Kelvin Smith Library celebrates scholarship at Case Western Reserve University by recognizing faculty authors in the Case School of Engineering, College of Arts and Sciences, and the Weatherhead School of Management who have written or edited books.
"Distributions in the Physical and Engineering Sciences" is a comprehensive exposition on analytic methods for solving science and engineering problems. It is written from the unifying viewpoint of distribution theory and enriched with many modern topics which are important for practitioners and researchers. The goal of the books is to give the reader, specialist and non-specialist, useable and modern mathematical tools in their research and analysis. "Volume 2: Linear and Nonlinear Dynamics of Continuous Media" continues the multivolume project which endeavors to show how the theory of distributions, also called the theory of generalized functions, can be used by graduate students and researchers in applied mathematics, physical sciences, and engineering. It contains an analysis of the three basic types of linear partial differential equations--elliptic, parabolic, and hyperbolic--as well as chapters on first-order nonlinear partial differential equations and conservation laws, and generalized solutions of first-order nonlinear PDEs. Nonlinear wave, growing interface, and Burger s equations, KdV equations, and the equations of gas dynamics and porous media are also covered. The careful explanations, accessible writing style, many illustrations/examples and solutions also make it suitable for use as a self-study reference by anyone seeking greater understanding and proficiency in the problem solving methods presented. The book is ideal for a general scientific and engineering audience, yet it is mathematically precise. Features . Application oriented exposition of distributional (Dirac delta) methods in the theory of partial differential equations. Abstract formalism is keep to a minimum. . Careful and rich selection of examples and problems arising in real-life situations. Complete solutions to all exercises appear at the end of the book. . Clear explanations, motivations, and illustration of all necessary mathematical concepts. "
This essentially self-contained, deliberately compact, and user-friendly textbook is designed for a first, one-semester course in statistical signal analysis for a broad audience of students in engineering and the physical sciences. The emphasis throughout is on fundamental concepts and relationships in the statistical theory of stationary random signals, explained in a concise, yet fairly rigorous presentation. Topics and Features: - Fourier series and transforms - fundamentally important in random signal analysis and processing - are developed from scratch, emphasizing the time-domain vs. frequency-domain duality. - Basic concepts of probability theory, laws of large numbers, the stability of fluctuations law, and statistical parametric inference procedures are presented so that no prior knowledge of probability and statistics is required; the only prerequisite is a basic two-three semester calculus sequence. - Introduction of the fundamental concept of a stationary random signal and its autocorrelation structure. - Power spectra of stationary signals and transmission analysis. - Filter design with optimal signal-to-noise ratio. power spectrum density. - Complementary bibliography for readers who wish to pursue the study of random signals in greater depth. - Problems and exercises at the end of each chapter. Developed by the author over the course of several years of classroom use, this text may be used by junior/senior undergraduates or graduate students in electrical, systems, computer, and biomedical engineering, as well as the physical sciences. The work is also an excellent resource of educational and training materials for industrial audiences
A comprehensive exposition on analytic methods for solving science and engineering problems, written from the unifying viewpoint of distribution theory and enriched with many modern topics which are important to practioners and researchers. The book is ideal for a general scientific and engineering audience, yet it is mathematically precise.
This IMA Volume in Mathematics and its Applications NONLINEAR STOCHASTIC PDEs: HYDRODYNAMIC LIMIT AND BURGERS' TURBULENCE is based on the proceedings of the period of concentration on Stochas tic Methods for Nonlinear PDEs which was an integral part of the 1993- 94 IMA program on "Emerging Applications of Probability." We thank Tadahisa Funaki and Wojbor A. Woyczynski for organizing this meeting and for editing the proceedings. We also take this opportunity to thank the National Science Foundation and the Army Research Office, whose financial support made this workshop possible. A vner Friedman Willard Miller, Jr. xiii PREFACE A workshop on Nonlinear Stochastic Partial Differential Equations was held during the week of March 21 at the Institute for Mathematics and Its Applications at the University of Minnesota. It was part of the Special Year on Emerging Applications of Probability program put together by an organizing committee chaired by J. Michael Steele. The selection of topics reflected personal interests of the organizers with two areas of emphasis: the hydrodynamic limit problems and Burgers' turbulence and related models. The talks and the papers appearing in this volume reflect a number of research directions that are currently pursued in these areas."
This self-contained and user-friendly textbook is designed for a first, one-semester course in statistical signal analysis for a broad audience of students in engineering and the physical sciences. The emphasis throughout is on fundamental concepts and relationships in the statistical theory of stationary random signals, which are explained in a concise, yet rigorous presentation. With abundant practice exercises and thorough explanations, A First Course in Statistics for Signal Analysis is an excellent tool for both teaching students and training laboratory scientists and engineers. Improvements in the second edition include considerably expanded sections, enhanced precision, and more illustrative figures.