I am trying to find additional information on the important geographic factors and technologic advances that encouraged America to grow in the 1800s.

The main geographic factor was the huge amount of American territory, spanning the continent from the Atlantic to the Pacific.

Two of the most important inventions were the McCormick reaper and the John Deere steel plow. These enabled farmers to plow the prairie soil more easily and harvest wheat faster.

http://www.state.il.us/hpa/PrairiePages/Vol4n3ILAgPP.pdf

The telegraph and intercontinental railroad helped people and messages move from coast to coast.

The discovery of gold in the West had a hand in the westward expansion also, as another geographical factor.

the discovery of vast coal mining areas made a large difference in the rate of advancement in development and expantion.