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| example of a mathematical model: An Introduction to Mathematical Modeling Edward A. Bender, 2012-05-23 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. |
| example of a mathematical model: Mathematical Modeling Sandip Banerjee, 2021-11-11 Mathematical Modeling: Models, Analysis and Applications, Second Edition introduces models of both discrete and continuous systems. This book is aimed at newcomers who desires to learn mathematical modeling, especially students taking a first course in the subject. Beginning with the step-by-step guidance of model formulation, this book equips the reader about modeling with difference equations (discrete models), ODE’s, PDE’s, delay and stochastic differential equations (continuous models). This book provides interdisciplinary and integrative overview of mathematical modeling, making it a complete textbook for a wide audience. A unique feature of the book is the breadth of coverage of different examples on mathematical modelling, which include population models, economic models, arms race models, combat models, learning model, alcohol dynamics model, carbon dating, drug distribution models, mechanical oscillation models, epidemic models, tumor models, traffic flow models, crime flow models, spatial models, football team performance model, breathing model, two neuron system model, zombie model and model on love affairs. Common themes such as equilibrium points, stability, phase plane analysis, bifurcations, limit cycles, period doubling and chaos run through several chapters and their interpretations in the context of the model have been highlighted. In chapter 3, a section on estimation of system parameters with real life data for model validation has also been discussed. Features Covers discrete, continuous, spatial, delayed and stochastic models. Over 250 illustrations, 300 examples and exercises with complete solutions. Incorporates MATHEMATICA® and MATLAB®, each chapter contains Mathematica and Matlab codes used to display numerical results (available at CRC website). Separate sections for Projects. Several exercise problems can also be used for projects. Presents real life examples of discrete and continuous scenarios. The book is ideal for an introductory course for undergraduate and graduate students, engineers, applied mathematicians and researchers working in various areas of natural and applied sciences. |
| example of a mathematical model: Guide to Mathematical Modelling David A Towers, Dilwyn Edwards, Mike Hamson, 2020-06-06 A basic introduction to Mathematical Modelling, this book encourages the reader to participate in the investigation of a wide variety of modelling examples. These are carefully paced so that the readers can identify and develop the skills which are required for successful modelling. The examples also promote an appreciation of the enormous range of problems to which mathematical modelling skills can be usefully applied. |
| example of a mathematical model: Principles of Mathematical Modelling Alexander A. Samarskii, Alexander P. Mikhailov, 2001-12-20 Mathematical modeling is becoming increasingly versatile and multi-disciplinary. This text demonstrates the broadness of this field as the authors consider the principles of model construction and use common approaches to build models from a range of subject areas. The book reflects the interests and experiences of the authors, but it explores mathematical modeling across a wide range of applications, from mechanics to social science. A general approach is adopted, where ideas and examples are favored over rigorous mathematical procedures. This insightful book will be of interest to specialists, teachers, and students across a wide range of disciplines.. |
| example of a mathematical model: Mathematical Modeling for the Life Sciences Jacques Istas, 2005-10-04 Provides a wide range of mathematical models currently used in the life sciences Each model is thoroughly explained and illustrated by example Includes three appendices to allow for independent reading |
| example of a mathematical model: Mathematical Modelling Techniques Rutherford Aris, 1994-01-01 Engaging, elegantly written. — Applied Mathematical Modelling. A distinguished theoretical chemist and engineer discusses the types of models — finite, statistical, stochastic, and more — as well as how to formulate and manipulate them for best results. Filled with numerous examples, the book includes three appendices offering further examples treated in more detail. |
| example of a mathematical model: Mathematical Modeling And Computation In Finance: With Exercises And Python And Matlab Computer Codes Cornelis W Oosterlee, Lech A Grzelak, 2019-10-29 This book discusses the interplay of stochastics (applied probability theory) and numerical analysis in the field of quantitative finance. The stochastic models, numerical valuation techniques, computational aspects, financial products, and risk management applications presented will enable readers to progress in the challenging field of computational finance.When the behavior of financial market participants changes, the corresponding stochastic mathematical models describing the prices may also change. Financial regulation may play a role in such changes too. The book thus presents several models for stock prices, interest rates as well as foreign-exchange rates, with increasing complexity across the chapters. As is said in the industry, 'do not fall in love with your favorite model.' The book covers equity models before moving to short-rate and other interest rate models. We cast these models for interest rate into the Heath-Jarrow-Morton framework, show relations between the different models, and explain a few interest rate products and their pricing.The chapters are accompanied by exercises. Students can access solutions to selected exercises, while complete solutions are made available to instructors. The MATLAB and Python computer codes used for most tables and figures in the book are made available for both print and e-book users. This book will be useful for people working in the financial industry, for those aiming to work there one day, and for anyone interested in quantitative finance. The topics that are discussed are relevant for MSc and PhD students, academic researchers, and for quants in the financial industry. |
| example of a mathematical model: Mathematical Models in Biology Leah Edelstein-Keshet, 1988-01-01 Mathematical Models in Biology is an introductory book for readers interested in biological applications of mathematics and modeling in biology. A favorite in the mathematical biology community, it shows how relatively simple mathematics can be applied to a variety of models to draw interesting conclusions. Connections are made between diverse biological examples linked by common mathematical themes. A variety of discrete and continuous ordinary and partial differential equation models are explored. Although great advances have taken place in many of the topics covered, the simple lessons contained in this book are still important and informative. Audience: the book does not assume too much background knowledge--essentially some calculus and high-school algebra. It was originally written with third- and fourth-year undergraduate mathematical-biology majors in mind; however, it was picked up by beginning graduate students as well as researchers in math (and some in biology) who wanted to learn about this field. |
| example of a mathematical model: An Invitation to Arithmetic Geometry Dino Lorenzini, 2021-12-23 Extremely carefully written, masterfully thought out, and skillfully arranged introduction … to the arithmetic of algebraic curves, on the one hand, and to the algebro-geometric aspects of number theory, on the other hand. … an excellent guide for beginners in arithmetic geometry, just as an interesting reference and methodical inspiration for teachers of the subject … a highly welcome addition to the existing literature. —Zentralblatt MATH The interaction between number theory and algebraic geometry has been especially fruitful. In this volume, the author gives a unified presentation of some of the basic tools and concepts in number theory, commutative algebra, and algebraic geometry, and for the first time in a book at this level, brings out the deep analogies between them. The geometric viewpoint is stressed throughout the book. Extensive examples are given to illustrate each new concept, and many interesting exercises are given at the end of each chapter. Most of the important results in the one-dimensional case are proved, including Bombieri's proof of the Riemann Hypothesis for curves over a finite field. While the book is not intended to be an introduction to schemes, the author indicates how many of the geometric notions introduced in the book relate to schemes, which will aid the reader who goes to the next level of this rich subject. |
| example of a mathematical model: Mathematical Modeling and Simulation Kai Velten, 2009-06-01 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). |
| example of a mathematical model: Modelling Nature Edward Gillman, Michael Gillman, 2019-05-30 This short textbook introduces students to the concept of describing natural systems using mathematical models. We highlight the variety of ways in which natural systems lend themselves to mathematical description and the importance of models in revealing fundamental processes. The process of science via the building, testing and use of models (theories) is described and forms the structure of the book. The book covers a broad range from the molecular to ecosystems and whole-Earth phenomena. Themes running through the chapters include scale (temporal and spatial), change (linear and nonlinear), emergent phenomena and uncertainty. Mathematical descriptions are kept to a minimum and we illustrate mechanisms and results in graphical form wherever possible. Essential mathematical details are described fully, with the use of boxes. The mathematics supports but does not lead the text. |
| example of a mathematical model: Modeling Mathematical Ideas Jennifer M. Suh, Padmanabhan Seshaiyer, 2016-12-27 Modeling Mathematical Ideas combining current research and practical strategies to build teachers and students strategic competence in problem solving.This must-have book supports teachers in understanding learning progressions that addresses conceptual guiding posts as well as students’ common misconceptions in investigating and discussing important mathematical ideas related to number sense, computational fluency, algebraic thinking and proportional reasoning. In each chapter, the authors opens with a rich real-world mathematical problem and presents classroom strategies (such as visible thinking strategies & technology integration) and other related problems to develop students’ strategic competence in modeling mathematical ideas. |
| example of a mathematical model: The Nature of Mathematical Modeling Neil A. Gershenfeld, 1999 This is a book about the nature of mathematical modeling, and about the kinds of techniques that are useful for modeling. The text is in four sections. The first covers exact and approximate analytical techniques; the second, numerical methods; the third, model inference based on observations; and the last, the special role of time in modeling. Each of the topics in the book would be the worthy subject of a dedicated text, but only by presenting the material in this way is it possible to make so much material accessible to so many people. Each chapter presents a concise summary of the core results in an area. The text is complemented by extensive worked problems. |
| example of a mathematical model: Principles of Mathematical Modelling Alexander A. Samarskii, Alexander P. Mikhailov, 2001-12-20 Mathematical modeling is becoming increasingly versatile and multi-disciplinary. This text demonstrates the broadness of this field as the authors consider the principles of model construction and use common approaches to build models from a range of subject areas. The book reflects the interests and experiences of the authors, but it explores mathematical modeling across a wide range of applications, from mechanics to social science. A general approach is adopted, where ideas and examples are favored over rigorous mathematical procedures. This insightful book will be of interest to specialists, teachers, and students across a wide range of disciplines.. |
| example of a mathematical model: Mathematical Modelling of Zombies Robert Smith?, 2014-10-14 You’re outnumbered, in fear for your life, surrounded by flesheating zombies. What can save you now? Mathematics, of course. Mathematical Modelling of Zombies engages the imagination to illustrate the power of mathematical modelling. Using zombies as a “hook,” you’ll learn how mathematics can predict the unpredictable. In order to be prepared for the apocalypse, you’ll need mathematical models, differential equations, statistical estimations, discretetime models, and adaptive strategies for zombie attacks—as well as baseball bats and Dire Straits records (latter two items not included). In Mathematical Modelling of Zombies, Robert Smith? brings together a highly skilled team of contributors to fend off a zombie uprising. You’ll also learn how modelling can advise government policy, how theoretical results can be communicated to a nonmathematical audience and how models can be formulated with only limited information. A forward by Andrew Cartmel—former script editor of Doctor Who, author, zombie fan and all-round famous person in science-fiction circles—even provides a genealogy of the undead. By understanding how to combat zombies, readers will be introduced to a wide variety of modelling techniques that are applicable to other real-world issues (biology, epidemiology, medicine, public health, etc.). So if the zombies turn up, reach for this book. The future of the human race may depend on it. |
| example of a mathematical model: Mathematical Models for Communicable Diseases Fred Brauer, Carlos Castillo-Chaavez, 2012-01-01 This graduate-level textbook appeals to readers interested in the mathematical theory of disease transmission models. It is self-contained and accessible to readers who are comfortable with calculus, elementary differential equations, and linear algebra. The book provides insight into modeling cross-immunity between different disease strains (such as influenza) and the synergistic interactions between multiple diseases (e.g., HIV and tuberculosis); diseases transmitted by viral agents, bacteria, and vectors (e.g., mosquitos transmitting malaria to humans); and both epidemic and endemic disease occurrences. |
| example of a mathematical model: Mathematical Models in Biology Elizabeth Spencer Allman, John A. Rhodes, 2004 This introductory textbook on mathematical biology focuses on discrete models across a variety of biological subdisciplines. Biological topics treated include linear and non-linear models of populations, Markov models of molecular evolution, phylogenetic tree construction, genetics, and infectious disease models. The coverage of models of molecular evolution and phylogenetic tree construction from DNA sequence data is unique among books at this level. Computer investigations with MATLAB are incorporated throughout, in both exercises and more extensive projects, to give readers hands-on experience with the mathematical models developed. MATLAB programs accompany the text. Mathematical tools, such as matrix algebra, eigenvector analysis, and basic probability, are motivated by biological models and given self-contained developments, so that mathematical prerequisites are minimal. |
| example of a mathematical model: Concepts of Mathematical Modeling Walter J. Meyer, 2012-10-23 Appropriate for undergraduate and graduate students, this text features independent sections that illustrate the most important principles of mathematical modeling, a variety of applications, and classic models. Students with a solid background in calculus and some knowledge of probability and matrix theory will find the material entirely accessible. The range of subjects includes topics from the physical, biological, and social sciences, as well as those of operations research. Discussions cover related mathematical tools and the historical eras from which the applications are drawn. Each section is preceded by an abstract and statement of prerequisites, and answers or hints are provided for selected exercises. 1984 edition. |
| example of a mathematical model: Mathematical Models in the Applied Sciences A. C. Fowler, 1997-11-28 Presents a thorough grounding in the techniques of mathematical modelling, and proceeds to explore a range of classical and continuum models from an array of disciplines. |
| example of a mathematical model: Mathematical Modeling of Earth's Dynamical Systems Rudy Slingerland, Lee Kump, 2011-03-28 A concise guide to representing complex Earth systems using simple dynamic models Mathematical Modeling of Earth's Dynamical Systems gives earth scientists the essential skills for translating chemical and physical systems into mathematical and computational models that provide enhanced insight into Earth's processes. Using a step-by-step method, the book identifies the important geological variables of physical-chemical geoscience problems and describes the mechanisms that control these variables. This book is directed toward upper-level undergraduate students, graduate students, researchers, and professionals who want to learn how to abstract complex systems into sets of dynamic equations. It shows students how to recognize domains of interest and key factors, and how to explain assumptions in formal terms. The book reveals what data best tests ideas of how nature works, and cautions against inadequate transport laws, unconstrained coefficients, and unfalsifiable models. Various examples of processes and systems, and ample illustrations, are provided. Students using this text should be familiar with the principles of physics, chemistry, and geology, and have taken a year of differential and integral calculus. Mathematical Modeling of Earth's Dynamical Systems helps earth scientists develop a philosophical framework and strong foundations for conceptualizing complex geologic systems. Step-by-step lessons for representing complex Earth systems as dynamical models Explains geologic processes in terms of fundamental laws of physics and chemistry Numerical solutions to differential equations through the finite difference technique A philosophical approach to quantitative problem-solving Various examples of processes and systems, including the evolution of sandy coastlines, the global carbon cycle, and much more Professors: A supplementary Instructor's Manual is available for this book. It is restricted to teachers using the text in courses. For information on how to obtain a copy, refer to: http://press.princeton.edu/class_use/solutions.html |
| example of a mathematical model: Measuring Professional Competence for the Teaching of Mathematical Modelling Raphael Wess, Heiner Klock, Hans-Stefan Siller, Gilbert Greefrath, 2021-07-14 This open access book presents a structural model and an associated test instrument designed to provide a detailed analysis of professional competences for teaching mathematical modelling. The conceptualisation is based on the COACTIV model, which describes aspects, areas and facets of professional competences of teachers. The manual provides an overview of the essential teaching skills in application-related contexts and offers the tools needed to capture these aspects. It discusses the objectives and application areas of the instrument, as well as the development of the test. In addition, it describes the implementation and evaluates the quality and results of the structural equation analysis of the model. Teaching mathematical modelling is a cognitively challenging activity for (prospective) teachers. Thus, teacher education requires a detailed analysis of professional competence for teaching mathematical modelling. Measuring this competence requires theoretical models that accurately describe requirements placed upon teachers, as well as appropriate evaluation tools that adequately capture skills and abilities in this field. This book presents an instrument that measures the professional competences in a sample of 349 prospective teachers. |
| example of a mathematical model: A Celebration of Mathematical Modeling Dan Givoli, Marcus J. Grote, George Papanicolaou, 2004-04-30 This volume celebrates the eightieth birthday of the famous applied mathematician Joseph B. Keller. The book contains 12 chapters, each on a specific area of mathematical modeling, written by established researchers who have collaborated with J.B. Keller during his long career. These chapters, all inspired by J.B. Keller, deal with a variety of application fields and together span the broad subject of mathematical modeling. The models discussed in the book describe the behavior of various systems such as those related to finance, waves, microorganisms, shocks, DNA, flames, contact, optics, fluids, bubbles and jets. The book also contains a preface written by the Editors, a full list of J.B. Keller's publications, and a comprehensive index. The book is intended for mathematicians, scientists and engineers, as well as graduate students in these fields, who are interested in mathematical models of physical phenomena. |
| example of a mathematical model: Mathematical Models in Epidemiology Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng, 2019-10-10 The book is a comprehensive, self-contained introduction to the mathematical modeling and analysis of disease transmission models. It includes (i) an introduction to the main concepts of compartmental models including models with heterogeneous mixing of individuals and models for vector-transmitted diseases, (ii) a detailed analysis of models for important specific diseases, including tuberculosis, HIV/AIDS, influenza, Ebola virus disease, malaria, dengue fever and the Zika virus, (iii) an introduction to more advanced mathematical topics, including age structure, spatial structure, and mobility, and (iv) some challenges and opportunities for the future. There are exercises of varying degrees of difficulty, and projects leading to new research directions. For the benefit of public health professionals whose contact with mathematics may not be recent, there is an appendix covering the necessary mathematical background. There are indications which sections require a strong mathematical background so that the book can be useful for both mathematical modelers and public health professionals. |
| example of a mathematical model: Introduction to Mathematical Modeling and Computer Simulations Vladimir Mityushev, Wojciech Nawalaniec, Natalia Rylko, 2018-02-19 Introduction to Mathematical Modeling and Computer Simulations is written as a textbook for readers who want to understand the main principles of Modeling and Simulations in settings that are important for the applications, without using the profound mathematical tools required by most advanced texts. It can be particularly useful for applied mathematicians and engineers who are just beginning their careers. The goal of this book is to outline Mathematical Modeling using simple mathematical descriptions, making it accessible for first- and second-year students. |
| example of a mathematical model: Mathematical Modelling Reinhard Illner, 2005 This is an ideal text for classes on modelling. It can also be used in seminars or as preparation for mathematical modelling competitions.--BOOK JACKET. |
| example of a mathematical model: Mathematical Models for Society and Biology Edward Beltrami, 2013-06-19 Mathematical Models for Society and Biology, 2e, is a useful resource for researchers, graduate students, and post-docs in the applied mathematics and life science fields. Mathematical modeling is one of the major subfields of mathematical biology. A mathematical model may be used to help explain a system, to study the effects of different components, and to make predictions about behavior. Mathematical Models for Society and Biology, 2e, draws on current issues to engagingly relate how to use mathematics to gain insight into problems in biology and contemporary society. For this new edition, author Edward Beltrami uses mathematical models that are simple, transparent, and verifiable. Also new to this edition is an introduction to mathematical notions that every quantitative scientist in the biological and social sciences should know. Additionally, each chapter now includes a detailed discussion on how to formulate a reasonable model to gain insight into the specific question that has been introduced. - Offers 40% more content – 5 new chapters in addition to revisions to existing chapters - Accessible for quick self study as well as a resource for courses in molecular biology, biochemistry, embryology and cell biology, medicine, ecology and evolution, bio-mathematics, and applied math in general - Features expanded appendices with an extensive list of references, solutions to selected exercises in the book, and further discussion of various mathematical methods introduced in the book |
| example of a mathematical model: Advanced Mathematical Modeling with Technology William P. Fox, Robert E. Burks, 2021-05-19 Mathematical modeling is both a skill and an art and must be practiced in order to maintain and enhance the ability to use those skills. Though the topics covered in this book are the typical topics of most mathematical modeling courses, this book is best used for individuals or groups who have already taken an introductory mathematical modeling course. This book will be of interest to instructors and students offering courses focused on discrete modeling or modeling for decision making. |
| example of a mathematical model: Professional Societies and Ecologically Based Pest Management National Research Council, Board on Agriculture and Natural Resources, 2000-08-07 The National Research Council's (NRC) Board on Agriculture and Natural Resources invited professional societies associated with agriculture and ecology to participate in a two-day workshop to explore leadership and a common vision for ecologically based pest management (EBPM). These proceedings describe the challenges of and opportunities for EBPM discussed by participants in the workshop. |
| example of a mathematical model: Mathematical Modeling Christof Eck, Harald Garcke, Peter Knabner, 2017-04-11 Mathematical models are the decisive tool to explain and predict phenomena in the natural and engineering sciences. With this book readers will learn to derive mathematical models which help to understand real world phenomena. At the same time a wealth of important examples for the abstract concepts treated in the curriculum of mathematics degrees are given. An essential feature of this book is that mathematical structures are used as an ordering principle and not the fields of application. Methods from linear algebra, analysis and the theory of ordinary and partial differential equations are thoroughly introduced and applied in the modeling process. Examples of applications in the fields electrical networks, chemical reaction dynamics, population dynamics, fluid dynamics, elasticity theory and crystal growth are treated comprehensively. |
| example of a mathematical model: Mathematical Modeling Mark M. Meerschaert, 2007-06-18 Mathematical Modeling, Third Edition is a general introduction to an increasingly crucial topic for today's mathematicians. Unlike textbooks focused on one kind of mathematical model, this book covers the broad spectrum of modeling problems, from optimization to dynamical systems to stochastic processes. Mathematical modeling is the link between mathematics and the rest of the world. Meerschaert shows how to refine a question, phrasing it in precise mathematical terms. Then he encourages students to reverse the process, translating the mathematical solution back into a comprehensible, useful answer to the original question. This textbook mirrors the process professionals must follow in solving complex problems. Each chapter in this book is followed by a set of challenging exercises. These exercises require significant effort on the part of the student, as well as a certain amount of creativity. Meerschaert did not invent the problems in this book--they are real problems, not designed to illustrate the use of any particular mathematical technique. Meerschaert's emphasis on principles and general techniques offers students the mathematical background they need to model problems in a wide range of disciplines. Increased support for instructors, including MATLAB material New sections on time series analysis and diffusion models Additional problems with international focus such as whale and dolphin populations, plus updated optimization problems |
| example of a mathematical model: Modelling and Applications in Mathematics Education Peter L. Galbraith, Hans-Wolfgang Henn, Mogens Niss, 2007-12-05 The book aims at showing the state-of-the-art in the field of modeling and applications in mathematics education. This is the first volume to do this. The book deals with the question of how key competencies of applications and modeling at the heart of mathematical literacy may be developed; with the roles that applications and modeling may play in mathematics teaching, making mathematics more relevant for students. |
| example of a mathematical model: Mathematical Modelling of Haemodialysis Leszek Pstras, Jacek Waniewski, 2019-07-03 Beginning with an introduction to kidney function, renal replacement therapies, and an overview of clinical problems associated with haemodialysis, this book explores the principles of the short-term baroreflex regulation of the cardiovascular system and the mechanisms of water and solute transport across the human body from a mathematical model perspective. It synthesizes theoretical physiological concepts and practical aspects of mathematical modelling needed for simulation and quantitative analysis of the haemodynamic response to dialysis therapy. Including an up-to-date review of the literature concerning the modelled physiological mechanisms and processes, the book serves both as an overview of transport and regulatory mechanisms related to the cardiovascular system and body fluids and as a useful reference for the study and development of mathematical models of dynamic physiological processes. Mathematical Modelling of Haemodialysis: Cardiovascular Response, Body Fluid Shifts, and Solute Kinetics is intended for researchers and graduate students in biomedical engineering, physiology, or medicine interested in mathematical modelling of cardiovascular dynamics and fluid and solute transport across the human body, both under physiological conditions and during haemodialysis therapy. |
| example of a mathematical model: Teaching and Learning Mathematical Modelling Gilbert Greefrath, Katrin Vorhölter, 2016-08-20 This survey provides an overview of the German discussion on modelling and applications in schools. It considers the development from the beginning of the 20th century to the present, and discusses the term “mathematical model” as well as different representations of the modelling process as modelling cycles. Different trends in the historical and current debate on applications and modelling can be differentiated as perspectives of modelling. Modelling is now one of the six general mathematical competencies defined in the educational standards for mathematics introduced in Germany in 2003, and there have been several initiatives to implement modelling in schools, as well as a whole range of empirical research projects focusing on teachers or students in modelling processes. As a special kind for implementing modelling into school, modelling weeks and days carried out by various German universities have been established. |
| example of a mathematical model: Scaling of Differential Equations Hans Petter Langtangen, Geir K. Pedersen, 2016-06-15 The book serves both as a reference for various scaled models with corresponding dimensionless numbers, and as a resource for learning the art of scaling. A special feature of the book is the emphasis on how to create software for scaled models, based on existing software for unscaled models. Scaling (or non-dimensionalization) is a mathematical technique that greatly simplifies the setting of input parameters in numerical simulations. Moreover, scaling enhances the understanding of how different physical processes interact in a differential equation model. Compared to the existing literature, where the topic of scaling is frequently encountered, but very often in only a brief and shallow setting, the present book gives much more thorough explanations of how to reason about finding the right scales. This process is highly problem dependent, and therefore the book features a lot of worked examples, from very simple ODEs to systems of PDEs, especially from fluid mechanics. The text is easily accessible and example-driven. The first part on ODEs fits even a lower undergraduate level, while the most advanced multiphysics fluid mechanics examples target the graduate level. The scientific literature is full of scaled models, but in most of the cases, the scales are just stated without thorough mathematical reasoning. This book explains how the scales are found mathematically. This book will be a valuable read for anyone doing numerical simulations based on ordinary or partial differential equations. |
| example of a mathematical model: Methods of Mathematical Modelling Thomas Witelski, Mark Bowen, 2015-09-18 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. |
| example of a mathematical model: Mathematical Modelling Murray S. Klamkin, 1987-01-01 Designed for classroom use, this book contains short, self-contained mathematical models of problems in the physical, mathematical, and biological sciences first published in the Classroom Notes section of the SIAM Review from 1975-1985. The problems provide an ideal way to make complex subject matter more accessible to the student through the use of concrete applications. Each section has extensive supplementary references provided by the editor from his years of experience with mathematical modelling. |
| example of a mathematical model: Applied Mathematical Modeling Douglas R. Shier, K.T. Wallenius, 1999-11-11 The practice of modeling is best learned by those armed with fundamental methodologies and exposed to a wide variety of modeling experience. Ideally, this experience could be obtained by working on actual modeling problems. But time constraints often make this difficult. Applied Mathematical Modeling provides a collection of models illustrating the power and richness of the mathematical sciences in supplying insight into the operation of important real-world systems. It fills a gap within modeling texts, focusing on applications across a broad range of disciplines. The first part of the book discusses the general components of the modeling process and highlights the potential of modeling in practice. These chapters discuss the general components of the modeling process, and the evolutionary nature of successful model building. The second part provides a rich compendium of case studies, each one complete with examples, exercises, and projects. In keeping with the multidimensional nature of the models presented, the chapters in the second part are listed in alphabetical order by the contributor's last name. Unlike most mathematical books, in which you must master the concepts of early chapters to prepare for subsequent material, you may start with any chapter. Begin with cryptology, if that catches your fancy, or go directly to bursty traffic if that is your cup of tea. Applied Mathematical Modeling serves as a handbook of in-depth case studies that span the mathematical sciences, building upon a modest mathematical background. Readers in other applied disciplines will benefit from seeing how selected mathematical modeling philosophies and techniques can be brought to bear on problems in their disciplines. The models address actual situations studied in chemistry, physics, demography, economics, civil engineering, environmental engineering, industrial engineering, telecommunications, and other areas. |
| example of a mathematical model: A First Course in Mathematical Modeling Frank R. Giordano, William P. Fox, Steven B. Horton, Maurice D. Weir, 2008-07-03 Offering a solid introduction to the entire modeling process, A FIRST COURSE IN MATHEMATICAL MODELING, 4th Edition delivers an excellent balance of theory and practice, giving students hands-on experience developing and sharpening their skills in the modeling process. Throughout the book, students practice key facets of modeling, including creative and empirical model construction, model analysis, and model research. The authors apply a proven six-step problem-solving process to enhance students' problem-solving capabilities -- whatever their level. Rather than simply emphasizing the calculation step, the authors first ensure that students learn how to identify problems, construct or select models, and figure out what data needs to be collected. By involving students in the mathematical process as early as possible -- beginning with short projects -- the book facilitates their progressive development and confidence in mathematics and modeling. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version. |
| example of a mathematical model: Mathematical Models in Finance S.D. Howison, F.P. Kelly, P. Wilmott, 1995-05-15 Mathematical Models in Finance compiles papers presented at the Royal Society of London discussion meeting. Topics range from the foundations of classical theory to sophisticated, up-to-date mathematical modeling and analysis. In the wake of the increased level of mathematical awareness in the financial research community, attention has focused on fundamental issues of market modelling that are not adequately allowed for in the standard analyses. Examples include market anomalies and nonlinear coupling effects, and demand new synthesis of mathematical and numerical techniques. This line of inquiry is further stimulated by ever tightening profits due to increased competition. Several papers in this volume offer pointers to future developments in this area. |
| example of a mathematical model: Model and Mathematics: From the 19th to the 21st Century Michael Friedman, Karin Krauthausen, 2022-08-08 This open access book collects the historical and medial perspectives of a systematic and epistemological analysis of the complicated, multifaceted relationship between model and mathematics, ranging from, for example, the physical mathematical models of the 19th century to the simulation and digital modelling of the 21st century. The aim of this anthology is to showcase the status of the mathematical model between abstraction and realization, presentation and representation, what is modeled and what models. This book is open access under a CC BY 4.0 license. |
Using Mathematics to Solve Real World Problems - Simon …
Today we will do this using straight lines as our equations, and we will solve the problem by drawing these lines (graphing). This process is called “Linear Programming” and is one of the …
Physical and Mathematical Models Chap 2 - IOE Notes
There are many examples in the field of mathematical physics where the same equations apply to different physical phenomena. For example, the flow of heat and the distribution of electric …
N. L. Gibson - Oregon State University
conceptual model represents our ideas about how the system works. It can be expressed visually in a model diagram, for example, involving boxes (state variables) and arrows (material flows …
MATHEMATICAL MODELING AND ANALYSIS: AN EXAMPLE …
Aug 8, 2020 · mathematical model based upon certain assumptions, collect their own data, and use their model to hit a target at some predetermined distance during class. In our courses at …
Mathematical Modelling Appendix 2 - NCERT
We shall first talk about what a mathematical model is, then we discuss the steps involved in the process of modelling. Mathematical modelling is an essential tool for understanding the world.
STRAND: PROBLEM SOLVING Unit 1 Mathematical Modelling
Mathematical modelling is central to all the CORE MATHS syllabi so we will start by looking at a number of contrasting case studies illustrating how mathematics is used to solve problems.
Chapter 1 Problem Solving with Mathematical Models
– A mathematical model is the collection of variables and relationships needed to describe pertinent features of such a problem. – Is the study of how to form mathematical models of …
Chapter 0. Mathematical Models: Functions and Graphs
Section 0.1 deals with mathematical models, functions, and graphs. Notation and terminology for intervals of numbers are described and rules for solving inequalities are discussed in Section 0.2.
Example of Mathematical Modelling - Mathematical Association
The following is designed to explain the processes of mathematical modelling as it is an important form of mathematical inquiry and highlights how mathematical modelling can be used to …
Math Modeling - M3 Challenge
A mathematical model is a representation of a system or scenario that is used to gain qualitative and/ or quantitative understanding of some real-world problems and to predict future behavior. …
Introduction to Mathematical Modeling and Computer …
Mathematical Modeling of stochastic processes is based on the probabil ity theory, in particular, that leads to using of random walks, Monte Carlo methods and the standard statistics tools.
LECTURE 1 INTRODUCTION Formulating a “Mathematical” …
Developing/Using Mathematical-Numerical models requires a detailed understanding of the algorithms used as well as the physics of the problem!
What is Mathematical Modelling? - Simon Fraser University
There are many, many definitions of mathematical model: Wikipedia: “A description of a system using mathematical concepts and language.” (too vague) Vahid Dabbaghian (2013): “A …
Mathematical Modeling - Pomona College
Construction of a mathematical model consists of translating a real world problem into a mathematical problem involving parameters, variables, functions, equations and/or inequalities.
Introduction to Mathematical Modeling - New York University
I will start the class with an example of this, together with ways to assess the accuracy of the approximation and construct more accurate approximations to take into account the term we …
INTRODUCTION TO MATHEMATICAL MODELLING - NCERT
In this chapter, we will introduce you to the process of constructing mathematical models, which is called mathematical modelling. In mathematical modelling, we take a real-world problem and …
Problem-Solving Strategy—Mathematical Model - Bucknell …
Mathematical models are developed from first principles; that is, any axioms, laws, or abstractions assumed and regarded as representing the highest possible degree of generalization.
MATHEMATICAL MODELING A Comprehensive Introduction
Here we do a quick tour of several examples of the mathematical process. We present the models as finished results as opposed to attempting to develop the models.
WhatIsMathematical Modeling? - Simon Fraser University
For example, levels of desired power may be linked to demographic or economic data, so any assumptions made about population and economic growth should be spelled out.
Using Mathematics to Solve Real World Problems - Simon …
Today we will do this using straight lines as our equations, and we will solve the problem by drawing these lines (graphing). This process is called “Linear Programming” and is one of the …
An Introduction to Mathematical Modelling
Models describe our beliefs about how the world functions. In mathematical modelling, we translate those beliefs into the language of mathematics. This has many advantages. …
Physical and Mathematical Models Chap 2 - IOE Notes
There are many examples in the field of mathematical physics where the same equations apply to different physical phenomena. For example, the flow of heat and the distribution of electric …
N. L. Gibson - Oregon State University
conceptual model represents our ideas about how the system works. It can be expressed visually in a model diagram, for example, involving boxes (state variables) and arrows (material flows …
MATHEMATICAL MODELING AND ANALYSIS: AN …
Aug 8, 2020 · mathematical model based upon certain assumptions, collect their own data, and use their model to hit a target at some predetermined distance during class. In our courses at …
Mathematical Modelling Appendix 2 - NCERT
We shall first talk about what a mathematical model is, then we discuss the steps involved in the process of modelling. Mathematical modelling is an essential tool for understanding the world.
STRAND: PROBLEM SOLVING Unit 1 Mathematical …
Mathematical modelling is central to all the CORE MATHS syllabi so we will start by looking at a number of contrasting case studies illustrating how mathematics is used to solve problems.
Chapter 1 Problem Solving with Mathematical Models
– A mathematical model is the collection of variables and relationships needed to describe pertinent features of such a problem. – Is the study of how to form mathematical models of …
Chapter 0. Mathematical Models: Functions and Graphs
Section 0.1 deals with mathematical models, functions, and graphs. Notation and terminology for intervals of numbers are described and rules for solving inequalities are discussed in Section 0.2.
Example of Mathematical Modelling - Mathematical Association
The following is designed to explain the processes of mathematical modelling as it is an important form of mathematical inquiry and highlights how mathematical modelling can be used to …
Math Modeling - M3 Challenge
A mathematical model is a representation of a system or scenario that is used to gain qualitative and/ or quantitative understanding of some real-world problems and to predict future behavior. …
Introduction to Mathematical Modeling and Computer …
Mathematical Modeling of stochastic processes is based on the probabil ity theory, in particular, that leads to using of random walks, Monte Carlo methods and the standard statistics tools.
LECTURE 1 INTRODUCTION Formulating a “Mathematical” …
Developing/Using Mathematical-Numerical models requires a detailed understanding of the algorithms used as well as the physics of the problem!
What is Mathematical Modelling? - Simon Fraser University
There are many, many definitions of mathematical model: Wikipedia: “A description of a system using mathematical concepts and language.” (too vague) Vahid Dabbaghian (2013): “A …
Mathematical Modeling - Pomona College
Construction of a mathematical model consists of translating a real world problem into a mathematical problem involving parameters, variables, functions, equations and/or inequalities.
Introduction to Mathematical Modeling - New York University
I will start the class with an example of this, together with ways to assess the accuracy of the approximation and construct more accurate approximations to take into account the term we …
INTRODUCTION TO MATHEMATICAL MODELLING - NCERT
In this chapter, we will introduce you to the process of constructing mathematical models, which is called mathematical modelling. In mathematical modelling, we take a real-world problem and …
Problem-Solving Strategy—Mathematical Model - Bucknell …
Mathematical models are developed from first principles; that is, any axioms, laws, or abstractions assumed and regarded as representing the highest possible degree of generalization.
MATHEMATICAL MODELING A Comprehensive …
Here we do a quick tour of several examples of the mathematical process. We present the models as finished results as opposed to attempting to develop the models.
WhatIsMathematical Modeling? - Simon Fraser University
For example, levels of desired power may be linked to demographic or economic data, so any assumptions made about population and economic growth should be spelled out.
