Introduction to Numerical Methods

Welcome

Welcome to my free interactive Numerical Methods text.

History and context of numerical methods

The majority of modern developments in numerical methods are from the post-World War II era, coinciding with the ever increasing use and power of digital computers.

Perhaps the most iconic example of this transition is the creation of the computer ENIAC, which was built in Philadelphia in 1945, and then moved to the Aberdeen Proving Ground in Maryland for military ballistic calculations in 1947. ENIAC was enormous, weighing 27 tons and consuming 150 kilowatts of electricity. The programmers for ENIAC were Kay McNulty, Betty Jennings, Betty Snyder, Marlyn Meltzer, Fran Bilas, and Ruth Lichterman. Shown below are Jennings and Bilas programming ENIAC (this is just the control panel!).

In 1947 the United States government began funding the Institute of Numerical Analysis (INA) at UCLA. The INA helped coordinate the rapid development of numerical linear algebra and numerical differential equations. Related efforts were made by the Office of Naval Research (ONR), led by Mina Rees, who also helped with the formation of the INA.

When computers were still very expensive they were mostly used to model large engineering projects such as nuclear reactors and submarines. Much of that modeling involved partial differential equations (PDEs), and so most of the "traditional" subjects of numerical analysis have some connection to providing approximations to PDEs. However, as the range of applications has expanded, so too has numerical analysis. In addition to its previous applications it is also very important in finance, computer graphics, and machine learning.