Restructure documentation and add examples from SciMLTutorials

Same motivation as SciML/ModelingToolkit.jl#1993

Author: ChrisRackauckas

docs/pages.jl

@@ -1,5 +1,6 @@
 pages = Any["index.md",
-            "Tutorials" => Any["tutorials/ode_example.md",
+            "getting_started.md",
+            "Tutorials" => Any[
                                "tutorials/faster_ode_example.md",
                                "tutorials/advanced_ode_example.md",
                                "tutorials/sde_example.md",
@@ -10,6 +11,20 @@ pages = Any["index.md",
                                "tutorials/jump_diffusion.md",
                                "tutorials/bvp_example.md",
                                "tutorials/additional.md"],
+            "Examples" => Any[
+                "Beginner" => Any[
+                    "examples/classical_physics.md",
+                    "examples/conditional_dosing.md",
+                    "examples/kepler_problem.md",
+                    "examples/outer_solar_system.md",
+                    "examples/min_and_max.md",
+                ],
+                "Advanced" => Any[
+                    "examples/spiking_neural_systems.md",
+                    "examples/beeler_reuter.md",
+                    "examples/diffusion_implicit_heat_equation.md",
+                ],
+            ],
             "Basics" => Any["basics/overview.md",
                             "basics/common_solver_opts.md",
                             "basics/solution.md",