Update 01-ode_introduction.jmd

Author: ChrisRackauckas

tutorials/introduction/01-ode_introduction.jmd

@@ -5,7 +5,7 @@ author: Chris Rackauckas
 
 ## Basic Introduction Via Ordinary Differential Equations
 
-This notebook will get you started with DifferentialEquations.jl by introducing you to the functionality for solving ordinary differential equations (ODEs). The corresponding documentation page is the [ODE tutorial](http://docs.juliadiffeq.org/latest/tutorials/ode_example.html). While some of the syntax may be different for other types of equations, the same general principles hold in each case. Our goal is to give a gentle and thorough introduction that highlights these principles in a way that will help you generalize what you have learned.
+This notebook will get you started with DifferentialEquations.jl by introducing you to the functionality for solving ordinary differential equations (ODEs). The corresponding documentation page is the [ODE tutorial](http://docs.juliadiffeq.org/dev/tutorials/ode_example.html). While some of the syntax may be different for other types of equations, the same general principles hold in each case. Our goal is to give a gentle and thorough introduction that highlights these principles in a way that will help you generalize what you have learned.
 
 ### Background
 
@@ -55,14 +55,14 @@ and that's it: we have succesfully solved our first ODE!
 
 #### Analyzing the Solution
 
-Of course, the solution type is not interesting in and of itself. We want to understand the solution! The documentation page which explains in detail the functions for analyzing the solution is the [Solution Handling](http://docs.juliadiffeq.org/latest/basics/solution.html) page. Here we will describe some of the basics. You can plot the solution using the plot recipe provided by [Plots.jl](http://docs.juliaplots.org/latest/):
+Of course, the solution type is not interesting in and of itself. We want to understand the solution! The documentation page which explains in detail the functions for analyzing the solution is the [Solution Handling](http://docs.juliadiffeq.org/dev/basics/solution.html) page. Here we will describe some of the basics. You can plot the solution using the plot recipe provided by [Plots.jl](http://docs.juliaplots.org/dev/):
 
 ```julia
 using Plots; gr()
 plot(sol)
 ```
 
-From the picture we see that the solution is an exponential curve, which matches our intuition. As a plot recipe, we can annotate the result using any of the [Plots.jl attributes](http://docs.juliaplots.org/latest/attributes/). For example:
+From the picture we see that the solution is an exponential curve, which matches our intuition. As a plot recipe, we can annotate the result using any of the [Plots.jl attributes](http://docs.juliaplots.org/dev/attributes/). For example:
 
 ```julia
 plot(sol,linewidth=5,title="Solution to the linear ODE with a thick line",
@@ -107,7 +107,7 @@ sol(0.45)
 
 #### Controlling the Solver
 
-DifferentialEquations.jl has a common set of solver controls among its algorithms which can be found [at the Common Solver Options](http://docs.juliadiffeq.org/latest/basics/common_solver_opts.html) page. We will detail some of the most widely used options.
+DifferentialEquations.jl has a common set of solver controls among its algorithms which can be found [at the Common Solver Options](http://docs.juliadiffeq.org/dev/basics/common_solver_opts.html) page. We will detail some of the most widely used options.
 
 The most useful options are the tolerances `abstol` and `reltol`. These tell the internal adaptive time stepping engine how precise of a solution you want. Generally, `reltol` is the relative accuracy while `abstol` is the accuracy when `u` is near zero. These tolerances are local tolerances and thus are not global guarantees. However, a good rule of thumb is that the total solution accuracy is 1-2 digits less than the relative tolerances. Thus for the defaults `abstol=1e-6` and `reltol=1e-3`, you can expect a global accuracy of about 1-2 digits. If we want to get around 6 digits of accuracy, we can use the commands:
 
@@ -157,7 +157,7 @@ sol = solve(prob,save_everystep=false,save_start = false)
 
 Note that similarly on the other side there is `save_end=false`.
 
-More advanced saving behaviors, such as saving functionals of the solution, are handled via the `SavingCallback` in the [Callback Library](http://docs.juliadiffeq.org/latest/features/callback_library.html#SavingCallback-1) which will be addressed later in the tutorial.
+More advanced saving behaviors, such as saving functionals of the solution, are handled via the `SavingCallback` in the [Callback Library](http://docs.juliadiffeq.org/dev/features/callback_library.html#SavingCallback-1) which will be addressed later in the tutorial.
 
 #### Choosing Solver Algorithms
 
@@ -316,7 +316,7 @@ Not only is the DSL convenient syntax, but it does some magic behind the scenes.
 lv!.Jex
 ```
 
-The DSL can derive many other functions; this ability is used to speed up the solvers. An extension to DifferentialEquations.jl, [Latexify.jl](https://korsbo.github.io/Latexify.jl/latest/tutorials/parameterizedfunctions.html), allows you to extract these pieces as LaTeX expressions.
+The DSL can derive many other functions; this ability is used to speed up the solvers. An extension to DifferentialEquations.jl, [Latexify.jl](https://korsbo.github.io/Latexify.jl/dev/tutorials/parameterizedfunctions.html), allows you to extract these pieces as LaTeX expressions.
 
 ## Internal Types