Returning a shared library symbol table

For instance:

void* sdl_library = dlopen("libSDL.so", RTLD_LAZY);
void* initializer = dlsym(sdl_library,"SDL_Init");

Assuming no errors, initializer will point to the function SD_Init in the shared library libSDK.so.

However this requires knowing the symbol "SDL_Init" exists.

Is it possibly to query a library for all its symbols? Eg, in this case it would return SDL_Init, the function pointer, and any other symbols exported by libSDL.so.