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Author: Ernst Hairer Publisher: Springer Science & Business Media ISBN: 0387770364 Category : Mathematics Languages : en Pages : 390
Book Description
This book presents first-year calculus roughly in the order in which it was first discovered. The first two chapters show how the ancient calculations of practical problems led to infinite series, differential and integral calculus and to differential equations. The establishment of mathematical rigour for these subjects in the 19th century for one and several variables is treated in chapters III and IV. Many quotations are included to give the flavor of the history. The text is complemented by a large number of examples, calculations and mathematical pictures and will provide stimulating and enjoyable reading for students, teachers, as well as researchers.
Author: Ernst Hairer Publisher: Springer Science & Business Media ISBN: 0387770364 Category : Mathematics Languages : en Pages : 390
Book Description
This book presents first-year calculus roughly in the order in which it was first discovered. The first two chapters show how the ancient calculations of practical problems led to infinite series, differential and integral calculus and to differential equations. The establishment of mathematical rigour for these subjects in the 19th century for one and several variables is treated in chapters III and IV. Many quotations are included to give the flavor of the history. The text is complemented by a large number of examples, calculations and mathematical pictures and will provide stimulating and enjoyable reading for students, teachers, as well as researchers.
Author: Hans Niels Jahnke Publisher: American Mathematical Soc. ISBN: 9780821890509 Category : Mathematics Languages : en Pages : 436
Book Description
Analysis as an independent subject was created as part of the scientific revolution in the seventeenth century. Kepler, Galileo, Descartes, Fermat, Huygens, Newton, and Leibniz, to name but a few, contributed to its genesis. Since the end of the seventeenth century, the historical progress of mathematical analysis has displayed unique vitality and momentum. No other mathematical field has so profoundly influenced the development of modern scientific thinking. Describing this multidimensional historical development requires an in-depth discussion which includes a reconstruction of general trends and an examination of the specific problems. This volume is designed as a collective work of authors who are proven experts in the history of mathematics. It clarifies the conceptual change that analysis underwent during its development while elucidating the influence of specific applications and describing the relevance of biographical and philosophical backgrounds. The first ten chapters of the book outline chronological development and the last three chapters survey the history of differential equations, the calculus of variations, and functional analysis. Special features are a separate chapter on the development of the theory of complex functions in the nineteenth century and two chapters on the influence of physics on analysis. One is about the origins of analytical mechanics, and one treats the development of boundary-value problems of mathematical physics (especially potential theory) in the nineteenth century. The book presents an accurate and very readable account of the history of analysis. Each chapter provides a comprehensive bibliography. Mathematical examples have been carefully chosen so that readers with a modest background in mathematics can follow them. It is suitable for mathematical historians and a general mathematical audience.
Author: Michael J. Crowe Publisher: Courier Corporation ISBN: 0486679101 Category : Mathematics Languages : en Pages : 306
Book Description
Prize-winning study traces the rise of the vector concept from the discovery of complex numbers through the systems of hypercomplex numbers to the final acceptance around 1910 of the modern system of vector analysis.
Author: Thomas Sonar Publisher: Springer Nature ISBN: 303058223X Category : Mathematics Languages : en Pages : 706
Book Description
What exactly is analysis? What are infinitely small or infinitely large quantities? What are indivisibles and infinitesimals? What are real numbers, continuity, the continuum, differentials, and integrals? You’ll find the answers to these and other questions in this unique book! It explains in detail the origins and evolution of this important branch of mathematics, which Euler dubbed the “analysis of the infinite.” A wealth of diagrams, tables, color images and figures serve to illustrate the fascinating history of analysis from Antiquity to the present. Further, the content is presented in connection with the historical and cultural events of the respective epochs, the lives of the scholars seeking knowledge, and insights into the subfields of analysis they created and shaped, as well as the applications in virtually every aspect of modern life that were made possible by analysis.
Author: Odd Aalen Publisher: Springer Science & Business Media ISBN: 038768560X Category : Mathematics Languages : en Pages : 550
Book Description
The aim of this book is to bridge the gap between standard textbook models and a range of models where the dynamic structure of the data manifests itself fully. The common denominator of such models is stochastic processes. The authors show how counting processes, martingales, and stochastic integrals fit very nicely with censored data. Beginning with standard analyses such as Kaplan-Meier plots and Cox regression, the presentation progresses to the additive hazard model and recurrent event data. Stochastic processes are also used as natural models for individual frailty; they allow sensible interpretations of a number of surprising artifacts seen in population data. The stochastic process framework is naturally connected to causality. The authors show how dynamic path analyses can incorporate many modern causality ideas in a framework that takes the time aspect seriously. To make the material accessible to the reader, a large number of practical examples, mainly from medicine, are developed in detail. Stochastic processes are introduced in an intuitive and non-technical manner. The book is aimed at investigators who use event history methods and want a better understanding of the statistical concepts. It is suitable as a textbook for graduate courses in statistics and biostatistics.
Author: H. H. Goldstine Publisher: Springer Science & Business Media ISBN: 1468494724 Category : Mathematics Languages : en Pages : 361
Book Description
In this book I have attempted to trace the development of numerical analysis during the period in which the foundations of the modern theory were being laid. To do this I have had to exercise a certain amount of selectivity in choosing and in rejecting both authors and papers. I have rather arbitrarily chosen, in the main, the most famous mathematicians of the period in question and have concentrated on their major works in numerical analysis at the expense, perhaps, of other lesser known but capable analysts. This selectivity results from the need to choose from a large body of literature, and from my feeling that almost by definition the great masters of mathematics were the ones responsible for the most significant accomplishments. In any event I must accept full responsibility for the choices. I would particularly like to acknowledge my thanks to Professor Otto Neugebauer for his help and inspiration in the preparation of this book. This consisted of many friendly discussions that I will always value. I should also like to express my deep appreciation to the International Business Machines Corporation of which I have the honor of being a Fellow and in particular to Dr. Ralph E. Gomory, its Vice-President for Research, for permitting me to undertake the writing of this book and for helping make it possible by his continuing encouragement and support.
Author: Barry Salt Publisher: ISBN: 9780950906652 Category : Performing Arts Languages : en Pages : 453
Book Description
Film Style and Technology is a history of film style and its relationship to film technology. It also includes a theory of film analysis and demonstrates this theory using the films of Max Ophuls.
Author: Paul David Allison Publisher: SAGE ISBN: 9780803920552 Category : Social Science Languages : en Pages : 92
Book Description
Drawing on recent "event history" analytical methods from biostatistics, engineering, and sociology, this clear and comprehensive monograph explains how longitudinal data can be used to study the causes of deaths, crimes, wars, and many other human events. Allison shows why ordinary multiple regression is not suited to analyze event history data, and demonstrates how innovative regression - like methods can overcome this problem. He then discusses the particular new methods that social scientists should find useful.
Author: Melinda Mills Publisher: SAGE ISBN: 1848601026 Category : Social Science Languages : en Pages : 301
Book Description
This book is an accessible, practical and comprehensive guide for researchers from multiple disciplines including biomedical, epidemiology, engineering and the social sciences. Written for accessibility, this book will appeal to students and researchers who want to understand the basics of survival and event history analysis and apply these methods without getting entangled in mathematical and theoretical technicalities. Inside, readers are offered a blueprint for their entire research project from data preparation to model selection and diagnostics. Engaging, easy to read, functional and packed with enlightening examples, ‘hands-on’ exercises, conversations with key scholars and resources for both students and instructors, this text allows researchers to quickly master advanced statistical techniques. It is written from the perspective of the ‘user’, making it suitable as both a self-learning tool and graduate-level textbook. Also included are up-to-date innovations in the field, including advancements in the assessment of model fit, unobserved heterogeneity, recurrent events and multilevel event history models. Practical instructions are also included for using the statistical programs of R, STATA and SPSS, enabling readers to replicate the examples described in the text.
Author: Judy L. Klein Publisher: Cambridge University Press ISBN: 9780521420464 Category : Business & Economics Languages : en Pages : 376
Book Description
"This work documents the history of techniques that statisticians use to manipulate economic, meteorological, biological, and physical data taken from observations recorded over time. The decomposition tools include index numbers, moving averages, relative time frameworks, and the use of differences (i.e., subtracting one observation from the previous value in the series). This history is accessible to students with a basic knowledge of statistics, as well as financial analysts, statisticians, and historians of economic thought and science."--BOOK JACKET.
Author: Ernst Hairer
Author: Ernst Hairer
Author: Hans Niels Jahnke
Author: Michael J. Crowe
Author: Thomas Sonar
Author: Odd Aalen
Author: H. H. Goldstine
Author: Barry Salt
Author: Paul David Allison
Author: Melinda Mills
Author: Judy L. Klein