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Asymptotic Series
The Taylor series expansions of Section 3.5 might have a large radius of convergence, but…
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Fourier Series
The Fourier series expansion was introduced briefly in Chapter 1, where the behaviour of this…
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Pointwise Convergence And Uniform Convergence
The previous section informed us that sequences can converge in different ways, assuming that they…
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Sequences and Series
Introduction Sequences and series have a major role to play in computational methods. In this…
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Number Representations
Introduction In this chapter we consider how numbers are represented on a computer largely with…
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The Discrete Fourier Series (Dfs)
The subject of discrete Fourier series (DFS) and its relationship to the complex Fourier series…
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Inner Products and Inner Product Spaces
The concept of an inner product is necessary before one can talk about orthogonal bases…
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Norms and Normed Spaces
So far our examples of function spaces have been metric spaces (Section 1.3.1). Such spaces…
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Some Special Mappings: Metrics, Norms, And Inner Products
Sets of objects (vectors, sequences, polynomials, functions, etc.) often have certain special mappings defined on…