An Introduction to Mathematical Modeling

Author: Edward A. Bender

Publisher: Courier Corporation

ISBN: 0486137120

Category: Mathematics

Page: 272

View: 3916

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.

An Introduction to Mathematical Modeling in Physiology, Cell Biology, and Immunology

American Mathematical Society, Short Course, January 8-9, 2001, New Orleans, Louisiana

Author: James Sneyd

Publisher: American Mathematical Soc.

ISBN: 0821828169

Category: Medical

Page: 177

View: 7319

In many respects, biology is the new frontier for applied mathematicians. This book demonstrates the important role mathematics plays in the study of some biological problems. It introduces mathematicians to the biological sciences and provides enough mathematics for bioscientists to appreciate the utility of the modelling approach. This book presents a number of diverse topics, such as neurophysiology, cell biology, immunology, and human genetics. It examines how research is done, what mathematics is used, what the outstanding questions are, and how to enter the field. Also given is a brief historical survey of each topic, putting current research into perspective. The book is suitable for mathematicians and biologists interested in mathematical methods in biology.

An Introduction to Mathematical Modeling

A Course in Mechanics

Author: J. Tinsley Oden

Publisher: John Wiley & Sons

ISBN: 1118105745

Category: Mathematics

Page: 348

View: 307

A modern approach to mathematical modeling, featuring unique applications from the field of mechanics An Introduction to Mathematical Modeling: A Course in Mechanics is designed to survey the mathematical models that form the foundations of modern science and incorporates examples that illustrate how the most successful models arise from basic principles in modern and classical mathematical physics. Written by a world authority on mathematical theory and computational mechanics, the book presents an account of continuum mechanics, electromagnetic field theory, quantum mechanics, and statistical mechanics for readers with varied backgrounds in engineering, computer science, mathematics, and physics. The author streamlines a comprehensive understanding of the topic in three clearly organized sections: Nonlinear Continuum Mechanics introduces kinematics as well as force and stress in deformable bodies; mass and momentum; balance of linear and angular momentum; conservation of energy; and constitutive equations Electromagnetic Field Theory and Quantum Mechanics contains a brief account of electromagnetic wave theory and Maxwell's equations as well as an introductory account of quantum mechanics with related topics including ab initio methods and Spin and Pauli's principles Statistical Mechanics presents an introduction to statistical mechanics of systems in thermodynamic equilibrium as well as continuum mechanics, quantum mechanics, and molecular dynamics Each part of the book concludes with exercise sets that allow readers to test their understanding of the presented material. Key theorems and fundamental equations are highlighted throughout, and an extensive bibliography outlines resources for further study. Extensively class-tested to ensure an accessible presentation, An Introduction to Mathematical Modeling is an excellent book for courses on introductory mathematical modeling and statistical mechanics at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for professionals working in the areas of modeling and simulation, physics, and computational engineering.

An Introduction to Mathematical Modeling of Infectious Diseases

Author: Michael Y. Li

Publisher: Springer

ISBN: 3319721224

Category: Mathematics

Page: 156

View: 4321

This text provides essential modeling skills and methodology for the study of infectious diseases through a one-semester modeling course or directed individual studies. The book includes mathematical descriptions of epidemiological concepts, and uses classic epidemic models to introduce different mathematical methods in model analysis. Matlab codes are also included for numerical implementations. It is primarily written for upper undergraduate and beginning graduate students in mathematical sciences who have an interest in mathematical modeling of infectious diseases. Although written in a rigorous mathematical manner, the style is not unfriendly to non-mathematicians.

Fundamentals of Algebraic Modeling

Author: Daniel L. Timmons,Catherine W. Johnson,Sonya McCook

Publisher: Cengage Learning

ISBN: 1285528719

Category: Mathematics

Page: 464

View: 2576

FUNDAMENTALS OF ALGEBRAIC MODELING 6e presents Algebraic concepts in non-threatening, easy-to-understand language and numerous step-by-step examples to illustrate ideas. This text aims to help you relate math skills to your daily life as well as a variety of professions including music, art, history, criminal justice, engineering, accounting, welding and many others. Available with InfoTrac Student Collections http://gocengage.com/infotrac. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Fundamentals of Algebraic Modeling: An Introduction to Mathematical Modeling with Algebra and Statistics

Author: Daniel L. Timmons,Catherine W. Johnson,Sonya McCook

Publisher: Cengage Learning

ISBN: 1111781036

Category: Mathematics

Page: 456

View: 5097

The fifth edition of FUNDAMENTALS OF ALGEBRAIC MODELING strives to show the student connections between math and their daily lives. Algebraic modeling concepts and solutions are presented in non-threatening, easy-to-understand language with numerous step-by-step examples to illustrate ideas. Whether they are going on to study early childhood education, graphic arts, automotive technologies, criminal justice, or something else, students will discover that the practical applications of mathematical modeling will continue to be useful well after they have finished this course. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Models for Life

An Introduction to Discrete Mathematical Modeling with Microsoft Office Excel

Author: Jeffrey T. Barton

Publisher: John Wiley & Sons

ISBN: 1119039819

Category: Mathematics

Page: 488

View: 3585

Features an authentic and engaging approach to mathematical modeling driven by real-world applications With a focus on mathematical models based on real and current data, Models for Life: An Introduction to Discrete Mathematical Modeling with Microsoft® Office Excel® guides readers in the solution of relevant, practical problems by introducing both mathematical and Excel techniques. The book begins with a step-by-step introduction to discrete dynamical systems, which are mathematical models that describe how a quantity changes from one point in time to the next. Readers are taken through the process, language, and notation required for the construction of such models as well as their implementation in Excel. The book examines single-compartment models in contexts such as population growth, personal finance, and body weight and provides an introduction to more advanced, multi-compartment models via applications in many areas, including military combat, infectious disease epidemics, and ranking methods. Models for Life: An Introduction to Discrete Mathematical Modeling with Microsoft® Office Excel® also features: A modular organization that, after the first chapter, allows readers to explore chapters in any order Numerous practical examples and exercises that enable readers to personalize the presented models by using their own data Carefully selected real-world applications that motivate the mathematical material such as predicting blood alcohol concentration, ranking sports teams, and tracking credit card debt References throughout the book to disciplinary research on which the presented models and model parameters are based in order to provide authenticity and resources for further study Relevant Excel concepts with step-by-step guidance, including screenshots to help readers better understand the presented material Both mathematical and graphical techniques for understanding concepts such as equilibrium values, fixed points, disease endemicity, maximum sustainable yield, and a drug’s therapeutic window A companion website that includes the referenced Excel spreadsheets, select solutions to homework problems, and an instructor’s manual with solutions to all homework problems, project ideas, and a test bank The book is ideal for undergraduate non-mathematics majors enrolled in mathematics or quantitative reasoning courses such as introductory mathematical modeling, applications of mathematics, survey of mathematics, discrete mathematical modeling, and mathematics for liberal arts. The book is also an appropriate supplement and project source for honors and/or independent study courses in mathematical modeling and mathematical biology. Jeffrey T. Barton, PhD, is Professor of Mathematics in the Mathematics Department at Birmingham-Southern College. A member of the American Mathematical Society and Mathematical Association of America, his mathematical interests include approximation theory, analytic number theory, mathematical biology, mathematical modeling, and the history of mathematics.

Numerical Analysis and Optimization

An Introduction to Mathematical Modelling and Numerical Simulation

Author: Grégoire Allaire

Publisher: Oxford University Press

ISBN: 0199205213

Category: Mathematics

Page: 455

View: 645

This work familiarises students with mathematical models (PDEs) and methods of numerical solution and optimisation. Including numerous exercises and examples, this is an ideal text for advanced students in Applied Mathematics, Engineering, Physical Science and Computer Science.

Mathematical Modeling in Systems Biology

An Introduction

Author: Brian P. Ingalls

Publisher: MIT Press

ISBN: 0262018888

Category: Science

Page: 408

View: 3075

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.

Fundamentals of Algebraic Modeling, An Introduction to Mathematical Modeling

Author: CTI Reviews

Publisher: Cram101 Textbook Reviews

ISBN: 1467280313

Category: Education

Page: 39

View: 7748

Facts101 is your complete guide to Fundamentals of Algebraic Modeling, An Introduction to Mathematical Modeling. In this book, you will learn topics such as as those in your book plus much more. With key features such as key terms, people and places, Facts101 gives you all the information you need to prepare for your next exam. Our practice tests are specific to the textbook and we have designed tools to make the most of your limited study time.

Fractional Calculus and Waves in Linear Viscoelasticity

An Introduction to Mathematical Models

Author: Francesco Mainardi

Publisher: World Scientific

ISBN: 1848163304

Category: Mathematics

Page: 368

View: 8037

This monograph provides a comprehensive overview of the author's work on the fields of fractional calculus and waves in linear viscoelastic media, which includes his pioneering contributions on the applications of special functions of the Mittag-Leffler and Wright types. It is intended to serve as a general introduction to the above-mentioned areas of mathematical modeling. The explanations in the book are detailed enough to capture the interest of the curious reader, and complete enough to provide the necessary background material needed to delve further into the subject and explore the research literature given in the huge general bibliography. This book is likely to be of interest to applied scientists and engineers.

An Introduction to the Mathematics of Neurons

Modeling in the Frequency Domain

Author: Frank C. Hoppensteadt

Publisher: Cambridge University Press

ISBN: 9780521599290

Category: Mathematics

Page: 211

View: 3952

This book describes signal processing aspects of neural networks, how we receive and assess information. Beginning with a presentation of the necessary background material in electronic circuits, mathematical modeling and analysis, signal processing, and neurosciences, it proceeds to applications. These applications include small networks of neurons, such as those used in control of warm-up and flight in moths and control of respiration during exercise in humans. Next, Hoppensteadt develops a theory of mnemonic surfaces and presents material on pattern formation and cellular automata. Finally, the text addresses the large networks, such as the thalamus-reticular complex circuit, that may be involved in focusing attention, and the development of connections in the visual cortex. This book will serve as an excellent text for advanced undergraduates and graduates in the physical sciences, mathematics, engineering, medicine and life sciences.

Solutions Manual to Accompany Models for Life

An Introduction to Discrete Mathematical Modeling with Microsoft Office Excel

Author: Jeffrey T. Barton

Publisher: John Wiley & Sons

ISBN: 1119040027

Category: Mathematics

Page: 182

View: 1040

A solutions manual to accompany An Introduction to Discrete Mathematical Modeling with Microsoft® Office Excel® With a focus on mathematical models based on real and current data, Models for Life: An Introduction to Discrete Mathematical Modeling with Microsoft® Office Excel® guides readers in the solution of relevant, practical problems by introducing both mathematical and Excel techniques. The book begins with a step-by-step introduction to discrete dynamical systems, which are mathematical models that describe how a quantity changes from one point in time to the next. Readers are taken through the process, language, and notation required for the construction of such models as well as their implementation in Excel. The book examines single-compartment models in contexts such as population growth, personal finance, and body weight and provides an introduction to more advanced, multi-compartment models via applications in many areas, including military combat, infectious disease epidemics, and ranking methods. Models for Life: An Introduction to Discrete Mathematical Modeling with Microsoft® Office Excel® also features: A modular organization that, after the first chapter, allows readers to explore chapters in any order Numerous practical examples and exercises that enable readers to personalize the presented models by using their own data Carefully selected real-world applications that motivate the mathematical material such as predicting blood alcohol concentration, ranking sports teams, and tracking credit card debt References throughout the book to disciplinary research on which the presented models and model parameters are based in order to provide authenticity and resources for further study Relevant Excel concepts with step-by-step guidance, including screenshots to help readers better understand the presented material Both mathematical and graphical techniques for understanding concepts such as equilibrium values, fixed points, disease endemicity, maximum sustainable yield, and a drug’s therapeutic window A companion website that includes the referenced Excel spreadsheets, select solutions to homework problems, and an instructor’s manual with solutions to all homework problems, project ideas, and a test bank

An Introduction to Physical Oncology

How Mechanistic Mathematical Modeling Can Improve Cancer Therapy Outcomes

Author: Vittorio Cristini,Eugene Koay,Zhihui Wang

Publisher: CRC Press

ISBN: 1315356880

Category: Mathematics

Page: 164

View: 4262

Physical oncology has the potential to revolutionize cancer research and treatment. The fundamental rationale behind this approach is that physical processes, such as transport mechanisms for drug molecules within tissue and forces exchanged by cancer cells with tissue, may play an equally important role as biological processes in influencing progression and treatment outcome. This book introduces the emerging field of physical oncology to a general audience, with a focus on recent breakthroughs that help in the design and discovery of more effective cancer treatments. It describes how novel mathematical models of physical transport processes incorporate patient tissue and imaging data routinely produced in the clinic to predict the efficacy of many cancer treatment approaches, including chemotherapy and radiation therapy. By helping to identify which therapies would be most beneficial for an individual patient, and quantifying their effects prior to actual implementation in the clinic, physical oncology allows doctors to design treatment regimens customized to each patient’s clinical needs, significantly altering the current clinical approach to cancer treatment and improving the outcomes for patients.

An Introduction to Mathematical Epidemiology

Author: Maia Martcheva

Publisher: Springer

ISBN: 1489976124

Category: Mathematics

Page: 453

View: 9442

The book is a comprehensive, self-contained introduction to the mathematical modeling and analysis of infectious diseases. It includes model building, fitting to data, local and global analysis techniques. Various types of deterministic dynamical models are considered: ordinary differential equation models, delay-differential equation models, difference equation models, age-structured PDE models and diffusion models. It includes various techniques for the computation of the basic reproduction number as well as approaches to the epidemiological interpretation of the reproduction number. MATLAB code is included to facilitate the data fitting and the simulation with age-structured models.