # Julia for People That Were Unfortunate Enough to Learn MATLAB 
@@ -265,6 +271,197 @@ f(1, 2, 3)
 ```
 """
 
+# ╔═╡ 916f5f09-1aa3-47a7-9c66-c42513eaccea
+md"""
+## Things Julia Does Well
+
+There are a few ways that Julia really shines that make it perfect for engineering and science. Below are a few examples.
+
+## Symbols
+
+Julia supports a wide variety of unicode symbols in the language that can be accessed with the syntax `\pi{tab}` to get π. This is a great way to make code closer to LaTex or handwritten examples which makes it easier to read or understand. 
+
+* `\theta{tab}` θ 
+* `q\bar{tab}` q̄ 
+* `x\ddot{tab}` ẍ
+
+## List Comprehension
+
+List comprehensions can be thought of single line for loops and can be very handy in a variety of scenarios. The syntax is:
+
+```julia
+# Add 1 to each number in a list of numbers
+[number + 1 for number in numbers]
+```
+
+and would return a new list of numbers.
+
+List comprehensions are especially useful instead of one line for loops, or when you need to create an array to pass into a function. List comprehensions can be nested, and also support `if` in order to filter values making them extremely powerful:
+
+"""
+
+# ╔═╡ 2172de3a-7dba-4cbc-9c04-444db595c328
+[x for x in 1:12 if x % 3 == 0]
+
+# ╔═╡ fd0f5cf6-c90b-4492-9c72-9e707803e736
+md"""
+Since `append!` is usually very slow you can see below that using a list comprehension to create a vector is almost 10x faster. 
+"""
+
+# ╔═╡ a2c7e472-2460-428e-bfec-acf925fad89d
+begin
+	t = []
+	for i in 1:1e6
+	    append!(t,i)
+	end
+	t
+end
+
+# ╔═╡ bce2eecc-dc01-4bf6-9eaa-880fd8a69768
+[i for i in 1:1e6]
+
+# ╔═╡ 9ea4584c-8177-4f69-9739-b2faa93281a8
+md"""
+---
+
+### Matrix Math
+"""
+
+# ╔═╡ a2df1c35-c0b2-45bb-86b7-57e208287392
+md"""
+---
+
+### Units
+
+Julia has an unofficial units library that is incredibly powerful and much easier to use than Matlabs units functionality. It is simply import as `Unitful`
+"""
+
+# ╔═╡ 7b9b11f2-c6d3-4dab-ab30-6e47a3a4bfb3
+md"""
+Making a value with a unit is as simple as using the `u` string macro like the following:
+"""
+
+# ╔═╡ 09bc71cd-7bc0-4d5a-bcf8-984abe273375
+mass = 10u"lb"
+
+# ╔═╡ 744b7e78-0e5b-468d-98b1-a5511f7db311
+gravity = 9.81u"m/s^2"
+
+# ╔═╡ ea6b28d5-f82b-4a21-9ca4-13215c6912b3
+mass + gravity # The library automatically detects if units can be added to eachother.
+
+# ╔═╡ 871664ac-5a93-4718-ae1a-c9f59f6b8374
+weight = mass * gravity # You can mix unit systems
+
+# ╔═╡ dd38ffe4-4efb-4571-b5b2-76b811901387
+md"""
+You'll notice that the weight was left as a gross collection of units instead of automatically converting to `N` like we woule expect. This is usually the case but can easily be fixed by using Julias pipe operator, `|>`.
+
+!!! note "The Pipe Operator"
+	The pipe operator, or `|>` is a great way to chain function calls in Julia. Using `x |> f` is the exact same as using `f(x)` but in many cases can be much clearer. 
+
+```julia
+inv(sum((x->x.^2 .+ 1)(1:10))) # Hard to read
+1:10 |> x -> x.^2 .+ 1 |> sum |> inv # Easier to read
+```
+
+"""
+
+# ╔═╡ ade2979d-155e-4f20-82db-6da141bb8eaa
+weight |> u"N"
+
+# ╔═╡ 8d4de01a-197f-40cb-942f-bfec335e3844
+md"""
+Units can also be stripped to give a normal number again.
+"""
+
+# ╔═╡ 86da848f-1e84-47c8-8a79-373f241b6025
+ustrip(u"N", weight)
+
+# ╔═╡ f43812d2-9f87-489a-9317-e7aa19ffd3bc
+md"""
+---
+
+### Custom Data Types
+"""
+
+# ╔═╡ 44daff45-f608-47e3-ad6e-fca43532f322
+struct Quaternion
+	i::Float64
+	j::Float64
+	k::Float64
+	r::Float64
+	
+	Quaternion(i, j, k, r) = norm([i, j, k, r]) ≈ 1 ? new(i, j, k, r) : error("Magnitude not equal to 1.") 
+	Quaternion(q) = Quaternion(q[1], q[2], q[3], q[4]) 
+	Quaternion() = new(0, 0, 0, 1)
+	
+	Quaternion(yaw, pitch, roll) = Quaternion([0 0 sin(yaw / 2) cos(yaw / 2)]) * Quaternion([0 sin(pitch / 2) 0 cos(pitch / 2)]) * Quaternion([sin(roll / 2) 0 0 cos(roll / 2)])
+	
+	function Quaternion(ē, ϕ)
+		if sum(ē) == 0
+			return Quaternion([0 0 0 cos(ϕ / 2)])
+		end
+		dir = normalize(ē) * sin(ϕ / 2)
+		return Quaternion(dir[1], dir[2], dir[3], cos(ϕ / 2))
+	end
+	
+end
+
+
+# ╔═╡ 37c4a8ef-d503-497a-a63c-3e43d0ebb2a7
+function QuaternionMultiplication(l::Quaternion, r::Quaternion)
+	R = [r.r r.k r.j r.i;
+		 -r.k r.r r.i r.j;
+		 r.j -r.i r.r r.k;
+		 -r.i -r.j -r.k r.r]
+	L = [l.i; l.j; l.k; l.r]
+	return Quaternion(R * L)
+	
+end
+
+# ╔═╡ 0d67e350-a87e-4a07-a01c-d348f3e62599
+Base.:*(l::Quaternion, r::Quaternion) = QuaternionMultiplication(l::Quaternion, r::Quaternion)
+
+# ╔═╡ cbf7d0fb-855b-442b-80c2-cfb6dcabe104
+begin
+	Base.iterate(q::Quaternion, state=1) = state > 4 ? nothing : (collect(q)[state], state + 1)
+	Base.length(q::Quaternion) = 4
+	Base.collect(q::Quaternion) = [q.i q.j q.k q.r]
+	Base.getindex(q::Quaternion, i) = collect(q)[i]
+end
+
+# ╔═╡ 84e6fb12-be8c-4e00-bf9c-d45748347def
+begin
+	LinearAlgebra.norm(q::Quaternion) = norm(collect(q))
+	LinearAlgebra.normalize(q::Quaternion) = collect(q) / norm(q)
+end
+
+# ╔═╡ 2ba455ff-70f5-47d5-9fe8-bf4ebee9386a
+q1 = Quaternion(1,0,0,0)
+
+# ╔═╡ 6895bcb2-9a11-4f0a-b1c2-6640f6fb509c
+q2 = Quaternion([1 2 3], π)
+
+# ╔═╡ fafa0a8d-5ae5-49e9-8d11-4abb5748431e
+q1*q2
+
+# ╔═╡ 8924673f-e99c-44b3-be6d-2abf0b2f5e23
+md"""
+---
+
+### Tabular Data
+"""
+
+# ╔═╡ fbc06121-d53a-4a64-9497-63d7f3583fbb
+md"""
+## Things Julia Does Poorly
+
+Performance
+Libraries
+Still young and breaking things
+"""
+
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@@ -310,3 +507,32 @@ f(1, 2, 3)
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