boot - How to delete a non-working kernel after update?

I have. a simple question. After I updated my kernel, I couldn't boot (stuck on purple screen) unless I chose the old kernel. So how do I delete the new kernel with synaptic. And how do I do this safely? I'm in Quantal Quetzel. My kernel is 3.5.0-40. The working kernel is 3.5.0-39. Also, how do I stop kernel updates from appearing in the update manager? Thanks.

To safely remove the unwanted kernel, open a terminal session and run the command:

Find the kernel package name

dpkg -l | grep linux-image

At the time of writing, on amd64/x86_64 architecture the image name was: linux-image-$(uname -r)-generic

For unsigned kernel images, like those created by nvidia drivers, the image could be: linux-image-unsigned-4.20.17-042017-generic

Remove (purge - remove all configuration files as well)

sudo apt-get purge linux-image-3.5.0-40-generic

NOTE: For Ubuntu 18.04 LTS or later, you may also want to remove any linux-modules or linux-headers packages of the same version to save disk spaces / keep you system lean.