many edits

quarto/alternatives/SciML.qmd

@@ -147,8 +147,8 @@ Incorporating parameters is readily done. For example to solve $f(x) = \cos(x) -
 
 ```{julia}
 f(x, p) = @. cos(x) - x/p
-u0 = (0, pi/2)
-p = 2
+u0 = (0.0, pi/2)
+p = 2.0
 prob = IntervalNonlinearProblem(f, u0, p)
 solve(prob, Bisection())
 ```
@@ -410,6 +410,7 @@ could be similarly approached:
 y = Area/x  # from A = xy
 P = 2x + 2y
 @named sys = OptimizationSystem(P, [x], [Area]);
+sys = structural_simplify(sys)
 
 u0 = [x => 4.0]
 p = [Area => 25.0]
@@ -730,6 +731,6 @@ For a trivial example, we have:
 
 ```{julia}
 f(x, p) = [x[1], x[2]^2]
-prob = IntegralProblem(f, [0,0],[3,4], nout=2)
+prob = IntegralProblem(f, [0,0],[3,4])
 solve(prob, HCubatureJL())
 ```