Methods

Investigation of the functional architecture of the human brain using modern noninvasive imaging techniques is a rapidly expanding area of research. A proper knowledge of methodology is needed to appreciate the burgeoning literature in the field. This timely publication provides an excellent catalogue of the main techniques.The authors offer an invaluable analysis of mapping strategies and techniques, providing everything from the foundations to the major pitfalls and practical applications of the modern techniques used in neuroimaging. Contains over 1000 full color pages with more than 200 color figures. Spanning the methodological gamut from the molecular level to the whole brain while discussing anatomy, physiology, and pathology, as well as their integration, Brain Mapping: The Methods, 2e, brings the reader a comprehensive, well-illustrated and entirely readable description of the methods for brain mapping. Drs. Toga and Mazziotta provide everything from the foundations to the maj

This well-known text and reference contains an account of those parts of mathematics that are most frequently needed in physics. As a working rule, it includes methods which have applications in at least two branches of physics. The authors have aimed at a high standard of rigour and have not accepted the often-quoted opinion that 'any argument is good enough if it is intended to be used by scientists'. At the same time, they have not attempted to achieve greater generality than is required for the physical applications: this often leads to considerable simplification of the mathematics. Particular attention is also paid to the conditions under which theorems hold. Examples of the practical use of the methods developed are given in the text: these are taken from a wide range of physics, including dynamics, hydrodynamics, elasticity, electromagnetism, heat conduction, wave motion and quantum theory. Exercises accompany each chapter.

This work provides a lucid and rigorous account of the foundations of algebraic geometry. The authors have confined themselves to fundamental concepts and geometrical methods, and do not give detailed developments of geometrical properties but geometrical meaning has been emphasised throughout. Here in this volume, the authors have again confined their attention to varieties defined on a ground field without characteristic. In order to familiarize the reader with the different techniques available to algebraic geometers, they have not confined themselves to one method and on occasion have deliberately used more advanced methods where elementary ones would serve, when by so doing it has been possible to illustrate the power of the more advanced techniques, such as valuation theory. The other two volumes of Hodge and Pedoe's classic work are also available. Together, these books give an insight into algebraic geometry that is unique and unsurpassed.

Most functions that occur in mathematics cannot be used directly in computer calculations. Instead they are approximated by manageable functions such as polynomials and piecewise polynomials. The general theory of the subject and its application to polynomial approximation are classical, but piecewise polynomials have become far more useful during the last twenty years. Thus many important theoretical properties have been found recently and many new techniques for the automatic calculation of approximations to prescribed accuracy have been developed. This book gives a thorough and coherent introduction to the theory that is the basis of current approximation methods. Professor Powell describes and analyses the main techniques of calculation supplying sufficient motivation throughout the book to make it accessible to scientists and engineers who require approximation methods for practical needs. Because the book is based on a course of lectures to third-year undergraduates in mathematic

A unique introduction to the design, analysis, and presentation of scientific projects, this is an essential textbook for undergraduate majors in science and mathematics. The textbook gives an overview of the main methods used in scientific research, including hypothesis testing, the measurement of functional relationships, and observational research. It describes important features of experimental design, such as the control of errors, instrument calibration, data analysis, laboratory safety, and the treatment of human subjects. Important concepts in statistics are discussed, focusing on standard error, the meaning of p values, and use of elementary statistical tests. The textbook introduces some of the main ideas in mathematical modeling, including order-of-magnitude analysis, function fitting, Fourier transforms, recursion relations, and difference approximations to differential equations. It also provides guidelines on accessing scientific literature, and preparing scientific paper

This work provides a lucid and rigorous account of the foundations of modern algebraic geometry. The authors have confined themselves to fundamental concepts and geometrical methods, and do not give detailed developments of geometrical properties, but geometrical meaning has been emphasised throughout. This first volume is divided into two parts. The first is devoted to pure algebra; the basic notions, the theory of matrices over a non-commutative ground field and a study of algebraic equations. The second part is concerned with the definitions and basic properties of projective space in n dimensions. It concludes with a purely algebraic account of collineations and correlations. The other two volumes of Hodge and Pedoe's classic work are also available. Together, these books give an insight into algebraic geometry that is unique and unsurpassed.

Learn how to plan for success with this hands-on guide to conducting high-quality engineering research. Plan and implement your next project for maximum impact: step-by-step instructions cover every stage in engineering research, from the identification of an appropriate research topic through to the successful presentation of results. Improve your research outcomes: discover essential tools and methods for producing high-quality, rigorous research, including statistical analysis, survey design, and optimisation techniques. Research with purpose and direction: clear explanations, real-world examples, and over 50 customisable end-of-chapter exercises, all written with the practical and ethical considerations of engineering in mind. A unique engineering perspective: written especially for engineers, and relevant across all engineering disciplines, this is the ideal book for graduate students, undergraduates, and new academics looking to launch their research careers.

Learn how to plan for success with this hands-on guide to conducting high-quality engineering research. Plan and implement your next project for maximum impact: step-by-step instructions cover every stage in engineering research, from the identification of an appropriate research topic through to the successful presentation of results. Improve your research outcomes: discover essential tools and methods for producing high-quality, rigorous research, including statistical analysis, survey design, and optimisation techniques. Research with purpose and direction: clear explanations, real-world examples, and over 50 customisable end-of-chapter exercises, all written with the practical and ethical considerations of engineering in mind. A unique engineering perspective: written especially for engineers, and relevant across all engineering disciplines, this is the ideal book for graduate students, undergraduates, and new academics looking to launch their research careers.

Written as both a textbook and a handy reference, this text deliberately avoids complex mathematics assuming only basic familiarity with geodynamic theory and calculus. Here, the authors have brought together the key numerical techniques for geodynamic modeling, demonstrations of how to solve problems including lithospheric deformation, mantle convection and the geodynamo. Building from a discussion of the fundamental principles of mathematical and numerical modeling, the text moves into critical examinations of each of the different techniques before concluding with a detailed analysis of specific geodynamic applications. Key differences between methods and their respective limitations are also discussed - showing readers when and how to apply a particular method in order to produce the most accurate results. This is an essential text for advanced courses on numerical and computational modeling in geodynamics and geophysics, and an invaluable resource for researchers looking to master

This is a one-stop introduction to the methods of ergodic theory applied to holomorphic iteration. The authors begin with introductory chapters presenting the necessary tools from ergodic theory thermodynamical formalism, and then focus on recent developments in the field of 1-dimensional holomorphic iterations and underlying fractal sets, from the point of view of geometric measure theory and rigidity. Detailed proofs are included. Developed from university courses taught by the authors, this book is ideal for graduate students. Researchers will also find it a valuable source of reference to a large and rapidly expanding field. It eases the reader into the subject and provides a vital springboard for those beginning their own research. Many helpful exercises are also included to aid understanding of the material presented and the authors provide links to further reading and related areas of research.

This graduate-level textbook on thermal physics covers classical thermodynamics, statistical mechanics and its applications. It describes theoretical methods to calculate thermodynamic properties, such as the equation of state, specific heat, Helmholtz free energy, magnetic susceptibility and phase transitions of macroscopic systems. In addition to the more standard material covered, this book also describes powerful techniques, which are not found elsewhere, to determine the correlation effects on which the thermodynamic properties are based. Particular emphasis is given to the cluster variation method and a novel formulation is developed for its expression in terms of correlation functions. Although a basic knowledge of quantum mechanics is required, the mathematical formulations are accessible and entirely self-contained. The book will therefore constitute an ideal companion text for graduate students studying courses on the theory of complex analysis, classical mechanics, classical

This graduate-level textbook on thermal physics covers classical thermodynamics, statistical mechanics and its applications. It describes theoretical methods to calculate thermodynamic properties, such as the equation of state, specific heat, Helmholtz free energy, magnetic susceptibility and phase transitions of macroscopic systems. In addition to the more standard material covered, this book also describes powerful techniques, which are not found elsewhere, to determine the correlation effects on which the thermodynamic properties are based. Particular emphasis is given to the cluster variation method and a novel formulation is developed for its expression in terms of correlation functions. Although a basic knowledge of quantum mechanics is required, the mathematical formulations are accessible and entirely self-contained. The book will therefore constitute an ideal companion text for graduate students studying courses on the theory of complex analysis, classical mechanics, classical

Samuel Squire Sprigge (1860–1937) was a qualified physician who worked for The Lancet from 1892 and was editor from 1909 until his death. He published several books including a history of the journal and its founder, and a volume of essays, Physic and Fiction. The Methods of Publishing first appeared in 1890 and is Sprigge's passionate contribution to the late-nineteenth-century discussion on how the question of literary property is best resolved. Sprigge argues that this matter is often treated in a cavalier manner that disadvantages authors, particularly in the relationship between publisher and author. In his view, book prices are too low, copyright protection for authors is insufficient, the royalty system is in chaos, and authors do not obtain a fair share of profits. He proposes that literary property questions be treated with the same legal formality and protection as is found in other business dealings.

This text focuses on a variety of topics in mathematics in common usage in graduate engineering programs including vector calculus, linear and nonlinear ordinary differential equations, approximation methods, vector spaces, linear algebra, integral equations and dynamical systems. The book is designed for engineering graduate students who wonder how much of their basic mathematics will be of use in practice. Following development of the underlying analysis, the book takes students through a large number of examples that have been worked in detail. Students can choose to go through each step or to skip ahead if they so desire. After seeing all the intermediate steps, they will be in a better position to know what is expected of them when solving assignments, examination problems, and when on the job. Chapters conclude with exercises for the student that reinforce the chapter content and help connect the subject matter to a variety of engineering problems. Students have grown up with com

In Methods of Social Study Sidney and Beatrice Webb describe in detail how they conducted their investigations into social history and institutions - from the collection, recording and classification of the data (both documentary and oral), through the processes of hypothesis and analysis, down to the preparation of the final report. The Webbs were in many respects pioneers, and what they achieved and the way in which they achieved it are of an importance that has been increasingly recognised as the passage of times gives us perspective. Their constant concern was to ensure that their work would be 'scientific'. They stress the need in scientific research for complete objectivity, to be achieved in their case by keeping their historical and sociological studies wholly separate from their political writings. Because the first drafts for the book were made by Beatrice in 1921 and the final text was written by Sidney in 1931/2, one can also see expressed here, more clearly than elsewhere,

Using participatory and practical action research models, this first-of-its kind text walks readers through the procedural steps in in designing, conducting, implementing, and reporting an action rese

This volume describes modern tools and techniques to study nuclear pore complexes and nucleocytoplasmic transport in diverse eukaryotic models systems (mammalian cells, Xenopus, C. elegans, yeast) The