Computation is a basic tool of modern applied mathematics. As discussed in the Approximation mini-essay it is used to repeatedly carry out calculation tasks when approximating solutions to complex problems that cannot be solved in closed form (or as formulae). The act of computing an approximate solution requires both mathematical approximation techniques and algorithms (hopefully better ones than the one pictured above).
However, computing an approximate solution is often only a start. The resulting data must be visualized and interpreted. Scientific Visualization is a mature discipline in itself with a strong aesthetic component. At times the effort put into post-processing scientific data is greater than that expended in obtaining the data. Some fields, like weather forecasting have their own specialized maps used to convey information in a standard way to all meteorologists. These often have historical ancestors that pre-date computers
A further development in modern applied mathematics is the development of so-called data products based on satellite data (GPS being the most well known example). Satellites have revolutionized the way we study the ocean, atmosphere and the climate. What is more, the advances made in post-processing have made it possible for data to be available for any scientist with access to a computer (see NASA’s wind applet, for example).
Computation
