Merge pull request #345 from SciML/rebuild/5a227e44

Rebuild type_handling/03-unitful.jmd

Author: ChrisRackauckas

html/type_handling/03-unitful.html

@@ -12,81 +12,71 @@ DifferentialEquations.jl allows for one to use Unitful.jl to have unit-checked a
 
 To use Unitful, you need to have the package installed. Then you can add units to your variables. For example:
 
-````julia
-
+```julia
 using Unitful
 t = 1.0u"s"
-````
-
+```
 
-````
+```
 1.0 s
-````
+```
 
 
 
 
 
 Notice that `t` is a variable with units in seconds. If we make another value with seconds, they can add
 
-````julia
-
+```julia
 t2 = 1.02u"s"
 t+t2
-````
-
+```
 
-````
+```
 2.02 s
-````
+```
 
 
 
 
 
 and they can multiply:
 
-````julia
-
+```julia
 t*t2
-````
-
+```
 
-````
+```
 1.02 s^2
-````
+```
 
 
 
 
 
 You can even do rational roots:
 
-````julia
-
+```julia
 sqrt(t)
-````
-
+```
 
-````
+```
 1.0 s^1/2
-````
+```
 
 
 
 
 
 Many operations work. These operations will check to make sure units are correct, and will throw an error for incorrect operations:
 
-````julia
-
+```julia
 t + sqrt(t)
-````
-
+```
 
-````
+```
 Error: DimensionError: 1.0 s and 1.0 s^1/2 are not dimensionally compatible.
-````
+```
 
 
 
@@ -96,19 +86,17 @@ Error: DimensionError: 1.0 s and 1.0 s^1/2 are not dimensionally compatible.
 
 Just like with other number systems, you can choose the units for your numbers by simply specifying the units of the initial condition and the timestep. For example, to solve the linear ODE where the variable has units of Newton's and `t` is in Seconds, we would use:
 
-````julia
-
+```julia
 using DifferentialEquations
 f = (y,p,t) -> 0.5*y
 u0 = 1.5u"N"
 prob = ODEProblem(f,u0,(0.0u"s",1.0u"s"))
 sol = solve(prob,Tsit5())
-````
-
+```
 
-````
+```
 Error: DimensionError: N s^-1 and 0.75 N are not dimensionally compatible.
-````
+```
 
 
 
@@ -120,15 +108,13 @@ $$\frac{dy}{dt} = f(t,y)$$
 
 we must have that `f` is a rate, i.e. `f` is a change in `y` per unit time. So we need to fix the units of `f` in our example to be `N/s`. Notice that we then do not receive an error if we do the following:
 
-````julia
-
+```julia
 f = (y,p,t) -> 0.5*y/3.0u"s"
 prob = ODEProblem(f,u0,(0.0u"s",1.0u"s"))
 sol = solve(prob,Tsit5())
-````
-
+```
 
-````
+```
 retcode: Success
 Interpolation: specialized 4th order "free" interpolation
 t: 3-element Array{Unitful.Quantity{Float64,𝐓,Unitful.FreeUnits{(s,),𝐓,nothing}},1}:
@@ -139,37 +125,33 @@ u: 3-element Array{Unitful.Quantity{Float64,𝐋 𝐌 𝐓^-2,Unitful.FreeUnits{
                 1.5 N
  1.5362091208988309 N
  1.7720406194871123 N
-````
+```
 
 
 
 
 
 This gives a a normal solution object. Notice that the values are all with the correct units:
 
-````julia
-
+```julia
 print(sol[:])
-````
-
+```
 
-````
+```
 Unitful.Quantity{Float64,𝐋 𝐌 𝐓^-2,Unitful.FreeUnits{(N,),𝐋 𝐌 𝐓^-2,nothing}}[1.5 N, 1.5362091208988309 N, 1.7720406194871123 N]
-````
+```
 
 
 
 
 
 We can plot the solution by removing the units:
 
-````julia
-
+```julia
 using Plots
 gr()
 plot(ustrip(sol.t),ustrip(sol[:]),lw=3)
-````
-
+```
 
 ![](figures/03-unitful_9_1.png)
 
@@ -212,8 +194,8 @@ Status `/builds/JuliaGPU/DiffEqTutorials.jl/tutorials/type_handling/Project.toml
 [abce61dc-4473-55a0-ba07-351d65e31d42] Decimals 0.4.1
 [0c46a032-eb83-5123-abaf-570d42b7fbaa] DifferentialEquations 6.15.0
 [497a8b3b-efae-58df-a0af-a86822472b78] DoubleFloats 1.1.13
-[eff96d63-e80a-5855-80a2-b1b0885c5ab7] Measurements 2.2.1
-[1dea7af3-3e70-54e6-95c3-0bf5283fa5ed] OrdinaryDiffEq 5.42.5
-[91a5bcdd-55d7-5caf-9e0b-520d859cae80] Plots 1.6.0
-[1986cc42-f94f-5a68-af5c-568840ba703d] Unitful 1.4.0
+[eff96d63-e80a-5855-80a2-b1b0885c5ab7] Measurements 2.3.0
+[1dea7af3-3e70-54e6-95c3-0bf5283fa5ed] OrdinaryDiffEq 5.43.0
+[91a5bcdd-55d7-5caf-9e0b-520d859cae80] Plots 1.6.12
+[1986cc42-f94f-5a68-af5c-568840ba703d] Unitful 1.5.0
 ```