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Undergraduate Texts in Mathematics (UTM) (ISSN 0172-6056) is a series of undergraduate-level textbooks in mathematics published by Springer-Verlag.The books in this series, like the other Springer-Verlag mathematics series, are small yellow books of a standard size.
In mathematical analysis, Parseval's identity, named after Marc-Antoine Parseval, is a fundamental result on the summability of the Fourier series of a function. The identity asserts the equality of the energy of a periodic signal (given as the integral of the squared amplitude of the signal) and the energy of its frequency domain representation (given as the sum of squares of the amplitudes).
The source free equations can be written by the action of the exterior derivative on this 2-form. But for the equations with source terms (Gauss's law and the Ampère-Maxwell equation), the Hodge dual of this 2-form is needed. The Hodge star operator takes a p-form to a (n − p)-form, where n is the number of dimensions.
Laws of Form (hereinafter LoF) is a book by G. Spencer-Brown, published in 1969, that straddles the boundary between mathematics and philosophy. LoF describes three distinct logical systems : The primary arithmetic (described in Chapter 4 of LoF ), whose models include Boolean arithmetic ;
Nevertheless, his views—however informal—are a valuable contribution to the philosophy and anthropology of mathematics. [2] His views anticipate, in some respects, the more detailed account of the cognitive basis of mathematics given by George Lakoff and Rafael E. Núñez in their Where Mathematics Comes From.
Complex color plot of the Laguerre polynomial L n(x) with n as -1 divided by 9 and x as z to the power of 4 from -2-2i to 2+2i. In mathematics, the Laguerre polynomials, named after Edmond Laguerre (1834–1886), are nontrivial solutions of Laguerre's differential equation: ″ + ′ + =, = which is a second-order linear differential equation.
Digital textbooks are a major component of technology-based education reform. They may serve as the texts for a traditional face-to-face class, an online course or degree, or massive open online courses (MOOCs). As with physical textbooks, digital textbooks can be either rented for a term or purchased for lifetime access.
If the reduced form model is estimated using empirical data, obtaining estimated values for the coefficients , some of the structural parameters can be recovered: By combining the two reduced form equations to eliminate Z, the structural coefficients of the supply side model (and ) can be derived: