# The inverse function theorem for everywhere differentiable maps

The classical inverse function theorem reads as follows:

Theorem 1 ($latex {C^1}&fg=000000$ inverse function theorem) Let $latex {\Omega \subset {\bf R}^n}&fg=000000$ be an open set, and let $latex {f: \Omega \rightarrow {\bf R}^n}&fg=000000$ be an continuously differentiable function, such that for every $latex {x_0 \in \Omega}&fg=000000$, the derivative map $latex {Df(x_0): {\bf R}^n \rightarrow {\bf R}^n}&fg=000000$ is invertible. Then $latex {f}&fg=000000$ is a local homeomorphism; thus, for every $latex {x_0 \in \Omega}&fg=000000$, there exists an open neighbourhood $latex {U}&fg=000000$ of $latex {x_0}&fg=000000$ and an open neighbourhood $latex {V}&fg=000000$ of $latex {f(x_0)}&fg=000000$ such that $latex {f}&fg=000000$ is a homeomorphism from $latex {U}&fg=000000$ to $latex {V}&fg=000000$.

# Get your Raspberry Pi kit together!

Okay, so you have "registered an interest" or pre-ordered or even (lucky few) ordered an RPi. It's time to get together the stuff you'll need.

1. A screen. The most obvious choice is a TV with an HDMI input.

2. A usb mouse. If you don't have a spare around, why not treat yourself to a new one - you're worth it!

# While you wait for your Raspberry Pi, why not use RacyPy2?

How to use RacyPy or WaryPy.

2. Download and install DVD Decrypter (or use you favourite .iso burning software).

3. Right click on the .iso file and choose "Burn with DVD Decrypter.

4. Reboot your PC. It should boot from the CD, if it doesn't do this by default, look for a message telling you what to press for boot options (often F2 or F9).