We already pointed out that numerical computations are subject to errors as soon as a variable is set, due to the fact that almost all numbers write with an infinite number of digits after the dot. Numerical analysis, though, is much more than the study of error propagation in calculation. Following Trefethen, we believe that Numerical Analysis is the study of algorithms to approximate solutions of problems of continuous mathematics. To keep things concrete, we present below two elementary examples of numerical algorithms. These examples will also introduce us to the other main source of errors in Numerical Analysis: the one due to truncation of expressions involving infinitely many terms or infinitely many steps.
