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diff --git a/README.md b/README.md
@@ -4,7 +4,7 @@ Easy to compile, fast ODE integrators as C++ classes
 
 This repo contains a collection of C++ classes for solving systems of ordinary differential equations (ODEs) in autonomous form. Documentation is [here](https://wordsworthgroup.github.io/libode/). All of the solvers are single-step, Runge-Kutta-like methods. There are explicit, adaptive solvers up to the ninth order. The repository also includes Rosenbrock methods, a singly-diagonal implicit Runge-Kutta (SDIRK) method, and several fully implicit Runge-Kutta methods. However, only a few of the implicit methods have solid adaptive time steppers at this point. With the current collection of solvers and features, `libode` is well suited to any non-stiff systems and to stiff systems that are tightly coupled and have a known Jacobian (ones that don't require sparse or banded matrix routines).
 
-The classes were originally styled after [Chris Rycroft](https://people.seas.harvard.edu/~chr/)'s [example classes](https://github.com/chr1shr/am225_examples/tree/master/1a_ode_solvers). Their structure makes it easy to build a templated integrator on top of an arbitrary solver class and easily switch the solver/method. Implicit methods can be given a function for the ODE system's Jacobian or, if none is provided, the Jacobian is estimated using finite differences.
+The classes were originally styled after [Chris Rycroft](https://people.seas.harvard.edu/~chr/)'s [example classes](https://github.com/chr1shr/am225_examples/tree/master/1a_ode_solvers). Their structure makes it easy to build a templated integrator on top of an arbitrary solver class and switch the solver/method. Implicit methods can be given a function for the ODE system's Jacobian or, if none is provided, the Jacobian is estimated using finite differences.
 
 Several of the solvers and much more detail on the methods can be found in these amazing books:
 * Hairer, E., Nørsett, S. P. & Wanner, G. Solving Ordinary Differential Equations I: Nonstiff Problems. (Springer-Verlag, 1987).
@@ -52,7 +52,7 @@ SDIRK 4(3) | `OdeSDIRK43` | `ode_sdirk_43.h` | implicit | yes | 4 | 4 | L
 
 First, before any of the `libode` classes can be compiled, you must copy the `_config.mk` file to `config.mk` and edit that file to specify the compiler settings you'd like the Makefile to use. This shouldn't be complicated. If you are using a current version of the GNU C++ compiler (g++), the contents of the template config file can likely be used without modification. There are also commented lines for use with the Intel C++ compiler (icpc), if that is available. To compile all the classes, simply run `make` in the top directory.
 
-The Makefile compiles all of the necessary code into the `obj` folder, then archives it in the `bin` directory as a file called `libode.a`. To use the solvers, you can link `libode.a` (in the `bin` directory) or the object files directly (in the `obj` directory) when compiling your derived class. You must also include the appropriate header files from the `src` directory, as there is not a single header file for the library. All of the classes have their header file name displayed in the documentation. Linking the solver classes requires something like
+The Makefile compiles all of the necessary code into the `obj` folder, then archives it in the `bin` directory as a file called `libode.a`. To use the solvers, you can link `libode.a` (in the `bin` directory) or the object files directly (in the `obj` directory) when compiling your derived class. You must also include the appropriate header files from the `src` directory, as there is not a single header file for the library. All of the classes have their header file name displayed in the documentation and in the table above. Linking the solver classes requires something like
 
 `-I<path>/libode/src -L<path>/libode/bin -lode`
 
@@ -69,9 +69,9 @@ Several example programs for interesting/famous systems of ODEs are in the "exam
 #### Define a Class
 
 To integrate a specific system of ODEs, a new class must be created to inherit from one of the solver classes. This new inheriting class must
-1. Define the system of ODEs to be solved by implementing the `ode_fun()` function. This is a virtual function in the base classes. Once it is implemented, it can be used by the stepping and solving functions.
+1. Define the system of ODEs to be solved by implementing the `ode_fun()` function. This is a virtual function in the base classes. Once implemented, it's used by the stepping and solving functions.
 2. Set initial conditions using the `set_sol()` function.
-3. Optionally implement the `ode_jac()` function for implicit methods. This is also a virtual function in the base classes. If it's not overridden, a finite-difference estimate of the Jacobian is used.
+3. Optionally implement the `ode_jac()` function for implicit methods. This is also a virtual function in the base classes. If it's not overridden but is needed, a (crude) finite-difference estimate of the Jacobian is used.
 
 For flexibility, the derived class could be a template, so that the solver/method can be chosen when the class is constructed. Other than defining the system of equations and setting initial conditions, the derived class can store whatever information and implement whatever other methods are necessary. This could be something simple like an extra function for setting initial conditions. It could, however, comprise any other system that needs to run on top of an ODE solver, like the spatial discretization of a big PDE solver.
 
@@ -113,11 +113,14 @@ The convergence and accuracy of all the solvers have been tested using a few pro
 ```
 ./test.sh adapt
 ```
-will compile and run the `test_adapt.exe` program, then plot the results (assuming Python and matplotlib are available). The image below shows the results of this program using the adaptive, fifth order `OdeDoPri54` class to solve a system of two coupled oscillators. The plot was generated from the top directory with these commands:
-
+will compile and run the `test_adapt.exe` program, then plot the results (assuming Python and matplotlib are available). The image below shows the results of this program using the adaptive, fifth order `OdeDoPri54` class to solve a system of two coupled oscillators.
 ![-](img/adapt.png)
 
-The `test_work` program examines how many function evaluations (the number of times the system of ODEs is evaluated) are required for different levels of accuracy for several methods. Each method solves an identical initial value problem and the final values are compared to a known solution. The plot below, generated with `./test.sh work`, shows the results. As expected, but still amazingly, the eighth order method of Dormand and Prince (`OdeDoPri87`) achieves error reduction by a factor of about 100,000,000 when the number of function calls is increased by a factor of 10.
+The `test_work` program examines how many function evaluations (the number of times the system of ODEs is evaluated) are required for different levels of accuracy for several methods. Each method solves an identical initial value problem and the final values are compared to a known solution. The plot below, generated by running
+```
+./test.sh work
+```
+shows the results. As expected, but still amazingly, the eighth order method of Dormand and Prince (`OdeDoPri87`) achieves error reduction by a factor of about 100,000,000 when the number of function calls is increased by a factor of 10.
 
 ![-](img/work.png)
 

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diff --git a/docs/class_newton_backward_euler-members.html b/docs/class_newton_backward_euler-members.html
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