tutorial

Author: shashi

docs/src/tutorials/converting_to_C.md

@@ -25,7 +25,7 @@ lotka_volterra!(du, u, p, t)
 which gives:
 
 ```julia
-du = Operation[p₁ * u₁ - (p₂ * u₁) * u₂, -p₃ * u₂ + (p₄ * u₁) * u₂]
+du = Num[p₁ * u₁ - (p₂ * u₁) * u₂, -p₃ * u₂ + (p₄ * u₁) * u₂]
 ```
 
 Now we build the equations we want to solve:

docs/src/tutorials/ode_modeling.md

@@ -69,8 +69,8 @@ eqs = [D(x) ~ σ*(y-x),
        D(z) ~ x*y - β*z]
 ```
 
-Each operation builds an `Operation` type, and thus `eqs` is an array of
-`Operation` and `Variable`s. This holds a tree of the full system that can be
+Each operation builds an `Term` type, and thus `eqs` is an array of
+`Term` and `Sym`s (possibly wrapped in Num). This holds a tree of the full system that can be
 analyzed by other programs. We can turn this into a `ODESystem` via:
 
 ```julia

docs/src/tutorials/symbolic_functions.md

@@ -8,14 +8,14 @@ The way to define symbolic variables is via the `@variables` macro:
 ```
 
 After defining variables as symbolic, symbolic expressions, which we
-call an `Operation`, can be generated by utilizing Julia expressions.
+call a `Term`, can be generated by utilizing Julia expressions.
 For example:
 
 ```julia
 z = x^2 + y
 ```
 
-Here, `z` is the `Operation` for "square `x` and add `y`". To
+Here, `z` is the `Term` for "square `x` and add `y`". To
 make an array of symbolic expressions, simply make an array of
 symbolic expressions:
 
@@ -30,6 +30,8 @@ A = [x^2+y 0 2x
   y ^ 2 + x  0  0
 ```
 
+Note that by default, `@variables` returns `Sym` or `Term` objects wrapped in `Num` in order to make them behave like subtypes of `Real`. Any operation on these `Num` objects will return a new `Num` object, wrapping the result of computing symbolically on the underlying values.
+
 To better view the results, we can use [Latexify.jl](https://github.com/korsbo/Latexify.jl).
 ModelingToolkit.jl comes with Latexify recipes so it works automatically: