New opening tutorial

[ChrisRackauckas]

We want a longer opening tutorial that progresses like:

• Defines and solves a simple ODE
• Adds some output observables?
• Adds some connections?

I kind of think @pbouffard's example is something nice to show off:

using ModelingToolkit, OrdinaryDiffEq

@parameters t a
@variables x(t) f(t)
D = Differential(t)

function decay(;name)
  eqs = [
    D(x) ~ -a*x + f
  ]
  ODESystem(eqs, name=name)
end

@named decay1 = decay()
@named decay2 = decay()

@named connected = ODESystem([
  decay2.f ~ decay1.x
  D(decay1.f) ~ 0
], t, systems=[decay1, decay2])

reduced_system = structural_simplify(connected)

x0 = [
  decay1.x => 1.0
  decay1.f => 0.0
  decay2.x => 1.0
]
p = [
  decay1.a => 0.1
  decay2.a => 0.2
]

prob = ODEProblem(reduced_system, x0, (0.0, 20.0), p)
sol = solve(prob, Tsit5())

as something that is useful to show too, since forcing functions and using another system to complete a system is a standard practice that should be demonstrated.

[asprionj]

Also show...?

• Macro-free usage (for dynamically defined stuff); at least mention / quickly show the possibility
• Vector-valued parameters, variables (probably wait for new handling of this before showing it)
• Re-running simulations with changed initial state and/or parameters without recompilation (the thing with the state/parameter mapping)

[ChrisRackauckas]

Macro-free usage (for dynamically defined stuff); at least mention / quickly show the possibility

Separate tutorial, not the opening tutorial.

Re-running simulations with changed initial state and/or parameters without recompilation (the thing with the state/parameter mapping)

I don't think we want to keep that API (we want to just fix it), so I'd exclude it from the first tutorial and keep it in the FAQ.

[asprionj]

Ok, I'll give it a shot. When working on the docs anyway, I'll probably also address #564. Anything else that could be worth cleaning up (and at the same time helping me getting into MTK)?

BTW, with "opening tutorial", you do mean Composing Ordinary Differential Equations, right?

One further point to mention in the opening tutorial (?): defaults.

[asprionj]

Plots for new example

[asprionj]

Anything left to do (just let me know...) or can we close this?