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.
Calculus is the mathematical method for the analysis of things that change, and since in the natural world we are surrounded by change, the development of calculus was a huge breakthrough in the history of mathematics. David Acheson charts the historical development of calculus and takes readers through the basic ideas, step by step.
The interest earned on a bank account, the arrangement of seeds in a sunflower, and the shape of the Gateway Arch in St. Louis are all intimately connected with the mysterious number e. In this informal and engaging history, Eli Maor portrays the curious characters and the elegant mathematics that lie behind the number. Designed for a reader with only a modest mathematical background, this biography brings out the central importance of e to mathematics and illuminates a golden era in the age of science.
Thucydides´ History of the Peloponnesian War is generally acknowledged as the first great work in the fields of both history and political theory. It uses a combination of narrative, debate, and analysis to document the war between Athens and Sparta (431-404 BC). But the importance of the work lies less in the story than in the way Thucydides tells it. History was the first major work of political inquiry that did not relate events to divine influences. It introduced instead a critical method of looking to the facts of human actions as the basis of our understanding - a method that continues to be used today, more than two millennia later. Many of the most important political thinkers in the Western tradition cite Thucydides as an influence, and major figures including Thomas Hobbes, David Hume, and Friedrich Nietzsche have praised his writing. 1. Language: English. Narrator: Macat.com. Audio sample: http://samples.audible.de/bk/acx0/060532/bk_acx0_060532_sample.mp3. Digital audiobook in aax.
Phenomenology in a New Key - Between Analysis and History:Essays in Honor of Richard Cobb-Stevens. Auflage 2015
Phenomenology in a New Key: Between Analysis and History:Essays in Honor of Richard Cobb-Stevens Contributions to Phenomenology. Softcover reprint of the original 1st ed. 2015
The general purpose of this book is to show how broad classes of stochastic processes can be of considerable use in the statistical modelling and analysis of survival data, or more broadly, in event history analysis. The authors will show a number of connections between process theory and statistics, focusing on the intuitive aspects and playing down theoretical details. The book shall also be practical, directed to people who want to apply the methods, and with reference to computer programs. 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.
Polymetrical Analysis. History Concepts Applications.: Petro Trokhimchuck
An Analysis and History of Inflation: Don Paarlberg