Mathematical Modeling For The Scientific Method

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Mathematical Modeling for the Scientific Method

David Pravica,Michael Spurr
Mathematical Modeling for the Scientific Method Book PDF

Author : David Pravica,Michael Spurr
Publisher : Jones & Bartlett Learning
Page : 521 pages
File Size : 42,6 Mb
Release : 2011-08-24
Category : Mathematics
ISBN : 9780763779467

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Mathematical Modeling for the Scientific Method by David Pravica,Michael Spurr Pdf

Part of the International Series in Mathematics Mathematical Modeling for the Scientific Method is intended for the sophomore/junior-level student seeking to be well-grounded in mathematical modeling for their studies in biology, the physical sciences, engineering, and/or medicine. It clarifies the connection between deductive and inductive reasoning as used in Mathematics and Science and urges students to think critically about concepts and applications. The authors’ goal is to be introductory in level while covering a broad range of techniques. They unite topics in statistics, linear algebra, calculus and differential equations, while discussing how these subjects are interrelated and utilized. Mathematical Modeling for the Scientific Method leaves students with a clearer perspective of the role of mathematics within the sciences and the understanding of how to rationally work through even rigorous applications with ease.

Mathematical Modeling in Science and Engineering

Ismael Herrera,George F. Pinder
Mathematical Modeling in Science and Engineering Book PDF

Author : Ismael Herrera,George F. Pinder
Publisher : John Wiley & Sons
Page : 259 pages
File Size : 47,5 Mb
Release : 2012-03-19
Category : Technology & Engineering
ISBN : 9781118207208

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Mathematical Modeling in Science and Engineering by Ismael Herrera,George F. Pinder Pdf

A powerful, unified approach to mathematical and computational modeling in science and engineering Mathematical and computational modeling makes it possible to predict the behavior of a broad range of systems across a broad range of disciplines. This text guides students and professionals through the axiomatic approach, a powerful method that will enable them to easily master the principle types of mathematical and computational models used in engineering and science. Readers will discover that this axiomatic approach not only enables them to systematically construct effective models, it also enables them to apply these models to any macroscopic physical system. Mathematical Modeling in Science and Engineering focuses on models in which the processes to be modeled are expressed as systems of partial differential equations. It begins with an introductory discussion of the axiomatic formulation of basic models, setting the foundation for further topics such as: Mechanics of classical and non-classical continuous systems Solute transport by a free fluid Flow of a fluid in a porous medium Multiphase systems Enhanced oil recovery Fluid mechanics Throughout the text, diagrams are provided to help readers visualize and better understand complex mathematical concepts. A set of exercises at the end of each chapter enables readers to put their new modeling skills into practice. There is also a bibliography in each chapter to facilitate further investigation of individual topics. Mathematical Modeling in Science and Engineering is ideal for both students and professionals across the many disciplines of science and engineering that depend on mathematical and computational modeling to predict and understand complex systems.

Modelling Mathematical Methods and Scientific Computation

Nicola Bellomo,Luigi Preziosi
Modelling Mathematical Methods and Scientific Computation Book PDF

Author : Nicola Bellomo,Luigi Preziosi
Publisher : CRC Press
Page : 516 pages
File Size : 41,8 Mb
Release : 1994-12-22
Category : Mathematics
ISBN : 0849383315

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Modelling Mathematical Methods and Scientific Computation by Nicola Bellomo,Luigi Preziosi Pdf

Addressed to engineers, scientists, and applied mathematicians, this book explores the fundamental aspects of mathematical modelling in applied sciences and related mathematical and computational methods. After providing the general framework needed for mathematical modelling-definitions, classifications, general modelling procedures, and validation methods-the authors deal with the analysis of discrete models. This includes modelling methods and related mathematical methods. The analysis of models is defined in terms of ordinary differential equations. The analysis of continuous models, particularly models defined in terms of partial differential equations, follows. The authors then examine inverse type problems and stochastic modelling. Three appendices provide a concise guide to functional analysis, approximation theory, and probability, and a diskette included with the book includes ten scientific programs to introduce the reader to scientific computation at a practical level.

An Introduction to Mathematical Modeling

Edward A. Bender
An Introduction to Mathematical Modeling Book PDF

Author : Edward A. Bender
Publisher : Courier Corporation
Page : 273 pages
File Size : 41,7 Mb
Release : 2012-05-23
Category : Mathematics
ISBN : 9780486137124

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An Introduction to Mathematical Modeling by Edward A. Bender Pdf

Employing a practical, "learn by doing" approach, this first-rate text fosters the development of the skills beyond the pure mathematics needed to set up and manipulate mathematical models. The author draws on a diversity of fields — including science, engineering, and operations research — to provide over 100 reality-based examples. Students learn from the examples by applying mathematical methods to formulate, analyze, and criticize models. Extensive documentation, consisting of over 150 references, supplements the models, encouraging further research on models of particular interest. The lively and accessible text requires only minimal scientific background. Designed for senior college or beginning graduate-level students, it assumes only elementary calculus and basic probability theory for the first part, and ordinary differential equations and continuous probability for the second section. All problems require students to study and create models, encouraging their active participation rather than a mechanical approach. Beyond the classroom, this volume will prove interesting and rewarding to anyone concerned with the development of mathematical models or the application of modeling to problem solving in a wide array of applications.

Mathematical Modeling and Computation of Real-Time Problems

Rakhee Kulshrestha,Chandra Shekhar,Madhu Jain,Srinivas R. Chakravarthy
Mathematical Modeling and Computation of Real Time Problems Book PDF

Author : Rakhee Kulshrestha,Chandra Shekhar,Madhu Jain,Srinivas R. Chakravarthy
Publisher : CRC Press
Page : 172 pages
File Size : 44,6 Mb
Release : 2021-01-04
Category : Mathematics
ISBN : 9781000288674

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Mathematical Modeling and Computation of Real-Time Problems by Rakhee Kulshrestha,Chandra Shekhar,Madhu Jain,Srinivas R. Chakravarthy Pdf

This book covers an interdisciplinary approach for understanding mathematical modeling by offering a collection of models, solved problems related to the models, the methodologies employed, and the results using projects and case studies with insight into the operation of substantial real-time systems. The book covers a broad scope in the areas of statistical science, probability, stochastic processes, fluid dynamics, supply chain, optimization, and applications. It discusses advanced topics and the latest research findings, uses an interdisciplinary approach for real-time systems, offers a platform for integrated research, and identifies the gaps in the field for further research. The book is for researchers, students, and teachers that share a goal of learning advanced topics and the latest research in mathematical modeling.

Mathematical Modeling and Simulation

Kai Velten
Mathematical Modeling and Simulation Book PDF

Author : Kai Velten
Publisher : John Wiley & Sons
Page : 362 pages
File Size : 42,8 Mb
Release : 2009-06-01
Category : Science
ISBN : 9783527627615

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Mathematical Modeling and Simulation by Kai Velten Pdf

This concise and clear introduction to the topic requires only basic knowledge of calculus and linear algebra - all other concepts and ideas are developed in the course of the book. Lucidly written so as to appeal to undergraduates and practitioners alike, it enables readers to set up simple mathematical models on their own and to interpret their results and those of others critically. To achieve this, many examples have been chosen from various fields, such as biology, ecology, economics, medicine, agricultural, chemical, electrical, mechanical and process engineering, which are subsequently discussed in detail. Based on the author`s modeling and simulation experience in science and engineering and as a consultant, the book answers such basic questions as: What is a mathematical model? What types of models do exist? Which model is appropriate for a particular problem? What are simulation, parameter estimation, and validation? The book relies exclusively upon open-source software which is available to everybody free of charge. The entire book software - including 3D CFD and structural mechanics simulation software - can be used based on a free CAELinux-Live-DVD that is available in the Internet (works on most machines and operating systems).

Mathematical and Computational Approaches in Advancing Modern Science and Engineering

Jacques Bélair,Ian A. Frigaard,Herb Kunze,Roman Makarov,Roderick Melnik,Raymond J. Spiteri
Mathematical and Computational Approaches in Advancing Modern Science and Engineering Book PDF

Author : Jacques Bélair,Ian A. Frigaard,Herb Kunze,Roman Makarov,Roderick Melnik,Raymond J. Spiteri
Publisher : Springer
Page : 806 pages
File Size : 43,5 Mb
Release : 2016-08-10
Category : Computers
ISBN : 9783319303796

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Mathematical and Computational Approaches in Advancing Modern Science and Engineering by Jacques Bélair,Ian A. Frigaard,Herb Kunze,Roman Makarov,Roderick Melnik,Raymond J. Spiteri Pdf

Focusing on five main groups of interdisciplinary problems, this book covers a wide range of topics in mathematical modeling, computational science and applied mathematics. It presents a wealth of new results in the development of modeling theories and methods, advancing diverse areas of applications and promoting interdisciplinary interactions between mathematicians, scientists, engineers and representatives from other disciplines. The book offers a valuable source of methods, ideas, and tools developed for a variety of disciplines, including the natural and social sciences, medicine, engineering, and technology. Original results are presented on both the fundamental and applied level, accompanied by an ample number of real-world problems and examples emphasizing the interdisciplinary nature and universality of mathematical modeling, and providing an excellent outline of today’s challenges. Mathematical modeling, with applied and computational methods and tools, plays a fundamental role in modern science and engineering. It provides a primary and ubiquitous tool in the context making new discoveries, as well as in the development of new theories and techniques for solving key problems arising in scientific and engineering applications. The contributions, which are the product of two highly successful meetings held jointly in Waterloo, Ontario, Canada on the main campus of Wilfrid Laurier University in June 2015, i.e. the International Conference on Applied Mathematics, Modeling and Computational Science, and the Annual Meeting of the Canadian Applied and Industrial Mathematics (CAIMS), make the book a valuable resource for any reader interested in a broader overview of the methods, ideas and tools involved in mathematical and computational approaches developed for other disciplines, including the natural and social sciences, engineering and technology.

Mathematical Modelling Techniques

Rutherford Aris
Mathematical Modelling Techniques Book PDF

Author : Rutherford Aris
Publisher : Courier Corporation
Page : 290 pages
File Size : 44,7 Mb
Release : 2012-06-29
Category : Mathematics
ISBN : 9780486138893

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Mathematical Modelling Techniques by Rutherford Aris Pdf

"Engaging, elegantly written." — Applied Mathematical Modelling Mathematical modelling is a highly useful methodology designed to enable mathematicians, physicists and other scientists to formulate equations from a given nonmathematical situation. In this elegantly written volume, a distinguished theoretical chemist and engineer sets down helpful rules not only for setting up models but also for solving the mathematical problems they pose and for evaluating models. The author begins with a discussion of the term "model," followed by clearly presented examples of the different types of models (finite, statistical, stochastic, etc.). He then goes on to discuss the formulation of a model and how to manipulate it into its most responsive form. Along the way Dr. Aris develops a delightful list of useful maxims for would-be modellers. In the final chapter he deals not only with the empirical validation of models but also with the comparison of models among themselves, as well as with the extension of a model beyond its original "domain of validity." Filled with numerous examples, this book includes three appendices offering further examples treated in more detail. These concern longitudinal diffusion in a packed bed, the coated tube chromatograph with Taylor diffusion and the stirred tank reactor. Six journal articles, a useful list of references and subject and name indexes complete this indispensable, well-written guide. "A most useful, readable-and stimulating-book, to be read both for pleasure and for enlightenment." — Bulletin of the Institute of Mathematics and Its Applications

Scientific Models

Philip Gerlee,Torbjörn Lundh
Scientific Models Book PDF

Author : Philip Gerlee,Torbjörn Lundh
Publisher : Springer
Page : 96 pages
File Size : 47,8 Mb
Release : 2016-07-07
Category : Mathematics
ISBN : 9783319270814

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Scientific Models by Philip Gerlee,Torbjörn Lundh Pdf

A zebrafish, the hull of a miniature ship, a mathematical equation and a food chain - what do these things have in common? They are examples of models used by scientists to isolate and study particular aspects of the world around us. This book begins by introducing the concept of a scientific model from an intuitive perspective, drawing parallels to mental models and artistic representations. It then recounts the history of modelling from the 16th century up until the present day. The iterative process of model building is described and discussed in the context of complex models with high predictive accuracy versus simpler models that provide more of a conceptual understanding. To illustrate the diversity of opinions within the scientific community, we also present the results of an interview study, in which ten scientists from different disciplines describe their views on modelling and how models feature in their work. Lastly, it includes a number of worked examples that span different modelling approaches and techniques. It provides a comprehensive introduction to scientific models and shows how models are constructed and used in modern science. It also addresses the approach to, and the culture surrounding modelling in different scientific disciplines. It serves as an inspiration for model building and also facilitates interdisciplinary collaborations by showing how models are used in different scientific fields. The book is aimed primarily at students in the sciences and engineering, as well as students at teacher training colleges but will also appeal to interested readers wanting to get an overview of scientific modelling in general and different modelling approaches in particular.

Mathematical Modeling in Biology

Shandelle M. Henson,James L. Hayward
Mathematical Modeling in Biology Book PDF

Author : Shandelle M. Henson,James L. Hayward
Publisher : CRC Press
Page : 285 pages
File Size : 48,8 Mb
Release : 2022-12-29
Category : Mathematics
ISBN : 9781000806106

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Mathematical Modeling in Biology by Shandelle M. Henson,James L. Hayward Pdf

Mathematical Modeling in Biology: A Research Methods Approach is a textbook written primarily for advanced mathematics and science undergraduate students and graduate-level biology students. Although the applications center on ecology, the expertise of the authors, the methodology can be imported to any other science, including social science and economics. The aim of the book, beyond being a useful aid to teaching and learning the core modeling skills needed for mathematical biology, is to encourage students to think deeply and clearly about the meaning of mathematics in science and to learn significant research methods. Most importantly, it is hoped that students will experience some of the excitement of doing research. Features Minimal pre-requisites beyond a solid background in calculus, such as a calculus I course. Suitable for upper division mathematics and sciences students and graduate-level biology students. Provides sample MATLAB codes and instruction in Appendices along with datasets available on https://bit.ly/3fcLF3D

Statistics and Scientific Method

Peter J. Diggle,Amanda Chetwynd
Statistics and Scientific Method Book PDF

Author : Peter J. Diggle,Amanda Chetwynd
Publisher : Oxford University Press
Page : 192 pages
File Size : 43,5 Mb
Release : 2011-08-11
Category : Mathematics
ISBN : 9780199543182

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Statistics and Scientific Method by Peter J. Diggle,Amanda Chetwynd Pdf

An antidote to technique-orientated approaches, this text avoids the recipe-book style, giving the reader a clear understanding of how core statistical ideas of experimental design, modelling, and data analysis are integral to the scientific method. No prior knowledge of statistics is required and a range of scientific disciplines are covered.

Mathematical Modeling in Science and Engineering

Ismael Herrera,George F. Pinder
Mathematical Modeling in Science and Engineering Book PDF

Author : Ismael Herrera,George F. Pinder
Publisher : John Wiley & Sons
Page : 257 pages
File Size : 46,8 Mb
Release : 2012-03-13
Category : Technology & Engineering
ISBN : 9781118087572

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Mathematical Modeling in Science and Engineering by Ismael Herrera,George F. Pinder Pdf

A powerful, unified approach to mathematical and computational modeling in science and engineering Mathematical and computational modeling makes it possible to predict the behavior of a broad range of systems across a broad range of disciplines. This text guides students and professionals through the axiomatic approach, a powerful method that will enable them to easily master the principle types of mathematical and computational models used in engineering and science. Readers will discover that this axiomatic approach not only enables them to systematically construct effective models, it also enables them to apply these models to any macroscopic physical system. Mathematical Modeling in Science and Engineering focuses on models in which the processes to be modeled are expressed as systems of partial differential equations. It begins with an introductory discussion of the axiomatic formulation of basic models, setting the foundation for further topics such as: Mechanics of classical and non-classical continuous systems Solute transport by a free fluid Flow of a fluid in a porous medium Multiphase systems Enhanced oil recovery Fluid mechanics Throughout the text, diagrams are provided to help readers visualize and better understand complex mathematical concepts. A set of exercises at the end of each chapter enables readers to put their new modeling skills into practice. There is also a bibliography in each chapter to facilitate further investigation of individual topics. Mathematical Modeling in Science and Engineering is ideal for both students and professionals across the many disciplines of science and engineering that depend on mathematical and computational modeling to predict and understand complex systems.

Mathematical Modeling

Ludmilla A. Uvarova,Anatolii V. Latyshev
Mathematical Modeling Book PDF

Author : Ludmilla A. Uvarova,Anatolii V. Latyshev
Publisher : Springer Science & Business Media
Page : 285 pages
File Size : 44,7 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475733976

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Mathematical Modeling by Ludmilla A. Uvarova,Anatolii V. Latyshev Pdf

This volume contains review articles and original results obtained in various fields of modern science using mathematical simulation methods. The basis of the articles are the plenary and some section reports that were made and discussed at the Fourth International Mathematical Simulation Conference, held in Moscow on June 27 through July 1, 2000. The conference was devoted to the following scientific areas: • mathematical and computer discrete systems models; • non-linear excitation in condensed media; • complex systems evolution; • mathematical models in economics; • non-equilibrium processes kinematics; • dynamics and structure of the molecular and biomolecular systems; • mathematical transfer models in non-linear systems; • numerical simulation and algorithms; • turbulence and determined chaos; • chemical physics of polymer. This conference was supported by the Russian Ministry of Education, Russian foundation for Basic Research and Federal Program "Integration". This volume contains the following sections: 1. models of non-linear phenomena in physics; 2. numerical methods and computer simulations; 3. mathematical computer models of discrete systems; 4. mathematical models in economics; 5. non-linear models in chemical physics and physical chemistry; 6. mathematical models of transport processes in complex systems. In Sections One and Five a number of fundamental and sufficiently general problems, concerning real physical and physical-chemical systems simulation, is discussed.

Methods of Mathematical Modelling

Thomas Witelski,Mark Bowen
Methods of Mathematical Modelling Book PDF

Author : Thomas Witelski,Mark Bowen
Publisher : Springer
Page : 305 pages
File Size : 44,7 Mb
Release : 2015-09-18
Category : Mathematics
ISBN : 9783319230429

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Methods of Mathematical Modelling by Thomas Witelski,Mark Bowen Pdf

This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences.

Mathematical Modeling for System Analysis in Agricultural Research

K. Vohnout
Mathematical Modeling for System Analysis in Agricultural Research Book PDF

Author : K. Vohnout
Publisher : Elsevier
Page : 452 pages
File Size : 49,9 Mb
Release : 2003-03-27
Category : Mathematics
ISBN : 9780080535883

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Mathematical Modeling for System Analysis in Agricultural Research by K. Vohnout Pdf

This book provides a clear picture of the use of applied mathematics as a tool for improving the accuracy of agricultural research. For decades, statistics has been regarded as the fundamental tool of the scientific method. With new breakthroughs in computers and computer software, it has become feasible and necessary to improve the traditional approach in agricultural research by including additional mathematical modeling procedures. The difficulty with the use of mathematics for agricultural scientists is that most courses in applied mathematics have been designed for engineering students. This publication is written by a professional in animal science targeting professionals in the biological, namely agricultural and animal scientists and graduate students in agricultural and animal sciences. The only prerequisite for the reader to understand the topics of this book is an introduction to college algebra, calculus and statistics. This is a manual of procedures for the mathematical modeling of agricultural systems and for the design and analyses of experimental data and experimental tests. It is a step-by-step guide for mathematical modeling of agricultural systems, starting with the statement of the research problem and up to implementing the project and running system experiments.