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This concise and up-to-date textbook is designed for the standard sophomore course in differential equations. It treats the basic ideas, models, and solution methods in a user friendly format that is accessible to engineers, scientists, economists, and mathematics majors. It emphasizes analytical, graphical, and numerical techniques, and it provides the tools needed by students to continue to the next level in applying the methods to more advanced problems. There is a strong connection to applications with motivations in mechanics and heat transfer, circuits, biology, economics, chemical reactors, and other areas. Exceeding the first edition by over one hundred pages, this new edition has a large increase in the number of worked examples and practice exercises, and it continues to provide templates for MATLAB and Maple commands and codes that are useful in differential equations. Sample examination questions are included for students and instructors. Solutions of many of the exercises are contained in an appendix. Moreover, the text contains a new, elementary chapter on systems of differential equations, both linear and nonlinear, that introduces key ideas without matrix analysis. Two subsequent chapters treat systems in a more formal way. Briefly, the topics include: * First-order equations: separable, linear, autonomous, and bifurcation phenomena; * Second-order linear homogeneous and non-homogeneous equations; * Laplace transforms; and * Linear and nonlinear systems, and phase plane properties.

Differential equations --- Mathematics --- Planning (firm) --- differentiaalvergelijkingen --- toegepaste wiskunde --- mathematische modellen

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Regression is the branch of Statistics in which a dependent variable of interest is modelled as a linear combination of one or more predictor variables, together with a random error. The subject is inherently two- or higher- dimensional, thus an understanding of Statistics in one dimension is essential. Regression: Linear Models in Statistics fills the gap between introductory statistical theory and more specialist sources of information. In doing so, it provides the reader with a number of worked examples, and exercises with full solutions. The book begins with simple linear regression (one predictor variable), and analysis of variance (ANOVA), and then further explores the area through inclusion of topics such as multiple linear regression (several predictor variables) and analysis of covariance (ANCOVA). The book concludes with special topics such as non-parametric regression and mixed models, time series, spatial processes and design of experiments. Aimed at 2nd and 3rd year undergraduates studying Statistics, Regression: Linear Models in Statistics requires a basic knowledge of (one-dimensional) Statistics, as well as Probability and standard Linear Algebra. Possible companions include John Haigh's Probability Models, and T. S. Blyth & E.F. Robertsons' Basic Linear Algebra and Further Linear Algebra.

Statistical science --- Mathematics --- Applied physical engineering --- toegepaste wiskunde --- economie --- statistiek --- wiskunde --- statistisch onderzoek --- Regression Analysis

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Regression is the branch of Statistics in which a dependent variable of interest is modelled as a linear combination of one or more predictor variables, together with a random error. The subject is inherently two- or higher- dimensional, thus an understanding of Statistics in one dimension is essential. Regression: Linear Models in Statistics fills the gap between introductory statistical theory and more specialist sources of information. In doing so, it provides the reader with a number of worked examples, and exercises with full solutions. The book begins with simple linear regression (one predictor variable), and analysis of variance (ANOVA), and then further explores the area through inclusion of topics such as multiple linear regression (several predictor variables) and analysis of covariance (ANCOVA). The book concludes with special topics such as non-parametric regression and mixed models, time series, spatial processes and design of experiments. Aimed at 2nd and 3rd year undergraduates studying Statistics, Regression: Linear Models in Statistics requires a basic knowledge of (one-dimensional) Statistics, as well as Probability and standard Linear Algebra. Possible companions include John Haigh’s Probability Models, and T. S. Blyth & E.F. Robertsons’ Basic Linear Algebra and Further Linear Algebra.

Statistical science --- Mathematics --- Applied physical engineering --- toegepaste wiskunde --- economie --- statistiek --- wiskunde --- statistisch onderzoek

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This new approach to real analysis stresses the use of the subject in applications, showing how the principles and theory of real analysis can be applied in various settings. Applications cover approximation by polynomials, discrete dynamical systems, differential equations, Fourier series and physics, Fourier series and approximation, wavelets, and convexity and optimization. Each chapter has many useful exercises. The treatment of the basic theory covers the real numbers, functions, and calculus, while emphasizing the role of normed vector spaces, and particularly of Rn. The applied chapters are mostly independent, giving the reader a choice of topics. This book is appropriate for students with a prior knowledge of both calculus and linear algebra who want a careful development of both analysis and its use in applications. Review of the previous version of this book, Real Analysis with Real Applications: "A well balanced book! The first solid analysis course, with proofs, is central in the offerings of any math.-dept.; ---and yet, the new books that hit the market don't always hit the mark: the balance between theory and applications, ---between technical proofs and intuitive ideas, ---between classical and modern subjects, and between real life exercises vs. the ones that drill a new concept. The Davidson-Donsig book is outstanding, and it does hit the mark." Palle E. T. Jorgenson, Review from Amazon.com Kenneth R. Davidson is University Professor of Mathematics at the University of Waterloo. Allan P. Donsig is Associate Professor of Mathematics at the University of Nebraska-Lincoln.

Functional analysis --- Differential equations --- Mathematical analysis --- Mathematics --- Applied physical engineering --- analyse (wiskunde) --- toegepaste wiskunde --- economie --- mathematische modellen --- wiskunde

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Proper management of evacuation processes is one of the basic requirements within life safety concepts, and it helps to prevent critical situations from getting out of control. Super high-rise buildings, deep underground stations or shopping areas, airplanes for the mass transportation, sport stadiums or meeting places with tens of thousands of visitors they all call for new dim- sionsinsafeevacuationplanning. Researchresultsinevacuationdynamicsgive answers to these challenges. PED-conferences are the prime address for all research in this ?eld. The increasing number of participants from di?erent ?elds of research re?ect theirimportance. AfterPED-conferencesinGermany(Duisburg,2001),Great Britain (Greenwich, 2003) and Austria (Vienna, 2005), the PED 2008 C- ference in Wuppertal/Germany reached new heights with more than 120 p- ticipants from 20 countries and nearly 100 presentations. The wide ?eld of topics discussed in presentations also re?ects deeper understanding of fun- mental e?ects as well as the stronger interactions between di?erent research areas. New test designs o?er new important basic data, new analysis pro- dures open a better understanding of complex interactions, new model - signs allow more realistic simulations, and the input from architectural - sign and the medical references on physical limitations help to realize a safe evacuation design. On the one hand all these data give an outlook of future possibilities and sometimes they open an astonishing new understanding of seemingly well-known data. On the other hand, they make clear the limi- tions of our current knowledge.

Social psychology --- Mathematics --- Applied physical engineering --- Transport engineering --- Civil engineering. Building industry --- gedrag (mensen) --- toegepaste wiskunde --- economie --- motorrijtuigen --- wiskunde --- ingenieurswetenschappen