This work is an introductory course for undergraduate students. It is intended to achieve a balance between theory, algorithms and practical implementation aspects. Lloyd N. Trefethen proposed the following definition of Numerical Analysis: Numerical Analysis is the study of algorithms for the problems of continuous mathematics.
The keyword here is that of algorithms, and the main purpose of Numerical Analysis is devising and analyzing numerical algorithms to solve a certain class of problems. These are the problems of continuous mathematics. “Continuous” means here that input data are real and complex variables; its opposite is discrete. Shortly, one could say that Numerical analysis is continuous algorithmics, as opposed to classical algorithmics, that is discrete algorithmics.