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Sequences and Series

Introduction Sequences and series have a major role to play in computational methods. In this chapter we consider various types…

Number Representations

Introduction In this chapter we consider how numbers are represented on a computer largely with respect to the errors that…

The Discrete Fourier Series (Dfs)

The subject of discrete Fourier series (DFS) and its relationship to the complex Fourier series expansion is often deferred to…

Inner Products and Inner Product Spaces

The concept of an inner product is necessary before one can talk about orthogonal bases for vector spaces. Recall from…

Norms and Normed Spaces

So far our examples of function spaces have been metric spaces (Section 1.3.1). Such spaces are not necessarily associated with…

Some Special Mappings: Metrics, Norms, And Inner Products

Sets of objects (vectors, sequences, polynomials, functions, etc.) often have certain special mappings defined on them that turn these sets…

Some Sets

Functional Analysis Ideas

Introduction Many engineering analysis and design problems are far too complex to be solved without the aid of computers. However,…