Analysis Tools

Abstract

The development of numerical methods is based on fundamental mathematical analysis, and this chapter includes some of the basic concepts that are essential for later chapters. Even if numerical methods lead to a finite number of algebraic operations, it turns out that the theoretical analysis benefits from the introduction of the infinity concept, which will be discussed in the first section.

As we have seen in Chap.  2, we are dealing with small perturbations and small steps Δx when dealing with differential equations and their numerical solution. This makes it natural to discuss Taylor expansions, which we do in the second section.

The content of this chapter corresponds roughly to part of a first college course in mathematical analysis, and can be skipped by the reader who has this subject fresh in memory.