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Mathematical Modeling

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Concepts of Mathematical Modeling

Concepts of Mathematical Modeling Book
Author : Walter J. Meyer
Publisher : Courier Corporation
Release : 2004-01-01
ISBN : 9780486435152
Language : En, Es, Fr & De

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Book Description :

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. The range of subjects includes topics from the physical, biological, and social sciences, as well as those of operations research. Excerises. 1984 edition.

An Introduction to Mathematical Modeling

An Introduction to Mathematical Modeling Book
Author : Edward A. Bender
Publisher : Courier Corporation
Release : 2000-03-06
ISBN : 048641180X
Language : En, Es, Fr & De

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Book Description :

Accessible text features over 100 reality-based examples pulled from the science, engineering and operations research fields. Prerequisites: ordinary differential equations, continuous probability. Numerous references. Includes 27 black-and-white figures. 1978 edition.

Mathematical Modeling

Mathematical Modeling Book
Author : Sandip Banerjee
Publisher : CRC Press
Release : 2014-02-07
ISBN : 1439854513
Language : En, Es, Fr & De

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Book Description :

Almost every year, a new book on mathematical modeling is published, so, why another? The answer springs directly from the fact that it is very rare to find a book that covers modeling with all types of differential equations in one volume. Until now. Mathematical Modeling: Models, Analysis and Applications covers modeling with all kinds of differential equations, namely ordinary, partial, delay, and stochastic. The book also contains a chapter on discrete modeling, consisting of differential equations, making it a complete textbook on this important skill needed for the study of science, engineering, and social sciences. More than just a textbook, this how-to guide presents tools for mathematical modeling and analysis. It offers a wide-ranging overview of mathematical ideas and techniques that provide a number of effective approaches to problem solving. Topics covered include spatial, delayed, and stochastic modeling. The text provides real-life examples of discrete and continuous mathematical modeling scenarios. MATLAB® and Mathematica® are incorporated throughout the text. The examples and exercises in each chapter can be used as problems in a project. Since mathematical modeling involves a diverse range of skills and tools, the author focuses on techniques that will be of particular interest to engineers, scientists, and others who use models of discrete and continuous systems. He gives students a foundation for understanding and using the mathematics that is the basis of computers, and therefore a foundation for success in engineering and science streams.

Mathematical Modeling

Mathematical Modeling Book
Author : Mark M. Meerschaert
Publisher : Academic Press
Release : 2013-02-11
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Meerschaert's new edition strengthens his position as the survey text of choice for mathematical modeling courses, adding ample instructor support and leveraging on-line delivery for solutions manuals and software ancillaries. From genetic engineering to hurricane prediction, mathematical models guide much of the decision-making in our society, and if the assumptions and methods underlying the modeling are flawed, the outcome can be disastrously poor, as recent events have proved. Since mathematical modeling is a rapidly growing specialty with applications in so many scientific and technical disciplines, there is a need for mathematically rigorous treatments of the subject, and particularly for texts that expose students to a range of possible approaches. Offers increased support for instructors, including MATLAB material as well as other on-line resourcesFeatures new sections on time series analysis and diffusion modelsProvides additional problems with international focus such as whale and dolphin populations, plus updated optimization problems.

Principles of Mathematical Modeling

Principles of Mathematical Modeling Book
Author : Clive Dym
Publisher : Academic Press
Release : 2004-07-05
ISBN : 9780122265518
Language : En, Es, Fr & De

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Book Description :

This book provides a readable and informative introduction to the development and application of mathematical models in science and engineering. The first half of the book begins with a clearly defined set of modeling principles, and then introduces a set of foundational tools (dimensional analysis, scaling techniques, and approximation and validation techniques). The second half then applies these foundational tools to a broad variety of subjects, including exponenttial growth and decay in fields ranging from biology to economics, traffic flow, free and forced vibration of mechanical and other systems, and optimization problems in biology, structures, and social decision making. An extensive collection of more than 360 problems offer ample opportunity in both a formal course and for the individual reader. (Midwest).

Mathematical Modeling

Mathematical Modeling Book
Author : Christof Eck,Harald Garcke,Peter Knabner
Publisher : Springer
Release : 2017-04-21
ISBN : 9783319551609
Language : En, Es, Fr & De

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Book Description :

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.

Mathematical Modeling in Ecology

Mathematical Modeling in Ecology Book
Author : C. Jeffries
Publisher : Springer Science & Business Media
Release : 1989-01-01
ISBN : 9780817634216
Language : En, Es, Fr & De

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Book Description :

Mathematical ecology is the application of mathematics to describe and understand ecosystems. There are two main approaches. One is to describe natural communities and induce statistical patterns or relationships which should generally occur. However, this book is devoted entirely to introducing the student to the second approach: to study deterministic mathematical models and, on the basis of mathematical results on the models, to look for the same patterns or relationships in nature. This book is a compromise between three competing desiderata. It seeks to: maximize the generality of the models; constrain the models to "behave" realistically, that is, to exhibit stability and other features; and minimize the difficulty of presentations of the models. The ultimate goal of the book is to introduce the reader to the general mathematical tools used in building realistic ecosystem models. Just such a model is presented in Chapter Nine. The book should also serve as a stepping-stone both to advanced mathematical works like Stability of Biological Communities by Yu. M. Svirezhev and D. O. Logofet (Mir, Moscow, 1983) and to advanced modeling texts like Freshwater Ecosystems by M. Straskraba and A. H. Gnauch (Elsevier, Amsterdam, 1985).

Mathematical Modeling for the Life Sciences

Mathematical Modeling for the Life Sciences Book
Author : Jacques Istas
Publisher : Springer Science & Business Media
Release : 2005-06-09
ISBN : 9783540253051
Language : En, Es, Fr & De

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Book Description :

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

Modeling Students Mathematical Modeling Competencies

Modeling Students  Mathematical Modeling Competencies Book
Author : Richard Lesh,Peter L. Galbraith,Christopher R. Haines,Andrew Hurford
Publisher : Springer
Release : 2014-09-02
ISBN : 9781489983893
Language : En, Es, Fr & De

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Book Description :

As we enter the 21st century, there is an urgent need for new approaches to mathematics education emphasizing its relevance in young learners’ futures. Modeling Students’ Mathematical Modeling Competencies explores the vital trend toward using real-world problems as a basis for teaching mathematics skills, competencies, and applications. Blending theoretical constructs and practical considerations, the book presents papers from the latest conference of the ICTMA, beginning with the basics (Why are models necessary? Where can we find them?) and moving through intricate concepts of how students perceive math, how instructors teach—and how both can become better learners. Dispatches as varied as classroom case studies, analyses of math in engineering work, and an in-depth review of modeling-based curricula in the Netherlands illustrate modeling activities on the job, methods of overcoming math resistance, and the movement toward replicable models and lifelong engagement. A sampling of topics covered: How students recognize the usefulness of mathematics Creating the modeling-oriented classroom Assessing and evaluating students’ modeling capabilities The relationship between modeling and problem-solving Instructor methods for developing their own models of modeling New technologies for modeling in the classroom Modeling Students’ Mathematical Modeling Competencies offers welcome clarity and focus to the international research and professional community in mathematics, science, and engineering education, as well as those involved in the sciences of teaching and learning these subjects.

A First Course in Mathematical Modeling

A First Course in Mathematical Modeling Book
Author : Frank R. Giordano,William P. Fox,Steven B. Horton
Publisher : Cengage Learning
Release : 2013-03-05
ISBN : 1285531760
Language : En, Es, Fr & De

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Book Description :

Offering a solid introduction to the entire modeling process, A FIRST COURSE IN MATHEMATICAL MODELING, 5th Edition delivers an excellent balance of theory and practice, and gives you relevant, hands-on experience developing and sharpening your modeling skills. Throughout, the book emphasizes key facets of modeling, including creative and empirical model construction, model analysis, and model research, and provides myriad opportunities for practice. The authors apply a proven six-step problem-solving process to enhance your problem-solving capabilities -- whatever your level. In addition, rather than simply emphasizing the calculation step, the authors first help you learn how to identify problems, construct or select models, and figure out what data needs to be collected. By involving you in the mathematical process as early as possible -- beginning with short projects -- this text facilitates your 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.

Mathematical Modeling with Excel

Mathematical Modeling with Excel Book
Author : Brian Albright
Publisher : Jones & Bartlett Learning
Release : 2010
ISBN : 9780763765668
Language : En, Es, Fr & De

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Book Description :

Mathematical modeling is the use of applying mathematics to real-world problems and investigating important questions about their outcomes. Mathematical Modeling with Excel presents various methods used to build and analyze mathematical models in a format that students can quickly comprehend. Excel is used as a tool to accomplish this goal of building and analyzing the models. Ideal for math and secondary math education majors, this text presents a wide variety of common types of models, as well as some new types, and presents each in a unique, easy-to-understand format. End-of-chapter exercises ask students to modify or refine the existing model, analyze it further, or adapt it to similar scenarios.

Exploring Mathematical Modeling in Biology Through Case Studies and Experimental Activities

Exploring Mathematical Modeling in Biology Through Case Studies and Experimental Activities Book
Author : Rebecca Sanft,Anne Walter
Publisher : Academic Press
Release : 2020-04-15
ISBN : 0128195959
Language : En, Es, Fr & De

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Book Description :

Exploring Mathematical Modeling in Biology through Case Studies and Experimental Activities provides supporting materials for courses taken by students majoring in mathematics, computer science or in the life sciences. The book's cases and lab exercises focus on hypothesis testing and model development in the context of real data. The supporting mathematical, coding and biological background permit readers to explore a problem, understand assumptions, and the meaning of their results. The experiential components provide hands-on learning both in the lab and on the computer. As a beginning text in modeling, readers will learn to value the approach and apply competencies in other settings. Included case studies focus on building a model to solve a particular biological problem from concept and translation into a mathematical form, to validating the parameters, testing the quality of the model and finally interpreting the outcome in biological terms. The book also shows how particular mathematical approaches are adapted to a variety of problems at multiple biological scales. Finally, the labs bring the biological problems and the practical issues of collecting data to actually test the model and/or adapting the mathematics to the data that can be collected. Presents a single volume on mathematics and biological examples, with data and wet lab experiences suitable for non-experts Contains three real-world biological case studies and one wet lab for application of the mathematical models Includes R code templates throughout the text, which are also available through an online repository, along with the necessary data files to complete all projects and labs

Mathematical Modeling

Mathematical Modeling Book
Author : Stefan Heinz
Publisher : Springer Science & Business Media
Release : 2011-07-03
ISBN : 9783642203114
Language : En, Es, Fr & De

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Book Description :

The whole picture of Mathematical Modeling is systematically and thoroughly explained in this text for undergraduate and graduate students of mathematics, engineering, economics, finance, biology, chemistry, and physics. This textbook gives an overview of the spectrum of modeling techniques, deterministic and stochastic methods, and first-principle and empirical solutions. Complete range: The text continuously covers the complete range of basic modeling techniques: it provides a consistent transition from simple algebraic analysis methods to simulation methods used for research. Such an overview of the spectrum of modeling techniques is very helpful for the understanding of how a research problem considered can be appropriately addressed. Complete methods: Real-world processes always involve uncertainty, and the consideration of randomness is often relevant. Many students know deterministic methods, but they do hardly have access to stochastic methods, which are described in advanced textbooks on probability theory. The book develops consistently both deterministic and stochastic methods. In particular, it shows how deterministic methods are generalized by stochastic methods. Complete solutions: A variety of empirical approximations is often available for the modeling of processes. The question of which assumption is valid under certain conditions is clearly relevant. The book provides a bridge between empirical modeling and first-principle methods: it explains how the principles of modeling can be used to explain the validity of empirical assumptions. The basic features of micro-scale and macro-scale modeling are discussed – which is an important problem of current research.

Mathematical Modeling in Systems Biology

Mathematical Modeling in Systems Biology Book
Author : Brian P. Ingalls
Publisher : MIT Press
Release : 2013-07-05
ISBN : 0262018888
Language : En, Es, Fr & De

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Book Description :

An introduction to the mathematical concepts and techniques needed for the construction and analysis of models in molecular systems biology. Systems techniques are integral to current research in molecular cell biology, and system-level investigations are often accompanied by mathematical models. These models serve as working hypotheses: they help us to understand and predict the behavior of complex systems. This book offers an introduction to mathematical concepts and techniques needed for the construction and interpretation of models in molecular systems biology. It is accessible to upper-level undergraduate or graduate students in life science or engineering who have some familiarity with calculus, and will be a useful reference for researchers at all levels. The first four chapters cover the basics of mathematical modeling in molecular systems biology. The last four chapters address specific biological domains, treating modeling of metabolic networks, of signal transduction pathways, of gene regulatory networks, and of electrophysiology and neuronal action potentials. Chapters 3–8 end with optional sections that address more specialized modeling topics. Exercises, solvable with pen-and-paper calculations, appear throughout the text to encourage interaction with the mathematical techniques. More involved end-of-chapter problem sets require computational software. Appendixes provide a review of basic concepts of molecular biology, additional mathematical background material, and tutorials for two computational software packages (XPPAUT and MATLAB) that can be used for model simulation and analysis.

Mathematical Modeling of Biological Processes

Mathematical Modeling of Biological Processes Book
Author : Avner Friedman,Chiu-Yen Kao
Publisher : Springer
Release : 2014-10-08
ISBN : 9783319083131
Language : En, Es, Fr & De

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Book Description :

This book on mathematical modeling of biological processes includes a wide selection of biological topics that demonstrate the power of mathematics and computational codes in setting up biological processes with a rigorous and predictive framework. Topics include: enzyme dynamics, spread of disease, harvesting bacteria, competition among live species, neuronal oscillations, transport of neurofilaments in axon, cancer and cancer therapy, and granulomas. Complete with a description of the biological background and biological question that requires the use of mathematics, this book is developed for graduate students and advanced undergraduate students with only basic knowledge of ordinary differential equations and partial differential equations; background in biology is not required. Students will gain knowledge on how to program with MATLAB without previous programming experience and how to use codes in order to test biological hypothesis.

Mathematical Models in Epidemiology

Mathematical Models in Epidemiology Book
Author : Fred Brauer,Carlos Castillo-Chavez,Zhilan Feng
Publisher : Springer Nature
Release : 2019-10-10
ISBN : 1493998285
Language : En, Es, Fr & De

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Book Description :

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.

Mathematical Modeling of Collective Behavior in Socio Economic and Life Sciences

Mathematical Modeling of Collective Behavior in Socio Economic and Life Sciences Book
Author : Giovanni Naldi,Lorenzo Pareschi,Giuseppe Toscani
Publisher : Birkhäuser
Release : 2010-08-30
ISBN : 9780817649456
Language : En, Es, Fr & De

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Book Description :

Using examples from finance and modern warfare to the flocking of birds and the swarming of bacteria, the collected research in this volume demonstrates the common methodological approaches and tools for modeling and simulating collective behavior. The topics presented point toward new and challenging frontiers of applied mathematics, making the volume a useful reference text for applied mathematicians, physicists, biologists, and economists involved in the modeling of socio-economic systems.

Mathematical Modeling and Computation in Finance with Exercises and Python and MATLAB Computer Codes

Mathematical Modeling and Computation in Finance  with Exercises and Python and MATLAB Computer Codes Book
Author : Cornelis W. Oosterlee,Lech A. Grzelak
Publisher : World Scientific Publishing Europe Limited
Release : 2019-10-14
ISBN : 9781786347947
Language : En, Es, Fr & De

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Book Description :

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.

The Nature of Mathematical Modeling

The Nature of Mathematical Modeling Book
Author : Neil A. Gershenfeld,Neil Gershenfeld
Publisher : Cambridge University Press
Release : 1999
ISBN : 9780521570954
Language : En, Es, Fr & De

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Book Description :

Major text/reference work on computer modeling for students and researchers in any quantitative or semi-quantitative discipline, first published in 1998.

Mathematical Modeling and Computer Simulation

Mathematical Modeling and Computer Simulation Book
Author : Daniel P. Maki,Maynard Thompson
Publisher : Brooks/Cole Publishing Company
Release : 2006
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Daniel Maki and Maynard Thompson provide a conceptual framework for the process of building and using mathematical models, illustrating the uses of mathematical and computer models in a variety of situations. This text helps students learn that model building is a dynamic process involving simplification, approximation, abstraction, analysis, computation, and comparison. Students begin the process of model building with a consideration of phenomena arising in another academic area or in the real world.