So I've been reading about the general history of the Roman Empire lately, and I found it curious that the Romans seemed to try their hardest to expand west (until they hit the sea), north (Britanic and Germanic tribes) and east (Parthian Empire). Yet there seems to be very little information on the expansion south. Do we know why they stopped with only North Africa and not, say, expand down the west or east coast of the African continent?
It could be argued that a reason for this would be economic necessity coupled with geographic boundaries. To the east you would of had long established trade routes that helped to support the Roman Empire and previous empires before it. Therefore there was a real economic value in expanding towards the east, I am sure there was other factors to do with territorial considerations and such but the Romans were a very pragmatic bunch when it came to conquering. Therein lies the root answer to your question. The Romans initially expanded into North Africa because of the Punic Wars and the need to ensure another Carthage would not rise up once more. I imagine that once Carthage was dealt with they realized the potential of the trade routes Carthage cultivated with neighboring states and instead of becoming a trading Empire they instead sought to conquer. This would account for their expansion through North Africa. Then why didn't they expand southward? I believe there are Roman maps that show most of the African continent or at least the coastal areas so they would have known there was land to expand into. However with the major geographical boundary of the the Sahara desert along with the fact that little was known about the African interior leads me to think that at the time it was seen as a waste of resources to expand in that direction considering there were plenty of other regions closer to home with proven resources and less daunting geography. This however is a rough explanation as while I am studying to be a historian my area of knowledge has more to do with 15th to 18th century Europe. I am sure someone with a background in more classical history would be able to give a more thorough explanation.
They did expand South into North Africa, and in the 2nd/3rd Century had an emperor from the province of Africa (Septimius Severus, from what would now be Libya, I think). They basically expanded as far south as the Sahara, which is an obvious and very challenging natural barrier. Although the borders of the Empire often changed, stopping at a massive natural barrier was pretty common (like the Danube in the North or Euphrates in the South) - it's good for defence and you have to have a good reason to want to go a good way beyond it to make further incursion worthwhile. At the greatest extent of their empire, the Romans also controlled the Nile much further south, about as far as Sudan. Taking Carthage in the 2nd C BCE had great strategic value, and they wanted to keep hold of it as much to prevent other powers from doing so as anything else. Like a lot of frontier territories, this also required controlling surrounding lands to establish more secure borders. The African province suffered raids along its borders, and keeping the border at the Sahara made it easier to control.
Since Septimius Severus led the expansion to the south to its greatest extent during the empire, a good place to look for views on motivations for expansion and where they stopped is Anthony Birley's "Septimius Severus". There are some hints at motives and the Historia Augusta and in Cassius Dio, but you have to take these with a pretty hefty pinch of salt. This isn't my specialism, so I know I have oversimplified massively and that there are many more complex reasons and scholarly works about it than this!