Day 1 done

Day_1/Day_1.jl

@@ -4,6 +4,20 @@
 using Markdown
 using InteractiveUtils
 
+# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
+macro bind(def, element)
+    quote
+        local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end
+        local el = $(esc(element))
+        global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el)
+        el
+    end
+end
+
+# ╔═╡ 56ca47c1-6e4d-48a2-9f55-ca89362c7d3f
+# Import packages and export their (public) functions
+using Measurements, Unitful
+
 # ╔═╡ 1f347724-1db2-48f0-87df-4e63ad6e8820
 # Importing a builtin library that provides more functions for linear algebra.
 # The keyword `using` imports the package and exports (public) functions automatically.
@@ -45,17 +59,15 @@ md"""
 md"""
 ## Pluto notebooks
 - ⌨️ Press **`F1`** to see the full list of **shortcuts**.
+- ▶️ Most important shortcut: `Shift` + `Enter` to run a cell.
 - 📚️ Take a look at the **live docs** to the right.
 """
 
-# ╔═╡ b559ef1a-76cf-4464-b5ec-f7d6bfa892e6
-md"""
-# Basics
-"""
-
 # ╔═╡ 938adcfe-8d1b-4c77-8d82-c48415f5673e
 md"""
 ## Calculation
+
+You can use Julia as a calculator 🧮
 """
 
 # ╔═╡ 73190799-fd03-4cc4-9b4e-c523bc310468
@@ -85,6 +97,19 @@ md"""
 # Quotient of division
 5 ÷ 2
 
+# ╔═╡ 0dc9bbb4-fdde-4006-b04d-4509f7d041a7
+3^2 * 2 - 8
+
+# ╔═╡ 9c837673-79dd-4a6f-a11d-6f0f2c001587
+3^2 * (2 - 8)
+
+# ╔═╡ 0b6c6d50-e24c-43c7-8f04-4a53a3309bbf
+md"""
+Compare the results of the last two cells.
+
+The followed operation priority is the same as in math (multiplication before addition/subtraction and so on). Use brackets to make sure that you get the result you want!
+"""
+
 # ╔═╡ d1bf37f9-5135-48b8-8f9b-84ddd4a86157
 md"""
 ## Variables
@@ -107,23 +132,68 @@ a * b
 # You can also store the result of a computation
 c = a + b
 
+# ╔═╡ 4936c9fc-43da-4b8b-84ce-11e739802e07
+# You can also use variables with long names, but make sure to connect the words with an underscore (_)
+variable_with_a_long_name = 42
+
+# ╔═╡ 5e7f8a5e-9354-442b-aa13-7b9b3de536b1
+md"""
+There is a useful syntax to update the value of a variable using an operator acting on the variable itself.
+"""
+
+# ╔═╡ cf08cc65-7a9e-490d-b7e6-eecf6a1d9977
+md"""
+From now on, blocks will be used sometimes when manipulating a varialbe to prevent dependency on execution order in the notebooks.
+
+A block starts with `begin` and ends with `end`. Code in the block should be indented.
+
+The output of a cell with a block is the output of the last line of this block.
+"""
+
+# ╔═╡ 4774fa16-a6f6-48ae-b9b6-8a279118c99a
+begin
+	incr_var = 1
+	incr_var += 1
+	# Equivalent to the following:
+	# incr_var = incr_var + 1
+	
+	incr_var
+end
+
+# ╔═╡ 30000e9f-ec3d-416a-b402-010da80cd9ea
+md"""
+This syntax can also be used for all other operators (`*`, `/`, `^`, etc.)
+"""
+
+# ╔═╡ 72daf832-dba6-49ad-8d5a-f2c3aecdb630
+# Example with one more operator
+begin
+	doppel_var = 5
+	doppel_var *= 2
+	doppel_var
+end
+
 # ╔═╡ 2121b949-06e7-4079-a25a-d0518ee2ba50
 md"""
-## Primitive types
+## Types
-- **`Bool`**
-- **`Char`**
-- `Float16`, `Float32`, **`Float64`**
-- `Int8`, `Int16`, `Int32`, **`Int64`**, `Int128`
-- `UInt8`, `UInt16`, `UInt32`, `UInt64`, `UInt128`
 
-All other types (like strings) are composed.
+These are the most important primitive types:
+- `Bool`
+- `Char`
+- `Float64`
+- `Int64`
 
-Spoiler: You can compose your own types! More about this later 😉
+Most other types (like `String`) are composed.
+
+*Spoiler: You can compose your own types! More about this later* 😉
 """
 
 # ╔═╡ 534f3b32-1fc9-4eed-887a-2cac66c2bdb4
-# Bool
+# Bool has only two possible values: `true` or `false`.
-bo = true
+bo1 = true
+
+# ╔═╡ 3894b6b5-1952-409a-9966-502c277e26c3
+bo2 = false
 
 # ╔═╡ f20de3db-f270-4c43-aab7-692c313b5fa9
 # Char
@@ -148,9 +218,9 @@ hello = "Hello world!"
 
 # ╔═╡ 196682db-f5e1-4c07-9d35-644da3eecdd6
 md"""
-Pluto notebooks automatically print the output of the cell.
+Pluto notebooks automatically print the output of a cell.
 
-When using scripts instead of notebooks, `println` is needed.
+When using scripts instead of notebooks, `println` is needed to print to the console / terminal.
 """
 
 # ╔═╡ 10fdb32f-b66f-4c4e-abd9-e856549941b8
@@ -174,122 +244,6 @@ meaning_of_life = 42
 # Int64 is the default
 typeof(meaning_of_life)
 
-# ╔═╡ 944e2d37-8280-47b8-b874-97221955d048
-md"""
-## Type hierarchy
-
-Julia does have abstract types which are helpful for multiple dispatch.
-
-More about multiple dispatch later 😉
-"""
-
-# ╔═╡ 23d4ac67-05ec-4b3d-8368-86256076be62
-# The type hierarchy of Int64
-supertypes(Int64)
-
-# ╔═╡ e8d7de2f-7c7e-47cb-9364-27d583652167
-md"""
-All types showed in the output of the above cell except `Int64` are abstract.
-
-This means that you can not have a variable with an abstract type.
-
-You can only derive from an abstract type, but more about this when discussing structs and mutliple dispatch 😉
-
-`Any` is the abstract type of everything.
-"""
-
-# ╔═╡ 866edf5e-a76c-448d-98e8-925eaed5eba5
-# A number can either be real or complex
-subtypes(Number)
-
-# ╔═╡ a8ea4ac1-7f62-4485-a8c5-8ccf00c45720
-# There are some types of real numbers.
-subtypes(Real)
-
-# ╔═╡ 786a96be-16cd-4f1b-9b5f-138e232d3183
-# Integers can have a sign or no sign (only positive).
-# A Bool is also treated as an integer with the value 0 or 1.
-subtypes(Integer)
-
-# ╔═╡ dd8dad86-6bc2-4489-8469-7eac80fc41bb
-# Integers can have different number of bits.
-subtypes(Signed)
-
-# ╔═╡ fac04aa7-28e9-4f93-9312-a8f8f93c0877
-# Minimum and maximum value of a type
-typemin(Int8), typemax(Int8)
-
-# ╔═╡ 86bc0ff0-b6bf-4700-a741-36323be58391
-typemin(Int128), typemax(Int128)
-
-# ╔═╡ ef35a3a7-c1df-4952-aa41-1ed22d7f3981
-# BigInt does not have a minimum or maximum!
-BigInt(10)^1000 + 1
-
-# ╔═╡ c336d5f6-80ee-4994-a55f-2d6b3aa3d559
-# Hierarchy of Float64
-supertypes(Float64)
-
-# ╔═╡ 608d4433-6e68-4f95-8581-437234b58e87
-md"""
-## Convertion
-"""
-
-# ╔═╡ beadbfd3-0015-449a-b6e7-b5182b396c1d
-# Converting a float to an integer
-convert(Int64, 3.0)
-
-# ╔═╡ 552fafa4-fad5-4efe-895f-255b3ec5c858
-# Complex is a composed type for complex numbers
-convert(Complex, 3.0)
-
-# ╔═╡ d11fde7f-3238-4013-bd2d-546aab0d9f9c
-# This does not work! See rounding below.
-# convert(Int64, 3.2)
-
-# ╔═╡ 036a2c43-dbc9-487c-96aa-94324eeb4a52
-md"""
-## Rounding
-"""
-
-# ╔═╡ 1e954726-254e-41bb-a62f-17bdc9884bee
-# We have to tell Julia explicitely what to do when converting a float with non zero digits after the decimal point.
-round(Int64, 3.2)
-
-# ╔═╡ d74f6c46-f5a8-4720-bcaf-936f1508efda
-# The default is rounding to 0 digits after the decimal points, but keeping the float type.
-round(π)
-
-# ╔═╡ 3e5daca6-5aa8-42bf-988b-c09fb17388df
-# ; marks the start of keyword arguments. More about it later!
-round(π; digits=2)
-
-# ╔═╡ 7ff20c67-58d5-4095-bb8e-7ab7522791c7
-# You can provide a rounding mode, see the docs!
-round(π, RoundUp)
-
-# ╔═╡ 4a00035f-a1d1-409f-b73b-07f9073dc9d5
-md"""
-## Boolean operators
-"""
-
-# ╔═╡ d4ebb324-fa31-4058-9da1-35e07a971106
-# Boolean AND
-true && false
-
-# ╔═╡ f8259580-5a29-4a13-811f-c91d6811a291
-# Boolean OR
-true || false
-
-# ╔═╡ f813afd8-2e1b-43f7-beeb-ac9bd15fbeb6
-# Boolean NOT
-!false
-
-# ╔═╡ 7ab3a69d-ac31-49cf-8d34-3a427b02ed06
-md"""
-⚠️ Don't try to use `and`, `or` or `not` if you are coming from Python!
-"""
-
 # ╔═╡ 5e45b854-c173-452b-b62b-54037a3780fd
 md"""
 ## String operatorions
@@ -354,19 +308,335 @@ a_mult_b = a * b
 # Using the macro @show, helpful for usage in scripts
 @show a * b
 
+# ╔═╡ 1e7b103c-6cc9-4586-820b-9ec836b997da
+md"""
+### Why even string formatting?
+
+The following is an example of a possible calculation in a physical context.
+"""
+
+# ╔═╡ 7ade3f89-4838-4a8b-815c-4e2d6ccd7fea
+# Voltage
+U1 = 12.0 # V
+
+# ╔═╡ 35675b9b-a28a-427f-9da4-e6c756d2276a
+# Voltage uncertainty
+dU1 = 0.1 # V
+
+# ╔═╡ 66d39465-8244-483f-9a82-8d17b95cf41d
+# Current
+I1 = 0.30 # mA
+
+# ╔═╡ 879c5330-781f-44c2-b072-1ee0f9bd971d
+# Current uncertainty
+dI1 = 0.01 # mA
+
+# ╔═╡ df5914e3-b250-4824-80a5-cac5d0bed084
+# Resistance
+R1 = U1 / I1 # kΩ
+
+# ╔═╡ 099ac8f8-8c5c-410b-a11f-c98bc68230b2
+# Resistance uncertainty calculated with the Gaussian propagation of uncertainty.
+dR1 = R1 * ((dU1 / U1)^2 + (dI1 / I1)^2)^0.5 # kΩ
+
+# ╔═╡ cd46845b-4980-465c-a64f-3a8bcb66f53e
+# You can get the ± symbol by typing \pm and then pressing tab.
+println("""U: $U1 ± $dU1 V
+I: $I1 ± $dI1 mA
+R: $R1 ± $(round(dR1; digits=2)) kΩ""") # We will get to rounding later
+
+# ╔═╡ a0bd2da0-344d-470c-918e-e8760fc77355
+md"""
+Nice, we were able to generate a nice output 🤩
+
+But wait, Julia can automatically handle physical units and propagation of uncertainty for us! 🙀
+"""
+
+# ╔═╡ a2c4c4d9-4f06-41d4-baeb-b5f9f3b5b7c3
+md"""
+## Measurements and units
+"""
+
+# ╔═╡ f4122e58-a30c-45a4-8ede-492ddb8deba4
+U2 = (12.0 ± 0.1)u"V"
+
+# ╔═╡ 949e7fb8-8eff-49ea-8e76-0306857b05b9
+I2 = (0.30 ± 0.01)u"mA"
+
+# ╔═╡ 26869678-32f0-46e8-8cb2-d45b84441f03
+R2 = U2 / I2
+
+# ╔═╡ 0121add2-b42b-4dcd-8912-f8420a8b4c72
+R2_converted = uconvert(u"kΩ", R2)
+
+# ╔═╡ 9df364d6-0f43-4fe3-8a10-4bf0dc79e04d
+md"""
+Magic 🪄
+"""
+
+# ╔═╡ b8d7bd0b-a0ea-499f-9e61-3875535887e9
+md"""
+## Functions
+
+In the last example, we did calculate the resistance. The resistance is a function of two variables: `I` and `U`.
+
+In physics or mathematics, you would write this function this way:
+
+$R(U, I) = U / I$
+
+Guess what: In Julia, you can just write the same thing and you get a function!
+"""
+
+# ╔═╡ 13dd1d3c-dec8-4871-8ffa-b3db1bdd2847
+# Function definition
+R(U, I) = U / I
+
+# ╔═╡ 0078ea9a-9c94-4703-a878-3cdd2e11d625
+md"""
+Now, you can call the function with some arguments.
+"""
+
+# ╔═╡ 38d3105f-427b-427b-bf7b-8aa76dfb3bef
+R(12.0, 0.30)
+
+# ╔═╡ 41b17c21-5b57-4912-88ee-e33215c1e0c8
+# You can also pass units and uncertainties, Julia will just handle them.
+# You can store the result in a new variable.
+R3 = R((12.0 ± 0.1)u"V", (0.30 ± 0.01)u"mA")
+
+# ╔═╡ b6dcaf22-c075-442e-b0d0-e48eae2350ac
+# Now convert the result
+uconvert(u"kΩ", R3)
+
+# ╔═╡ 7f01c4a5-0e56-43aa-8d14-5fecfa04b370
+md"""
+OK, I guess you are asking what the benefit is. Why functions? You can just write `U / I`, right? 🤔
+
+It was just a demonstration! Functions are more useful when you have a long calculation.
+
+Lets write a function that does more than one thing. We want to calculate and show the results in a nice way.
+
+Function with more than one line start with the keyword `function` and end with `end`. After `function` the name of the function and the arguments follow.
+
+Everything inbetween should be indented (with tab). The result has to be returned with `return`.
+"""
+
+# ╔═╡ 105362be-572c-4a4d-9163-15ed8b4f1fbf
+function calc_and_print_R(U, I)
+	@show U
+	@show I
+	
+	R = U / I
+	R = uconvert(u"kΩ", R)
+	@show R
+	
+	return R
+end
+
+# ╔═╡ 18c2ffb9-a895-491b-96ee-a0b5c68da180
+# Test the function
+calc_and_print_R(U2, I2)
+
+# ╔═╡ 62cdf927-4e2b-40bb-be2d-eb32e0789548
+md"""
+Now, everytime you want to calculate a resistance, you just use this function and it calculates and outputs for you 😃
+"""
+
+# ╔═╡ 9847a224-701a-489a-b125-95158aa805d4
+# Take a look at this function doing some random calculation
+function complex_function(a, b, c, d)
+    result = a + b
+    result = result * c
+    result = result / d
+    return result
+end
+
+# ╔═╡ 21163504-972d-4362-8c57-dbd708b2fa04
+complex_function(1, 2, 3, 4)
+
+# ╔═╡ 9ef91243-04fc-44f2-ae69-76f372364f21
+# Try to access the variable `result`
+# result
+
+# ╔═╡ 3df766f0-38cb-4cdf-a68f-a4771c78fe31
+md"""
+Why can't we access the variable that we did define and use in the function? 😢
+
+It is because of the concept of *scopes*. The variable result is only defined inside the function and it is only accecable inside of this function (in the scope of the function), not outside it!
+
+`result` is called an *internal* variable. When you define a variable outside a function, it is called a *global* variable and is accecable everywhere.
+"""
+
+# ╔═╡ a6d882a0-c80e-4acf-b05b-c0ae120d698d
+md"""
+We will get back to data analysis. But first, we have to dive a bit deeper into the language 🤿
+"""
+
+# ╔═╡ 944e2d37-8280-47b8-b874-97221955d048
+md"""
+## Type hierarchy
+
+Julia does have abstract types which are helpful for multiple dispatch.
+
+More about multiple dispatch later 😉
+"""
+
+# ╔═╡ 23d4ac67-05ec-4b3d-8368-86256076be62
+# The type hierarchy of Int64
+supertypes(Int64)
+
+# ╔═╡ e8d7de2f-7c7e-47cb-9364-27d583652167
+md"""
+All types showed in the output of the above cell except `Int64` are abstract.
+
+This means that you can not have a variable with an abstract type.
+
+You can only derive from an abstract type, but more about this when discussing structs and mutliple dispatch 😉
+
+`Any` is the abstract type of everything.
+"""
+
+# ╔═╡ 866edf5e-a76c-448d-98e8-925eaed5eba5
+# A number can either be real or complex
+subtypes(Number)
+
+# ╔═╡ a8ea4ac1-7f62-4485-a8c5-8ccf00c45720
+# There are some types of real numbers.
+subtypes(Real)
+
+# ╔═╡ 786a96be-16cd-4f1b-9b5f-138e232d3183
+# Integers can have a sign or no sign (only positive).
+# A Bool is also treated as an integer with the value 0 or 1.
+subtypes(Integer)
+
+# ╔═╡ dd8dad86-6bc2-4489-8469-7eac80fc41bb
+# Integers can have different number of bits.
+subtypes(Signed)
+
+# ╔═╡ fac04aa7-28e9-4f93-9312-a8f8f93c0877
+# Minimum and maximum value of a type
+typemin(Int8), typemax(Int8)
+
+# ╔═╡ 86bc0ff0-b6bf-4700-a741-36323be58391
+typemin(Int128), typemax(Int128)
+
+# ╔═╡ ef35a3a7-c1df-4952-aa41-1ed22d7f3981
+# BigInt does not have a minimum or maximum!
+BigInt(10)^1000 + 1
+
+# ╔═╡ c336d5f6-80ee-4994-a55f-2d6b3aa3d559
+# Hierarchy of Float64
+supertypes(Float64)
+
+# ╔═╡ 608d4433-6e68-4f95-8581-437234b58e87
+md"""
+## Convertion
+
+You can convert some types to others if it is possible.
+"""
+
+# ╔═╡ beadbfd3-0015-449a-b6e7-b5182b396c1d
+# Converting a float to an integer
+convert(Int64, 3.0)
+
+# ╔═╡ 552fafa4-fad5-4efe-895f-255b3ec5c858
+# Complex is a composed type for complex numbers
+convert(Complex, 3.0)
+
+# ╔═╡ d11fde7f-3238-4013-bd2d-546aab0d9f9c
+# This does not work! See rounding below.
+# convert(Int64, 3.2)
+
+# ╔═╡ 036a2c43-dbc9-487c-96aa-94324eeb4a52
+md"""
+## Rounding
+"""
+
+# ╔═╡ 1e954726-254e-41bb-a62f-17bdc9884bee
+# We have to tell Julia explicitely what to do when converting a float with non zero digits after the decimal point.
+round(Int64, 3.2)
+
+# ╔═╡ d74f6c46-f5a8-4720-bcaf-936f1508efda
+# The default is rounding to 0 digits after the decimal points, but keeping the float type.
+round(π)
+
+# ╔═╡ 3e5daca6-5aa8-42bf-988b-c09fb17388df
+# ; marks the start of keyword arguments. More about it later!
+round(π; digits=2)
+
+# ╔═╡ 7ff20c67-58d5-4095-bb8e-7ab7522791c7
+# You can provide a rounding mode, see the docs!
+round(π, RoundUp)
+
 # ╔═╡ 3102810f-3467-4ed8-86c0-16e9177fa69d
 md"""
-## For loop
+## `for` loop
+
+You might be asking your self, why even bother learning a programming language when you can just use a calculator 🤨
+
+One very improtant aspect of computers is their ability to do a computation for many times, without getting tired or missing a step 😴
+
+To use this ability, programming languages provide `for` and `while` loops.
+
+In a `for` loop, Julia iterates over every element of a given collection and does a specific computation with this element.
+
+Lets see some examples!
 """
 
 # ╔═╡ c1c705d2-7e46-4811-9fb1-6b88b5a4140e
-for i in 1:3
+# This for loop iterates over the numbers 1, 2, 3 and 4 and prints them.
+for i in 1:4
 	println(i)
 end
 
+# ╔═╡ ddd3c019-6e70-4714-88fe-07d7a006ebc6
+# This loop iterates over some strings and prints a welcoming message.
+for name in ["Alice", "Bob", "everyone"]
+	println("Hello $name, welcome to this Julia course!")
+end
+
+# ╔═╡ 05db4e85-857d-4056-a576-5de992eabf29
+md"""
+Now, let's make our function for calculating and printing resistance more useful!
+
+We want to iterate over some measured values of voltage and current.
+
+To do so, we pair each element of one vector (list of measurements) with the corresponding element of the second vector.
+
+*Vectors will be explained later. Until then, it is enough to understand a vector as an ordered list of elements.*
+
+Lets take a look!
+"""
+
+# ╔═╡ 85c3c314-0f66-41be-8398-a5f9149ddfbd
+# Vector of measured voltage values to different resistances
+# The point is important, it will be explained later!
+measured_U = [12.0, 15.0, 16.0, 12.5, 23.2, 22.6] .* u"V" .± 0.1u"V"
+
+# ╔═╡ 566553a0-0202-4b59-b3ef-6954bf946b79
+# Vector of measured current values to the different resistances
+measured_I = [0.30, 0.25, 0.13, 0.22, 0.15, 0.75] .* u"mA" .± 0.05u"mA"
+
+# ╔═╡ b70a48ca-362c-40d6-b703-2553a0b01275
+for (u, i) in zip(measured_U, measured_I)
+	calc_and_print_R(u, i)
+	println("---") # Seperate output
+end
+
+# ╔═╡ c0b32101-5863-4c22-8ee5-8e29abe0da39
+md"""
+Now imagine that you have not only 6 measurements, but 1000 or more. How much time would you need with the calculator? ⏳️
+
+Later, we will learn how to plot and further analyze calculated values!
+"""
+
 # ╔═╡ 00456b15-5d1c-4c74-a875-31ff9c8e1789
 md"""
-## While loop
+## `while` loop
+
+A `while` loop is similar to a `for` loop. The loop does the same computation with different values over and over. Instead of going through elements of a vector, a `while` loop checks a condition and runs the computation until the condition is `false`.
+
+Lets see the following example!
 """
 
 # ╔═╡ 91c4c623-5680-4b35-a694-2bd2612def94
@@ -378,19 +648,56 @@ begin
 	end
 end
 
+# ╔═╡ 4a00035f-a1d1-409f-b73b-07f9073dc9d5
+md"""
+## Boolean operators
+
+Boolean operators are especially needed to check conditions, for `while`, `if` or `elseif`.
+"""
+
+# ╔═╡ d4ebb324-fa31-4058-9da1-35e07a971106
+# Boolean AND
+true && false
+
+# ╔═╡ f8259580-5a29-4a13-811f-c91d6811a291
+# Boolean OR
+true || false
+
+# ╔═╡ f813afd8-2e1b-43f7-beeb-ac9bd15fbeb6
+# Boolean NOT
+!false
+
+# ╔═╡ 7ab3a69d-ac31-49cf-8d34-3a427b02ed06
+md"""
+⚠️ Don't try to use `and`, `or` or `not` if you are coming from Python!
+"""
+
 # ╔═╡ 2a85d95b-51d2-4ea0-a2a2-43307a725f2a
 md"""
-## If, else, elseif
+## `if`, `elseif`, `else`
+"""
+
+# ╔═╡ eef07cd2-0a83-491f-a3ff-c51400aadebb
+md"""
+`if` checks for a condition and runs the code indented under it if the condition is `true`.
 """
 
 # ╔═╡ 9a78bf14-7fb4-448a-a8dd-69e244a0a297
-test_value = 1
+@bind test_value Slider(1:4)
+
+# ╔═╡ a5a71d00-bf30-4c07-bcd8-2bf99698522e
+test_value
 
 # ╔═╡ 5281ef32-5de6-4488-8430-e5652cbf8299
 if test_value == 1
 	println("The value is 1")
 end
 
+# ╔═╡ 9107a95e-6ef5-465f-bd28-9a774f99f4ab
+md"""
+`else` runs a piece of code indented under it if the condition of `if` is `false`.
+"""
+
 # ╔═╡ eec41279-e038-4415-81b3-ad5d4c396011
 # change the value of the variable `test_value` and see how the input changes
 if test_value == 1
@@ -399,6 +706,13 @@ else
 	println("The value is not 1")
 end
 
+# ╔═╡ 544368b2-3e39-41e7-97ea-e2bbf44a7749
+md"""
+`elseif` checks for further conditions if the conditions before it were `false`. If the condition is `true`, then the code indentet under it is executed and `else` is ignored. Otherwise, the next `elseif` is checked or `else` is executed if no `elseif` is left.
+
+Sounds complicated. It is best explained with an example.
+"""
+
 # ╔═╡ d2333817-e941-429b-b8e3-2ff07669096b
 # change the value of the variable `test_value` and see how the input changes
 if test_value == 1
@@ -417,8 +731,11 @@ if (test_value == 1) || (test_value == 2)
 	println("Value is 1 or 2")
 end
 
+# ╔═╡ 54d654cd-110f-4b1f-9578-109a80db4574
+@bind second_test_value Slider(1:2)
+
 # ╔═╡ 96803a1e-0779-4eab-b120-b5569a44ac7b
-second_test_value = 2
+second_test_value
 
 # ╔═╡ 5ab233d2-f360-4362-b1f8-3f3ae2a4fee1
 # change the value of the variable `second_test_value` and see how the input changes
@@ -506,13 +823,6 @@ md"""
 ## Mutation
 """
 
-# ╔═╡ 6fdc6add-a478-4707-876b-cf6d660870ba
-md"""
-From now on, blocks will be used sometimes when manipulating an array to prevent dependency on execution order.
-
-A block starts with `begin` and ends with `end`. Code in the block should be indented.
-"""
-
 # ╔═╡ e9e117af-1194-4d64-94a8-3e9fd51498aa
 # Setting the first element to 3
 begin
@@ -701,6 +1011,10 @@ vecs[:, 1]
 # Second eigenvector
 vecs[:, 2]
 
+# ╔═╡ 873be989-d587-4d9f-ad5d-5632ae24b0bf
+# Transpose a matrix
+first_matrix'
+
 # ╔═╡ a9f39e34-4c2c-48f2-9353-babe1bc3cd05
 md"""
 ## More dimensions
@@ -726,14 +1040,54 @@ ones(3, 2)
 # Fill with a value other than 0 or 1
 fill(42, (2, 2, 3))
 
+# ╔═╡ 91cc92b5-0be7-4ddf-91d1-bf56506e899c
+md"""
+## Range
+
+While using `for` loops, we used a synatax like the following:
+
+	for i in 1:4
+
+The `1:4` is a range. You can think of it as a vector that does not store all values in memory, but only the start, end and step values.
+
+To see what a range contains, you can convert it to a vector by *collecting* its elements using `collect`.
+"""
+
+# ╔═╡ c24f0bf2-0054-49f2-bffc-8b3e3ff6409b
+# Does not show the elements explicitely
+1:4
+
+# ╔═╡ 800d4999-d7d7-4818-95e7-d93027f23c53
+collect(1:4)
+
+# ╔═╡ a790ba58-c369-49eb-8f00-fdb73bcaab6c
+# Using a step different from 1
+collect(1:2:10)
+
+# ╔═╡ 28c9ef22-25b9-4640-bdd1-1b8dc7b33090
+# Ranges of floats are also possible
+collect(0.0:0.4:2.0)
+
+# ╔═╡ 1c4c05d7-455f-4a47-88aa-cf84a323a663
+# You can generate a range by providing the number of elements you want between start and end. The step is then calculated automatically.
+# This will be helpful for plotting later
+r = range(0.0, 2.0; length=5)
+
+# ╔═╡ e8c26d42-f841-4966-8d9e-3f11e9334551
+collect(r)
+
 # ╔═╡ 00000000-0000-0000-0000-000000000001
 PLUTO_PROJECT_TOML_CONTENTS = """
 [deps]
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+Measurements = "eff96d63-e80a-5855-80a2-b1b0885c5ab7"
 PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
+Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"
 
 [compat]
+Measurements = "~2.7.1"
 PlutoUI = "~0.7.37"
+Unitful = "~1.11.0"
 """
 
 # ╔═╡ 00000000-0000-0000-0000-000000000002
@@ -758,6 +1112,12 @@ uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
 [[deps.Base64]]
 uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
 
+[[deps.Calculus]]
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "f641eb0a4f00c343bbc32346e1217b86f3ce9dad"
+uuid = "49dc2e85-a5d0-5ad3-a950-438e2897f1b9"
+version = "0.5.1"
+
 [[deps.ColorTypes]]
 deps = ["FixedPointNumbers", "Random"]
 git-tree-sha1 = "024fe24d83e4a5bf5fc80501a314ce0d1aa35597"
@@ -768,6 +1128,12 @@ version = "0.11.0"
 deps = ["Artifacts", "Libdl"]
 uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
 
+[[deps.ConstructionBase]]
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "f74e9d5388b8620b4cee35d4c5a618dd4dc547f4"
+uuid = "187b0558-2788-49d3-abe0-74a17ed4e7c9"
+version = "1.3.0"
+
 [[deps.Dates]]
 deps = ["Printf"]
 uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"
@@ -843,6 +1209,12 @@ uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
 deps = ["Artifacts", "Libdl"]
 uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"
 
+[[deps.Measurements]]
+deps = ["Calculus", "LinearAlgebra", "Printf", "RecipesBase", "Requires"]
+git-tree-sha1 = "88cd033eb781c698e75ae0b680e5cef1553f0856"
+uuid = "eff96d63-e80a-5855-80a2-b1b0885c5ab7"
+version = "2.7.1"
+
 [[deps.Mmap]]
 uuid = "a63ad114-7e13-5084-954f-fe012c677804"
 
@@ -884,11 +1256,22 @@ uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"
 deps = ["SHA", "Serialization"]
 uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 
+[[deps.RecipesBase]]
+git-tree-sha1 = "6bf3f380ff52ce0832ddd3a2a7b9538ed1bcca7d"
+uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
+version = "1.2.1"
+
 [[deps.Reexport]]
 git-tree-sha1 = "45e428421666073eab6f2da5c9d310d99bb12f9b"
 uuid = "189a3867-3050-52da-a836-e630ba90ab69"
 version = "1.2.2"
 
+[[deps.Requires]]
+deps = ["UUIDs"]
+git-tree-sha1 = "838a3a4188e2ded87a4f9f184b4b0d78a1e91cb7"
+uuid = "ae029012-a4dd-5104-9daa-d747884805df"
+version = "1.3.0"
+
 [[deps.SHA]]
 uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
 
@@ -925,6 +1308,12 @@ uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
 [[deps.Unicode]]
 uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"
 
+[[deps.Unitful]]
+deps = ["ConstructionBase", "Dates", "LinearAlgebra", "Random"]
+git-tree-sha1 = "b649200e887a487468b71821e2644382699f1b0f"
+uuid = "1986cc42-f94f-5a68-af5c-568840ba703d"
+version = "1.11.0"
+
 [[deps.Zlib_jll]]
 deps = ["Libdl"]
 uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
@@ -946,7 +1335,6 @@ uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
 # ╟─2c5e32f4-1d7d-4494-b025-a90d17919756
 # ╟─21590bf1-1e1c-46b4-a2b6-7eb915e121ab
 # ╟─d04af0fd-5ced-4f4f-b157-dd170e2ef8c8
-# ╟─b559ef1a-76cf-4464-b5ec-f7d6bfa892e6
 # ╟─938adcfe-8d1b-4c77-8d82-c48415f5673e
 # ╠═73190799-fd03-4cc4-9b4e-c523bc310468
 # ╠═4c242a67-6445-48e7-a6c3-418a489b89ba
@@ -956,13 +1344,23 @@ uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
 # ╠═3f2c4ab8-4ba4-44d5-99d4-9d941e4df99e
 # ╠═02282f61-e1ca-483d-b6de-feeccedd7bc0
 # ╠═e4237ccd-b042-408b-8177-4c0d31a28caa
+# ╠═0dc9bbb4-fdde-4006-b04d-4509f7d041a7
+# ╠═9c837673-79dd-4a6f-a11d-6f0f2c001587
+# ╟─0b6c6d50-e24c-43c7-8f04-4a53a3309bbf
 # ╟─d1bf37f9-5135-48b8-8f9b-84ddd4a86157
 # ╠═8d005ddd-0308-4a06-8bae-251387facf6f
 # ╠═b7d27cd4-a655-492e-b2b3-cdc745b2c2da
 # ╠═141950e5-e9f8-414b-b08d-86777428cbec
 # ╠═2e7f29ce-3afa-4c12-838d-8051c0567e20
+# ╠═4936c9fc-43da-4b8b-84ce-11e739802e07
+# ╟─5e7f8a5e-9354-442b-aa13-7b9b3de536b1
+# ╟─cf08cc65-7a9e-490d-b7e6-eecf6a1d9977
+# ╠═4774fa16-a6f6-48ae-b9b6-8a279118c99a
+# ╟─30000e9f-ec3d-416a-b402-010da80cd9ea
+# ╠═72daf832-dba6-49ad-8d5a-f2c3aecdb630
 # ╟─2121b949-06e7-4079-a25a-d0518ee2ba50
 # ╠═534f3b32-1fc9-4eed-887a-2cac66c2bdb4
+# ╠═3894b6b5-1952-409a-9966-502c277e26c3
 # ╠═f20de3db-f270-4c43-aab7-692c313b5fa9
 # ╠═c72f187f-9626-45d9-870a-267c8530202c
 # ╠═e4295349-fc5c-48cb-975e-803e44d1a06e
@@ -974,6 +1372,52 @@ uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
 # ╠═204cf77f-bf37-4110-9c9f-1f9236301ba9
 # ╠═750bba32-e695-48f1-af70-70c94d13366b
 # ╠═0b663bcb-4ff4-4597-b28b-b58c9cbfa181
+# ╟─5e45b854-c173-452b-b62b-54037a3780fd
+# ╠═0596fe87-4201-476e-8e11-618c621c5474
+# ╠═28063282-5c60-4ffb-a715-9b1e88498df9
+# ╠═da5fb1f9-2a2d-4148-8ba5-8c4a529829e9
+# ╠═943da836-384d-4774-aaf4-54c27feb53d8
+# ╠═a96f3ae9-12df-4df8-85da-09b9b1e47de1
+# ╠═8d106ad2-5f92-4138-bfff-56ee21e098fa
+# ╠═f8bc4051-93c6-4376-abaa-7b4cb4b8f607
+# ╟─b25dc5f2-e186-4da1-b045-47b22c93799b
+# ╠═e0d7fbc8-39fc-4b70-9b92-0c19fffb0c05
+# ╠═398648e8-358e-4289-ae95-957e77d0c46f
+# ╠═28fa32e7-4e50-4890-a765-5cfb1d3f791b
+# ╠═d2607457-1794-4a0f-af41-cb80aadb598f
+# ╠═23dbbe13-d997-4f9f-a300-7cb78c4fb8ee
+# ╠═e767971a-7e1d-4a78-88d7-03e4ae4d51db
+# ╟─1e7b103c-6cc9-4586-820b-9ec836b997da
+# ╠═7ade3f89-4838-4a8b-815c-4e2d6ccd7fea
+# ╠═35675b9b-a28a-427f-9da4-e6c756d2276a
+# ╠═66d39465-8244-483f-9a82-8d17b95cf41d
+# ╠═879c5330-781f-44c2-b072-1ee0f9bd971d
+# ╠═df5914e3-b250-4824-80a5-cac5d0bed084
+# ╠═099ac8f8-8c5c-410b-a11f-c98bc68230b2
+# ╠═cd46845b-4980-465c-a64f-3a8bcb66f53e
+# ╟─a0bd2da0-344d-470c-918e-e8760fc77355
+# ╟─a2c4c4d9-4f06-41d4-baeb-b5f9f3b5b7c3
+# ╠═56ca47c1-6e4d-48a2-9f55-ca89362c7d3f
+# ╠═f4122e58-a30c-45a4-8ede-492ddb8deba4
+# ╠═949e7fb8-8eff-49ea-8e76-0306857b05b9
+# ╠═26869678-32f0-46e8-8cb2-d45b84441f03
+# ╠═0121add2-b42b-4dcd-8912-f8420a8b4c72
+# ╟─9df364d6-0f43-4fe3-8a10-4bf0dc79e04d
+# ╟─b8d7bd0b-a0ea-499f-9e61-3875535887e9
+# ╠═13dd1d3c-dec8-4871-8ffa-b3db1bdd2847
+# ╟─0078ea9a-9c94-4703-a878-3cdd2e11d625
+# ╠═38d3105f-427b-427b-bf7b-8aa76dfb3bef
+# ╠═41b17c21-5b57-4912-88ee-e33215c1e0c8
+# ╠═b6dcaf22-c075-442e-b0d0-e48eae2350ac
+# ╟─7f01c4a5-0e56-43aa-8d14-5fecfa04b370
+# ╠═105362be-572c-4a4d-9163-15ed8b4f1fbf
+# ╠═18c2ffb9-a895-491b-96ee-a0b5c68da180
+# ╟─62cdf927-4e2b-40bb-be2d-eb32e0789548
+# ╠═9847a224-701a-489a-b125-95158aa805d4
+# ╠═21163504-972d-4362-8c57-dbd708b2fa04
+# ╠═9ef91243-04fc-44f2-ae69-76f372364f21
+# ╟─3df766f0-38cb-4cdf-a68f-a4771c78fe31
+# ╟─a6d882a0-c80e-4acf-b05b-c0ae120d698d
 # ╟─944e2d37-8280-47b8-b874-97221955d048
 # ╠═23d4ac67-05ec-4b3d-8368-86256076be62
 # ╟─e8d7de2f-7c7e-47cb-9364-27d583652167
@@ -994,37 +1438,33 @@ uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
 # ╠═d74f6c46-f5a8-4720-bcaf-936f1508efda
 # ╠═3e5daca6-5aa8-42bf-988b-c09fb17388df
 # ╠═7ff20c67-58d5-4095-bb8e-7ab7522791c7
+# ╟─3102810f-3467-4ed8-86c0-16e9177fa69d
+# ╠═c1c705d2-7e46-4811-9fb1-6b88b5a4140e
+# ╠═ddd3c019-6e70-4714-88fe-07d7a006ebc6
+# ╟─05db4e85-857d-4056-a576-5de992eabf29
+# ╠═85c3c314-0f66-41be-8398-a5f9149ddfbd
+# ╠═566553a0-0202-4b59-b3ef-6954bf946b79
+# ╠═b70a48ca-362c-40d6-b703-2553a0b01275
+# ╟─c0b32101-5863-4c22-8ee5-8e29abe0da39
+# ╟─00456b15-5d1c-4c74-a875-31ff9c8e1789
+# ╠═91c4c623-5680-4b35-a694-2bd2612def94
 # ╟─4a00035f-a1d1-409f-b73b-07f9073dc9d5
 # ╠═d4ebb324-fa31-4058-9da1-35e07a971106
 # ╠═f8259580-5a29-4a13-811f-c91d6811a291
 # ╠═f813afd8-2e1b-43f7-beeb-ac9bd15fbeb6
 # ╟─7ab3a69d-ac31-49cf-8d34-3a427b02ed06
-# ╟─5e45b854-c173-452b-b62b-54037a3780fd
+# ╟─2a85d95b-51d2-4ea0-a2a2-43307a725f2a
-# ╠═0596fe87-4201-476e-8e11-618c621c5474
+# ╟─eef07cd2-0a83-491f-a3ff-c51400aadebb
-# ╠═28063282-5c60-4ffb-a715-9b1e88498df9
+# ╠═a5a71d00-bf30-4c07-bcd8-2bf99698522e
-# ╠═da5fb1f9-2a2d-4148-8ba5-8c4a529829e9
+# ╟─9a78bf14-7fb4-448a-a8dd-69e244a0a297
-# ╠═943da836-384d-4774-aaf4-54c27feb53d8
-# ╠═a96f3ae9-12df-4df8-85da-09b9b1e47de1
-# ╠═8d106ad2-5f92-4138-bfff-56ee21e098fa
-# ╠═f8bc4051-93c6-4376-abaa-7b4cb4b8f607
-# ╟─b25dc5f2-e186-4da1-b045-47b22c93799b
-# ╠═e0d7fbc8-39fc-4b70-9b92-0c19fffb0c05
-# ╠═398648e8-358e-4289-ae95-957e77d0c46f
-# ╠═28fa32e7-4e50-4890-a765-5cfb1d3f791b
-# ╠═d2607457-1794-4a0f-af41-cb80aadb598f
-# ╠═23dbbe13-d997-4f9f-a300-7cb78c4fb8ee
-# ╠═e767971a-7e1d-4a78-88d7-03e4ae4d51db
-# ╟─3102810f-3467-4ed8-86c0-16e9177fa69d
-# ╠═c1c705d2-7e46-4811-9fb1-6b88b5a4140e
-# ╟─00456b15-5d1c-4c74-a875-31ff9c8e1789
-# ╠═91c4c623-5680-4b35-a694-2bd2612def94
-# ╠═2a85d95b-51d2-4ea0-a2a2-43307a725f2a
-# ╠═9a78bf14-7fb4-448a-a8dd-69e244a0a297
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@@ -1042,7 +1482,6 @@ uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
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@@ -1075,10 +1514,18 @@ uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
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