## Solve Differential Equations in Milliseconds!

Berkeley Madonna is arguably the fastest, most convenient, general purpose differential equation solver available today. It is relatively inexpensive and runs on both Windows and Mac OS. Developed on the Berkeley campus under the sponsorship of NSF and NIH, it is currently used by academic and commercial institutions for constructing mathematical models for research and teaching.

### New for Windows and macOS

### Error in documentation for normal random number syntax

The correct syntax for generating a random number y with a normal distribution is y = normal(µ, sd) where µ is the mean and sd is the standard deviation. Older versions of the Equation Help menu as well as the User’s Guide erroneously stated that the second argument was the variance.

### What's going on with Berkeley Madonna

The compute engine of Berkeley Madonna was originally written in C, and later extended with the Flowchart graphical interface written in Java. Because of changes in Apple's Java implementation in OS X, it has been difficult to retain the same architecture on the Macintosh as in Windows.

A version of Berkeley Madonna, called JMadonna, is in development. It will have the user interface written in Java, while retaining the simulation engine in C for speed. This will allow us to extend Berkeley Madonna in many ways, including a Linux version. Before JMadonna is released, however, we are releasing an interim version of Madonna (8.3) for Windows and Macintosh with support for global variables in the Flowchart, nullclines on the phase plane (see below),as well as an improved Fourier transform, an improved pulse function and a more efficient web-based registration through Kagi.

The PC version works well in most versions of Windows. The Flowchart in the Mac version, however, works only in OS 10.4 (Tiger). The equation-only version works in all versions of OS X.

### Globals: Flowchart - Equation Window Hybridization

A "globals" dialog has been added which allows you to add equation definitions directly into the equation window without having to create flow chart icons. (Windows and Mac). These definitions are globally available to all icons in the flow chart through their usual dialogs. This can be used to reduce flow chart clutter by moving all secondary definitions off the flow chart into the equation window. E.g. use it for dimensional definitions, physical constants, secondary parameters and variables, etc. An example is given in the program under Help > How do I> Use global variables

### Nullclines: where derivatives change sign

Using a phase plane plot with a second order system, you can display the nullclines simply by clicking on the Nc button in the graph toolbar. The legend button identifies each nullcline. An example is given in the program under Help > How do I > Plot Nullclines