Analytical and Numerical Methods for Vibration Analyses

Scattering-based numerical methods are increasingly applied to the numerical simulation of distributed time-dependent physical systems. These methods, which possess excellent stability and stability verification properties, have appeared in various guises as the transmission line matrix (TLM) method, multidimensional wave digital (MDWD) filtering and digital waveguide (DWN) methods. This text provides a unified framework for all of these techniques and addresses the question of how they are related to more standard numerical simulation techniques. Covering circuit/scattering models in electromagnetics, transmission line modelling, elastic dynamics, as well as time-varying and nonlinear systems, this book highlights the general applicability of this technique across a variety of disciplines, as well as the inter-relationships between simulation techniques and digital filter design. provides a comprehensive overview of scattering-based numerical integration methods. reviews the basics of classical electrical network theory, wave digital filters, and digital waveguide networks. discusses applications for time-varying and nonlinear systems. includes an extensive bibliography containing over 250 references. Mixing theory and application with numerical simulation results, this book will be suitable for both experts and readers with a limited background in signal processing and numerical techniques.

Mathematical Methods for Physical and Analytical Chemistry presents mathematical and statistical methods to students of chemistry at the intermediate, post-calculus level. The content includes a review of general calculus; a review of numerical techniques often omitted from calculus courses, such as cubic splines and Newton’s method; a detailed treatment of statistical methods for experimental data analysis; complex numbers; extrapolation; linear algebra; and differential equations. With numerous example problems and helpful anecdotes, this text gives chemistry students the mathematical knowledge they need to understand the analytical and physical chemistry professional literature.

Food and dairy powders are created by dehydrating perishable produce, such as milk, eggs, fruit and meat, in order to extend their shelf life and stabilise them for storage or transport. These powders are in high demand for use as ingredients and as food products in their own right, and are of great economic importance to the food and dairy industry worldwide. Today, the ability to control food and dairy powder quality is a source of key competitive advantage. By varying the dehydration process design, and by controlling the technological and thermodynamic parameters during dehydration, it is possible for manufacturers to engineer the biochemical, microbiological and physical characteristics of the food powder to meet their specific product requirements. This book provides an overview of the existing, adapted or new techniques used to analyse safety and quality in modern food and dairy powders. Based on original research by the authors, the book uses 25 commercial dairy and non-dairy powders to illustrate a range of biochemical and physical methods used to evaluate and characterise powdered food products. Written from a practical perspective, each chapter focuses on a particular analytical technique, outlining the purpose, definition and principle of that method. The authors guide the reader through all of the instruments needed, the safety measures required, and the correct procedures to follow to ensure successful analysis. Instructions on accurate measurement and expression of results are included, and each chapter is richly illustrated with original data and worked examples. Analytical Methods for Food and Dairy Powders is a unique step-by-step handbook, which will be required reading for anyone involved in the development and manufacture of powdered food products. Food and dairy scientists based in industry will find it essential for new product development and improved quality control, while researchers in the laboratory will especially value the new techniques it comprises.

This book studies methods to concretely address inverse problems. An inverse problem arises when the causes that produced a given effect must be determined or when one seeks to indirectly estimate the parameters of a physical system. The author uses practical examples to illustrate inverse problems in physical sciences. He presents the techniques and specific methods chosen to solve inverse problems in a general domain of application, choosing to focus on a small number of methods that can be used in most applications. This book is aimed at readers with a mathematical and scientific computing background. Despite this, it is a book with a practical perspective. The methods described are applicable, have been applied, and are often illustrated by numerical examples.

Numerical Methods for Partial Differential Equations: An Introduction Vitoriano Ruas, Sorbonne Universit?s, UPMC – Universit? Paris 6, France A comprehensive overview of techniques for the computational solution of PDE's Numerical Methods for Partial Differential Equations: An Introduction covers the three most popular methods for solving partial differential equations: the finite difference method, the finite element method and the finite volume method. The book combines clear descriptions of the three methods, their reliability, and practical implementation aspects. Justifications for why numerical methods for the main classes of PDE's work or not, or how well they work, are supplied and exemplified. Aimed primarily at students of Engineering, Mathematics, Computer Science, Physics and Chemistry among others this book offers a substantial insight into the principles numerical methods in this class of problems are based upon. The book can also be used as a reference for research work on numerical methods for PDE’s. Key features: A balanced emphasis is given to both practical considerations and a rigorous mathematical treatment The reliability analyses for the three methods are carried out in a unified framework and in a structured and visible manner, for the basic types of PDE's Special attention is given to low order methods, as practitioner's overwhelming default options for everyday use New techniques are employed to derive known results, thereby simplifying their proof Supplementary material is available from a companion website.

This book is a compilation of summarized analytical methods designed to serve the needs of pharmacologists, toxicologists, and other allied health professionals involved the development, use, or monitoring of pharmaceuticals. The summaries are structured monographs on 511 different drug entities detailing 964 different analytical methods, providing the reader with a thorough description of method validation. These analytical methods include not only high performance liquid chromatography (HPLC), but also gas chromatography (GC), immunoassay, electrophoresis, ultra performance liquid chromatography (UPLC) coupled with UV (UPLC-UV) detection and mass spectrometry (UPLC-MS/MS). With more detailed and complete summaries than sketchy and abbreviated formats used in the other books, this book provides a thorough description of method validation and results, as well as the operating parameters.

The importance of partial differential equations (PDEs) in modeling phenomena in engineering as well as in the physical, natural, and social sciences is well known by students and practitioners in these fields. Striking a balance between theory and applications, Fourier Series and Numerical Methods for Partial Differential Equations presents an introduction to the analytical and numerical methods that are essential for working with partial differential equations. Combining methodologies from calculus, introductory linear algebra, and ordinary differential equations (ODEs), the book strengthens and extends readers' knowledge of the power of linear spaces and linear transformations for purposes of understanding and solving a wide range of PDEs. The book begins with an introduction to the general terminology and topics related to PDEs, including the notion of initial and boundary value problems and also various solution techniques. Subsequent chapters explore: The solution process for Sturm-Liouville boundary value ODE problems and a Fourier series representation of the solution of initial boundary value problems in PDEs The concept of completeness, which introduces readers to Hilbert spaces The application of Laplace transforms and Duhamel's theorem to solve time-dependent boundary conditions The finite element method, using finite dimensional subspaces The finite analytic method with applications of the Fourier series methodology to linear version of non-linear PDEs Throughout the book, the author incorporates his own class-tested material, ensuring an accessible and easy-to-follow presentation that helps readers connect presented objectives with relevant applications to their own work. Maple is used throughout to solve many exercises, and a related Web site features Maple worksheets for readers to use when working with the book's one- and multi-dimensional problems. Fourier Series and Numerical Methods for Partial Differential Equations is an ideal book for courses on applied mathematics and partial differential equations at the upper-undergraduate and graduate levels. It is also a reliable resource for researchers and practitioners in the fields of mathematics, science, and engineering who work with mathematical modeling of physical phenomena, including diffusion and wave aspects.

Discover how analytical chemistry supports the latest clinical research This book details the role played by analytical chemistry in fostering clinical research. Readers will discover how a broad range of analytical techniques support all phases of clinical research, from early stages to the implementation of practical applications. Moreover, the contributing authors' careful step-by-step guidance enables readers to better understand standardized techniques and steer clear of everyday problems that can arise in the lab. Analytical Techniques for Clinical Chemistry opens with an overview of the legal and regulatory framework governing clinical lab analysis. Next, it details the latest progress in instrumentation and applications in such fields as biomonitoring, diagnostics, food quality, biomarkers, pharmaceuticals, and forensics. Comprised of twenty-five chapters divided into three sections exploring Fundamentals, Selected Applications, and Future Trends, the book covers such critical topics as: Uncertainty in clinical chemistry measurements Metal toxicology in clinical, forensic, and chemical pathology Role of analytical chemistry in the safety of drug therapy Atomic spectrometric techniques for the analysis of clinical samples Biosensors for drug analysis Use of X-ray techniques in medical research Each chapter is written by one or more leading pioneers and experts in analytical chemistry. Contributions are based on a thorough review and analysis of the current literature as well as the authors' own firsthand experiences in the lab. References at the end of each chapter serve as a gateway to the literature, enabling readers to explore individual topics in greater depth. Presenting the latest achievements and challenges in the field, Analytical Techniques for Clinical Chemistry sets the foundation for future advances in laboratory research techniques.

A new edition of this classic work, comprehensively revised to present exciting new developments in this important subject The study of numerical methods for solving ordinary differential equations is constantly developing and regenerating, and this third edition of a popular classic volume, written by one of the world’s leading experts in the field, presents an account of the subject which reflects both its historical and well-established place in computational science and its vital role as a cornerstone of modern applied mathematics. In addition to serving as a broad and comprehensive study of numerical methods for initial value problems, this book contains a special emphasis on Runge-Kutta methods by the mathematician who transformed the subject into its modern form dating from his classic 1963 and 1972 papers. A second feature is general linear methods which have now matured and grown from being a framework for a unified theory of a wide range of diverse numerical schemes to a source of new and practical algorithms in their own right. As the founder of general linear method research, John Butcher has been a leading contributor to its development; his special role is reflected in the text. The book is written in the lucid style characteristic of the author, and combines enlightening explanations with rigorous and precise analysis. In addition to these anticipated features, the book breaks new ground by including the latest results on the highly efficient G-symplectic methods which compete strongly with the well-known symplectic Runge-Kutta methods for long-term integration of conservative mechanical systems. This third edition of Numerical Methods for Ordinary Differential Equations will serve as a key text for senior undergraduate and graduate courses in numerical analysis, and is an essential resource for research workers in applied mathematics, physics and engineering.

Basic theory, applications, and recent trends in analytical techniques used in crude oil and related products analysis This book covers the application of different spectroscopic methods to characterize crude oil and related products. Its topics are presented in a pedagogical manner so that those new to the subject can better understand the content. The book begins by familiarizing the reader with the rheological characterization of crude oil and related products. Subsequent chapters are directed towards the current trends of different spectroscopic methods for the characterization of crude oil. Analytical Characterization Methods for Crude Oil and Related Products features chapters on: optical interrogation of petroleum asphaltenes (myths and reality); ESR characterization of organic free radicals in petroleum products; high-field, pulsed, and double resonance studies of crude oils and their derivatives; NMR spectroscopy in bitumen characterization; applications of Raman spectroscopy in crude oil and bitumen characterization; and more. Uses a bottom-up approach—starting from the basic theory of the technique followed by its applications and recent trends in crude oil analysis Includes informative content so as to take a technician to the level of using a particular analytical method Covers relevany information so as to enable a manager in the industry to make purchasing decisions Analytical Characterization Methods for Crude Oil and Related Products is aimed at researchers in academia as well as technicians and developers of new analytical methods in the oil industry and related areas. It will also be of interest to professionals, scientists, and graduate students in analytical sciences dealing with oil and environmental analysis.