Complex Variables

This monograph presents the current status of a rapidly developing part of several complex variables, motivated by the applicability of effective results to algebraic geometry and differential geometr

Unique in its clarity, examples, and range, Physical Mathematics explains simply and succinctly the mathematics that graduate students and professional physicists need to succeed in their courses and research. The book illustrates the mathematics with numerous physical examples drawn from contemporary research. This second edition has new chapters on vector calculus, special relativity and artificial intelligence and many new sections and examples. In addition to basic subjects such as linear algebra, Fourier analysis, complex variables, differential equations, Bessel functions, and spherical harmonics, the book explains topics such as the singular value decomposition, Lie algebras and group theory, tensors and general relativity, the central limit theorem and Kolmogorov's theorems, Monte Carlo methods of experimental and theoretical physics, Feynman's path integrals, and the standard model of cosmology.

How we vary our speech is fundamental in signalling who we are, where we're from and where we're going. How and when does such variation arise? Here, leading experts Jennifer Smith and Mercedes Durham address this question through a sociolinguistic analysis of the speech of preschool children in interaction with their primary caregivers. Bringing together two fields of linguistic research - variationist sociolinguistics and first language acquisition - the study focusses both qualitative and quantitative analysis of a range of variables to show when and how variation is acquired by young children, and the effect the caregiver's interaction has on this process. In doing so, they tackle a fundamental question in language research: when and how do children acquire the highly complex patterns of variation widely attested in adult speech?