Update to 3.13 kernel on Ubuntu 13.10 [duplicate]

Since my ATI hybrid graphics card isn't working well under Linux, I wanted to try the new kernel. I don't want to update to 14.04 just yet, because of some missing dependencies and there doesn't seem to be a kernel for 13.10 in the Ubuntu mainline (kernel.ubuntu.com/~kernel-ppa/mainline/). Is there another way to install the new kernel?

Updating is quite easy, from this answer from Rinzwind:

Download the three .DEB files with the name starting with linux from here.

Example for i386 (take the 2 with amd64 in the name for 64-bit. Check uname -a if you are unsure):

linux-headers-3.13.0-031300_3.13.0-031300.201401192235_all.deb
linux-headers-3.13.0-031300-generic_3.13.0-031300.201401192235_i386.deb
linux-image-3.13.0-031300-generic_3.13.0-031300.201401192235_i386.deb

Install all 3 packages ...

Example for i386

dpkg -i linux-headers-3.13.0-031300_3.13.0-031300.201401192235_all.deb
dpkg -i linux-headers-3.13.0-031300-generic_3.13.0-031300.201401192235_i386.deb
dpkg -i linux-image-3.13.0-031300-generic_3.13.0-031300.201401192235_i386.deb