The objective of this textbook is the construction, analysis, and interpretation of mathematical models to help us understand the world we live in. Rather than follow a case study approach it develops the mathematical and physical ideas that are fundamental in understanding contemporary problems in science and engineering. Science evolves, and this means that the problems of current interest continually change. What does not change as quickly is the approach used to derive the relevant mathematical models, and the methods used to analyze the models. Consequently, this book is written in such a way as to establish the mathematical ideas underlying model development independently of a specific application. This does not mean applications are not considered, they are, and connections with experiment are a staple of this book. The book, as well as the individual chapters, is written in such a way that the material becomes more sophisticated as you progress. This provides some flexibility in how the book is used, allowing consideration for the breadth and depth of the material covered. Moreover, there are a wide spectrum of exercises and detailed illustrations that significantly enrich the material. Students and researchers interested in mathematical modelling in mathematics, physics, engineering and the applied sciences will find this text useful. The material, and topics, have been updated to include recent developments in mathematical modeling. The exercises have also been expanded to include these changes, as well as enhance those from the first edition. Review of first edition: "The goal of this book is to introduce the mathematical tools needed for analyzing and deriving mathematical models. ... Holmes is able to integrate the theory with application in a very nice way providing an excellent book on applied mathematics. ... One of the best features of the book is the abundant number of exercises found at the end of each chapter. ... I think this is a great book, and I recommend it for scholarly purposes by students, teachers, and researchers." Joe Latulippe, The Mathematical Association of America, December, 2009
This introductory graduate text is based on a graduate course the author has taught repeatedly over the last ten years to students in applied mathematics, engineering sciences, and physics. Each chapter begins with an introductory development involving ordinary differential equations, and goes on to cover such traditional topics as boundary layers and multiple scales. However, it also contains material arising from current research interest, including homogenisation, slender body theory, symbolic computing, and discrete equations. Many of the excellent exercises are derived from problems of up-to-date research and are drawn from a wide range of application areas. One hundred new pages added including new material on transcedentally small terms, Kummer's function, weakly coupled oscillators and wave interactions.
FOAM. This acronym has been used for over ?fty years at Rensselaer to designate an upper-division course entitled, Foundations of Applied Ma- ematics. This course was started by George Handelman in 1956, when he came to Rensselaer from the Carnegie Institute of Technology. His objective was to closely integrate mathematical and physical reasoning, and in the p- cess enable students to obtain a qualitative understanding of the world we live in. FOAM was soon taken over by a young faculty member, Lee Segel. About this time a similar course, Introduction to Applied Mathematics, was introduced by Chia-Ch’iao Lin at the Massachusetts Institute of Technology. Together Lin and Segel, with help from Handelman, produced one of the landmark textbooks in applied mathematics, Mathematics Applied to - terministic Problems in the Natural Sciences. This was originally published in 1974, and republished in 1988 by the Society for Industrial and Applied Mathematics, in their Classics Series. This textbook comes from the author teaching FOAM over the last few years. In this sense, it is an updated version of the Lin and Segel textbook.
This textbook provides an introduction to numerical computing and its applications in science and engineering. The topics covered include those usually found in an introductory course, as well as those that arise in data analysis. This includes optimization and regression-based methods using a singular value decomposition. The emphasis is on problem solving, and there are numerous exercises throughout the text concerning applications in engineering and science. The essential role of the mathematical theory underlying the methods is also considered, both for understanding how the method works, as well as how the error in the computation depends on the method being used. The codes used for most of the computational examples in the text are available on GitHub. This new edition includes material necessary for an upper division course in computational linear algebra.
This book shows how to derive, test and analyze numerical methods for solving differential equations, including both ordinary and partial differential equations. The objective is that students learn to solve differential equations numerically and understand the mathematical and computational issues that arise when this is done. Includes an extensive collection of exercises, which develop both the analytical and computational aspects of the material. In addition to more than 100 illustrations, the book includes a large collection of supplemental material: exercise sets, MATLAB computer codes for both student and instructor, lecture slides and movies.
Polymer chemistry and technology form one of the major areas of molecular and materials science. This field impinges on nearly every aspect of modern life, from electronics technology, to medicine, to the wide range of fibers, films, elastomers, and structural materials on which everyone depends. Although most of these polymers are organic materials, attention is being focused increasingly toward polymers that contain inorganic elements as well as organic components. The goal of Inorganic Polymers is to provide a broad overview of inorganic polymers in a way that will be useful to both the uninitiated and those already working in this field. There are numerous reasons for being interested in inorganic polymers. One is the simple need to know how structure affects the properties of a polymer, particularly outside the well-plowed area of organic materials. Another is the bridge that inorganic polymers provide between polymer science and ceramics. More and more chemistry is being used in the preparation of ceramics of carefully controlled structure, and inorganic polymers are increasingly important precursor materials in such approaches. This new edition begins with a brief introductory chapter. That is followed with a discussion of the characteristics and characterization of polymers, with examples taken from the field. Other chapters in the book detail the synthesis, reaction chemistry, molecular structure, and uses of polyphosphazenes, polysiloxanes, and polysilanes. The coverage in the second edition has been updated and expanded significantly to cover advances and interesting trends since the first edition appeared. Three new chapters have been added, focusing on ferrocene-based polymers, other phosphorous-containing polymers, and boron-containing polymers; inorganic-organic hybrid composites; and preceramic inorganic polymers.
This introductory graduate text is based on a graduate course the author has taught repeatedly over the last ten years to students in applied mathematics, engineering sciences, and physics. Each chapter begins with an introductory development involving ordinary differential equations, and goes on to cover such traditional topics as boundary layers and multiple scales. However, it also contains material arising from current research interest, including homogenisation, slender body theory, symbolic computing, and discrete equations. Many of the excellent exercises are derived from problems of up-to-date research and are drawn from a wide range of application areas. One hundred new pages added including new material on transcedentally small terms, Kummer's function, weakly coupled oscillators and wave interactions.
We are living in a stressful world, yet despite our familiarity with the notion, stress remains an elusive concept. In The Age of Stress, Mark Jackson explores the history of scientific studies of stress in the modern world. In particular, he reveals how the science that legitimates and fuels current anxieties about stress has been shaped by a wide range of socio-political and cultural, as well as biological, factors: stress, he argues, is both a condition and a metaphor. In order to understand the ubiquity and impact of stress in our own times, or to explain how stress has commandeered such a central place in the modern imagination, Jackson suggests that we need to comprehend not only the evolution of the medical science and technology that has gradually uncovered the biological pathways between stress and disease in recent decades, but also the shifting social, economic, and cultural contexts that have invested that scientific knowledge with meaning and authority. In particular, he argues, we need to acknowledge the manner in which enduring concerns about the effects of stress on mental and physical health are the product of broader historical preoccupations with the preservation of personal and political, as well as physiological, stability.
A comprehensive reference on diagnosis and evaluation of reproductive risks and genetically related high-risk pregnancies. Authored by international group of experts, this book is organized according to diagnostic method, source of reproductive risk, and system under evaluation. Features the latest imaging technology, a review of genetics, molecular biology, and cytogenetics, and special chapters on counseling, cross-cultural, legal, and ethical issues.
If most Americans accept the notion that the market is the most efficient means to distribute resources, why should body parts be excluded? Each year thousands of people die waiting for organ transplants. Many of these deaths could have been prevented were it not for the almost universal moral hand-wringing over the concept of selling human organs. Kidney for Sale by Owner, now with a new preface, boldly deconstructs the roadblocks that are standing in the way of restoring health to thousands of people. Author and bioethicist Mark Cherry reasserts the case that health care could be improved and lives saved by introducing a regulated transplant organs market rather than by well-meant, but misguided, prohibitions.
Advances in long-term improvement and outcomes of patients with kidney disease will require the use of novel biomarkers to identify patients at high risk for kidney disease and to diagnose kidney disease early for effective treatment. A biomarker is a substance found in the blood, body fluids or tissues that provides a measure of normal biological or pathological processes or response to pharmacological compounds or drugs. There are a wide variety of biomarkers including but not limited to mRNA, proteins and peptides, and lipid molecules. In AKI, important pathophysiological processes such as inflammation, apoptotic and necrotic cell death and, tubule regeneration may be reflected in blood or urine. An array of candidate markers along with clinical information in long-term clinical studies with appropriate analytical methodologies will likely provide prognostic information. Despite well-known limitations, currently the most widely used biomarkers for the early diagnosis of CKD and AKI are proteinuria, serum creatinine and blood urea nitrogen. Most clinicians are aware that serum creatinine and blood urea nitrogen are poor biomarkers due to inherent characteristics of these molecules and handling by the kidney. Creatinine is secreted and urea nitrogen is reabsorbed by the renal tubules. Many endogenous substances interfere in the assay for creatinine. Serum creatinine and urea appear late after acute kidney injury and the serum levels in part depend on the generation (large or small body mass). Acute kidney injury is a non steady state condition thus serum creatinine and urea nitrogen will lag behind kidney injury. For these reasons new biomarkers are imperative. With knowledge of these limitations in use of current biomarkers and the lack of progress in reducing the mortality and morbidity from kidney disease, there has been a great surge of interest in identifying novel biomarkers with a particular emphasis on the early diagnosis of kidney disease. A variety of methods have been employed including transcriptomics, proteomics, gene arrays and lipidomics. Currently, candidate biomarkers have been found in different disorders and have been tested in humans and many candidate biomarkers have yet to be identified. Most studies to date are preliminary and require validation in large multicentre studies followed by commercial assay development validation and testing. This new book outlines the rapid advances made in the field of biomarker development for kidney disease in which a variety of novel molecules have been identified and studied in humans.
This book's message--that change is inevitable and that response to change determines the success of recovery--applies not only to chemical dependents, but also to codependents. It offers time-proven strategies for meeting the challenges that are sure to arise.
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