This updated introduction to modern numerical analysis is a complete revision of a classic text originally written in Fortran but now featuring the programming language C++. It considers a relatively small number of basic concepts and techniques, focusing on how and why each method works. The authors offer careful consideration of error-analysis aspects related to the problems and algorithms. The treatment also reviews and solidifies basic concepts from elementary calculus, emphasizing theory and proofs. It makes repeated use of the mean-value theorem, intermediate-value theorem, and Taylor's series. Many exercises appear throughout the text, most with solutions, and an extensive tutorial explains how to solve problems with C++.