Email alerts while pool member up or down

The precise details of the solution, and the options available to you, depend on the version of BIG-IP code which you are running. Under 11.x, following SOL3667:

you could use the alertd mechanism. First, you need to follow the instructions in SOL13180 to configure outbound mail from the BIG-IP:

Then, add the following to /config/user_alert.conf:

alert BIGIP_MCPD_MCPDERR_POOL_MEMBER_MON_DOWN "Pool (.*?) member (.*?):(.*?) monitor status down." {
        email toaddress="receiver@yourcompany.com"
        fromaddress="root"
        body="A pool member went down"
}

alert BIGIP_MCPD_MCPDERR_POOL_MEMBER_MON_UP "Pool (.*?) member (.*?):(.*?) monitor status up." {
        email toaddress="receiver@yourcompany.com"
        fromaddress="root"
        body="A pool member came back up"
}

This will email every time any member of any pool goes "down" or "up".

If you are running BIG-IP version 11.4.x, you may also consider using iCall.