piecewise continuous

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11: 18.2 General Orthogonal Polynomials

… ►Here $w(x)$ is continuous or piecewise continuous or integrable such that …

12: 1.9 Calculus of a Complex Variable

… ►If $x(t)$ and $y(t)$ are continuous and $x^{\prime }(t)$ and $y^{\prime }(t)$ are piecewise continuous, then $z(t)$ defines a contour. …

13: About Color Map

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Continuous Phase Mapping

►For the continuous phase mapping, we map the phase continuously onto the hue, as both are periodic. … ►We therefore use a piecewise linear mapping as illustrated below, that takes phase $0$ to red, $\pi /2$ to yellow, $\pi$ to cyan and $3\pi /2$ to blue. ►

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Figure 3: Continuous phase mapping

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14: 1.6 Vectors and Vector-Valued Functions

… ►when $f$ is continuous, and … ►The curve $C$ is piecewise differentiable if $𝐜$ is piecewise differentiable. … … ►Sufficient conditions for this result to hold are that $F_1(x,y)$ and $F_2(x,y)$ are continuously differentiable on $S$, and $C$ is piecewise differentiable. … ►Suppose $S$ is a piecewise smooth surface which forms the complete boundary of a bounded closed point set $V$, and $S$ is oriented by its normal being outwards from $V$. …

15: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

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§1.18(vi) Continuous Spectra and Eigenfunction Expansions: Simple Cases

… ►and completeness relation … ► … ►For $f(x)$ piecewise continuously differentiable on $[0,\mathrm{\infty })$ … ►

§1.18(vii) Continuous Spectra: More General Cases

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