Merge pull request #1144 from lamorton/doc_t_var

Update docs to use `t` as a `variable` rather than `parameter`

Author: YingboMa

docs/src/tutorials/acausal_components.md

@@ -14,7 +14,7 @@ equalities before solving. Let's see this in action.
 ```julia
 using ModelingToolkit, Plots, DifferentialEquations
 
-@parameters t
+@variables t
 @connector function Pin(;name)
     sts = @variables v(t)=1.0 i(t)=1.0
     ODESystem(Equation[], t, sts, []; name=name)

docs/src/tutorials/higher_order.md

@@ -13,8 +13,8 @@ We utilize the derivative operator twice here to define the second order:
 ```julia
 using ModelingToolkit, OrdinaryDiffEq
 
-@parameters t σ ρ β
-@variables x(t) y(t) z(t)
+@parameters σ ρ β
+@variables t x(t) y(t) z(t)
 D = Differential(t)
 
 eqs = [D(D(x)) ~ σ*(y-x),

docs/src/tutorials/stochastic_diffeq.md

@@ -11,8 +11,8 @@ it to have multiplicative noise.
 using ModelingToolkit, StochasticDiffEq
 
 # Define some variables
-@parameters t σ ρ β
-@variables x(t) y(t) z(t)
+@parameters σ ρ β
+@variables t x(t) y(t) z(t)
 D = Differential(t)
 
 eqs = [D(x) ~ σ*(y-x),

docs/src/tutorials/tearing_parallelism.md

@@ -36,7 +36,7 @@ function connect_heat(ps...)
 end
 
 # Basic electric components
-@parameters t
+@variables t
 const D = Differential(t)
 function Pin(;name)
     @variables v(t)=1.0 i(t)=1.0

src/systems/diffeqs/odesystem.jl

@@ -11,8 +11,8 @@ $(FIELDS)
 ```julia
 using ModelingToolkit
 
-@parameters t σ ρ β
-@variables x(t) y(t) z(t)
+@parameters σ ρ β
+@variables t x(t) y(t) z(t)
 D = Differential(t)
 
 eqs = [D(x) ~ σ*(y-x),

src/systems/diffeqs/sdesystem.jl

@@ -11,8 +11,8 @@ $(FIELDS)
 ```julia
 using ModelingToolkit
 
-@parameters t σ ρ β
-@variables x(t) y(t) z(t)
+@parameters σ ρ β
+@variables t x(t) y(t) z(t)
 D = Differential(t)
 
 eqs = [D(x) ~ σ*(y-x),

src/systems/discrete_system/discrete_system.jl

@@ -11,8 +11,8 @@ $(FIELDS)
 ```
 using ModelingToolkit
 
-@parameters t σ ρ β
-@variables x(t) y(t) z(t) next_x(t) next_y(t) next_z(t)
+@parameters σ ρ β
+@variables t x(t) y(t) z(t) next_x(t) next_y(t) next_z(t)
 
 eqs = [next_x ~ σ*(y-x),
        next_y ~ x*(ρ-z)-y,

src/systems/jumps/jumpsystem.jl

@@ -13,8 +13,8 @@ $(FIELDS)
 ```julia
 using ModelingToolkit
 
-@parameters β γ t
-@variables S I R
+@parameters β γ 
+@variables t S(t) I(t) R(t)
 rate₁   = β*S*I
 affect₁ = [S ~ S - 1, I ~ I + 1]
 rate₂   = γ*I

src/systems/pde/pdesystem.jl

@@ -11,8 +11,8 @@ $(FIELDS)
 ```julia
 using ModelingToolkit
 
-@parameters t x
-@variables u(..)
+@parameters x
+@variables t u(..)
 Dxx = Differential(x)^2
 Dtt = Differential(t)^2
 Dt = Differential(t)

src/systems/reaction/reactionsystem.jl

@@ -11,8 +11,8 @@ $(FIELDS)
 
 ```julia
 using ModelingToolkit
-@parameters t k[1:20]
-@variables A(t) B(t) C(t) D(t)
+@parameters k[1:20]
+@variables t A(t) B(t) C(t) D(t)
 rxs = [Reaction(k[1], nothing, [A]),            # 0 -> A
        Reaction(k[2], [B], nothing),            # B -> 0
        Reaction(k[3],[A],[C]),                  # A -> C