First Course In Mathematical Modeling Pdf
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Modelling and Applications in Mathematics Education
Author: Peter L. Galbraith
language: en
Publisher: Springer Science & Business Media
Release Date: 2007-12-05
Among the themes that have been central to mathematics education dur ing the last 30 years are those of mathematical modelling and applications of mathematics to extra-mathematical fields. More generally we refer to these as relations between mathematics and the extra-mathematical world (some times also called the "real world") or preferably, according to Henry PoUak, the "rest of the world". That applications and modelling have been important themes in mathematics education can be inferred from the wealth of litera ture on these topics, including material generated from a multitude of na tional and international conferences. In particular let us mention firstly the ICMEs (the International Congresses on Mathematical Education), with their regular working or topic groups and lectures on applications and modelling; and secondly the series of ICTMAs (the International Conferences on the Teaching of Mathematical Modelling and Applications) which have been held biennially since 1983. Their Proceedings and Survey Lectures, have addressed the state-of-the-art at the relevant time, and contain many exam ples, studies, conceptual contributions and resources involving relations between the real world and mathematics, for all levels of the educational system. In curricula and textbooks we find today many more references to real world phenomena and problems than, say, twenty years ago.
Mathematical Modeling in the Age of the Pandemic
One cannot watch or read about the news these days without hearing about the models for COVID-19 or the testing that must occur to approve vaccines or treatments for the disease. The purpose of Mathematical Modeling in the Age of a Pandemic is to shed some light on the meaning and interpretations of many of the types of models that are or might be used in the presentation of analysis. Understanding the concepts presented is essential in the entire modeling process of a pandemic. From the virus itself and its infectious rates and deaths rates to explain the process for testing a vaccine or eventually a cure, the author builds, presents, and shows model testing. This book is an attempt, based on available data, to add some validity to the models developed and used, showing how close to reality the models are to predicting "results" from previous pandemics such as the Spanish flu in 1918 and more recently the Hong Kong flu. Then the author applies those same models to Italy, New York City, and the United States as a whole. Modeling is a process. It is essential to understand that there are many assumptions that go into the modeling of each type of model. The assumptions influence the interpretation of the results. Regardless of the modeling approach the results generally indicate approximately the same results. This book reveals how these interesting results are obtained.
A First Course In Partial Differential Equations
Author: J Robert Buchanan
language: en
Publisher: World Scientific Publishing Company
Release Date: 2017-10-30
This textbook gives an introduction to Partial Differential Equations (PDEs), for any reader wishing to learn and understand the basic concepts, theory, and solution techniques of elementary PDEs. The only prerequisite is an undergraduate course in Ordinary Differential Equations. This work contains a comprehensive treatment of the standard second-order linear PDEs, the heat equation, wave equation, and Laplace's equation. First-order and some common nonlinear PDEs arising in the physical and life sciences, with their solutions, are also covered.This textbook includes an introduction to Fourier series and their properties, an introduction to regular Sturm-Liouville boundary value problems, special functions of mathematical physics, a treatment of nonhomogeneous equations and boundary conditions using methods such as Duhamel's principle, and an introduction to the finite difference technique for the numerical approximation of solutions. All results have been rigorously justified or precise references to justifications in more advanced sources have been cited. Appendices providing a background in complex analysis and linear algebra are also included for readers with limited prior exposure to those subjects.The textbook includes material from which instructors could create a one- or two-semester course in PDEs. Students may also study this material in preparation for a graduate school (masters or doctoral) course in PDEs.