“Dirac delta function”的概念、定义、翻译、参考文献-科学参考

Dirac delta function

Mathematics

The Dirac delta function δ‎(x) has defining properties $\int_{- \infty}^{\infty} δ (x) d x = 1$ , and δ‎(x) = 0 for x ≠ 0. No function, in the traditional sense, has these properties, but δ‎(x) can be rigorously understood as the Schwartz distribution δ‎(φ‎) = φ‎(0), where φ‎ is a test function. The delta function is useful for modelling point masses or charges, or instantaneous impulses. As a distribution it is the derivative of the Heaviside function. See sifting property.

Electronics and Electrical Engineering

A spike or impulse with infinite amplitude for zero time but with unit area. It is designated as δ(t), which means a unit impulse at time zero, or, more generally as δ(t–a), which means a unit impulse at time a. Although the delta function is a mathematical conception, it can nonetheless be approximated to a pulse of sufficiently short duration to appear instantaneous in comparison with the time constant of the circuit, and constitutes a powerful analytic tool in circuit theory and analysis.

单词	Dirac delta function
释义	Dirac delta function Mathematics The Dirac delta function δ‎(x) has defining properties $\int_{- \infty}^{\infty} δ (x) d x = 1$ , and δ‎(x) = 0 for x ≠ 0. No function, in the traditional sense, has these properties, but δ‎(x) can be rigorously understood as the Schwartz distribution δ‎(φ‎) = φ‎(0), where φ‎ is a test function. The delta function is useful for modelling point masses or charges, or instantaneous impulses. As a distribution it is the derivative of the Heaviside function. See sifting property. Electronics and Electrical Engineering A spike or impulse with infinite amplitude for zero time but with unit area. It is designated as δ(t), which means a unit impulse at time zero, or, more generally as δ(t–a), which means a unit impulse at time a. Although the delta function is a mathematical conception, it can nonetheless be approximated to a pulse of sufficiently short duration to appear instantaneous in comparison with the time constant of the circuit, and constitutes a powerful analytic tool in circuit theory and analysis.
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