declared: in the include directory of your system/SDK (e.g.: /usr/include;/Developer/Platforms/iPhoneOS.platform/Developer/SDKs/iPhoneOS3.2.sdk/usr/include/architecture/arm/math.h)
defined (implemented):
- as library (compiled, binary code): in the library directory of your system/SDK (e.g.: /usr/lib (in case of the math library it's libm.dylib)
- as source (program code): this is the interesting part. I work on a Mac OS X 10.6.x right now. The sources for the functions declared in math.h (e.g.: extern double pow ( double, double ); ) are not shipped with the installation (at least I couldn't find it). You are likely to find those sources in your system/SDK's C library. In my case the math library (libm) is a separate project, some of its sources are provided by Apple: http://www.opensource.apple.com/tarballs/Libm/Libm-315.tar.gz
The extern keyword in the function declaration of pow means, that it's defined somewhere else. Math functions are low-level high-performance implementations mostly done in assembly code (*.s). The assembly routines (taking the arguments/giving the parameters via registers/stack) are linked with the rest of the C library. The linking/exporting of the function/routine names is platform specific and doesn't really matter if ones goal is not dive into assembly coding.
I hope this helped,
Raphael