# normal_ode

normal_ode, an Octave code which describes an ordinary differential equation (ODE) for the normal probability density function (PDF).

The normal probability density function (PDF) can be written as

```        y(t) = 1/sqrt(2 pi) e^(-t^2/2)
```
The derivative of the normal PDF is
```        y'(t) = -t/sqrt(2 pi) e^(-t^2/2) = - t * y(t)
```

Thus, along with an initial condition, an ODE for the normal PDF can be written either as:

```        y'(t) = -t/sqrt(2 pi) e^(-t^2/2)
```
or
```        y'(t) = -t * y(t)
```
While both of these ODE's have the same solution, an ODE solver will generally have more difficulty solving the second version.

### Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

### Languages:

normal_ode is available in a MATLAB version and an Octave version.

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### Source Code:

• euler.m, solves an ordinary differential equation (ODE) using the Euler method.
• normal_deriv.m, returns the right hand side of an ODE that defines the normal PDF.
• normal_solution.m, returns value of the normal PDF.
• rms.m, returns the root mean square (RMS) norm of a vector.
• timestamp.m, prints the YMDHMS date as a timestamp.

Last revised on 12 October 2020.