Numerical method 1 min read
Asymptotic Series
The Taylor series expansions of Section 3.5 might have a large radius of convergence, but practically speaking, if x is…
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Fourier Series
The Fourier series expansion was introduced briefly in Chapter 1, where the behaviour of this series with respect to its…
Numerical method 1 min read
Pointwise Convergence And Uniform Convergence
The previous section informed us that sequences can converge in different ways, assuming that they converge in any sense at…
Numerical method 1 min read
Sequences and Series
Introduction Sequences and series have a major role to play in computational methods. In this chapter we consider various types…
Numerical method 1 min read
Number Representations
Introduction In this chapter we consider how numbers are represented on a computer largely with respect to the errors that…
Numerical method 1 min read
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…
Numerical method 1 min read
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…
Numerical method 1 min read
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…
Numerical method 3 min read
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…
Numerical method 4 min read
Functional Analysis Ideas
Introduction Many engineering analysis and design problems are far too complex to be solved without the aid of computers. However,…