Merging Video Files
I had a need to merge 15 mp4 files recently and a simple tool for the job is Avidemux. Just open the first file and select Append from the File menu to select the next one. Repeat until all of your files have been added. The default encoding settings are copy for both video and audio so you shouldn't have to make any changes before saving the new file.
As with any encoding job it's always a good idea to test the output file. I have a new phone and for some reason the audio was getting messed up after the first clip. I've never experienced that problem in the past. If you run into this too the solution is to select a codec for the audio portion so it will be re-encoded. After that you should have the combined file you were looking for.