Methods of Mathematical Modelling

Continuous Systems and Differential Equations

Author: Thomas Witelski,Mark Bowen

Publisher: Springer

ISBN: 3319230425

Category: Mathematics

Page: 305

View: 6798

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

Mathematical Modelling Techniques

Author: Rutherford Aris

Publisher: Courier Corporation

ISBN: 0486138895

Category: Technology & Engineering

Page: 288

View: 3493

Highly useful volume discusses the types of models, how to formulate and manipulate them for best results. Numerous examples.

Principles of Mathematical Modelling

Ideas, Methods, Examples

Author: Alexander A. Samarskii,Alexander P. Mikhailov

Publisher: CRC Press

ISBN: 1482288133

Category: Mathematics

Page: 360

View: 779

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..

An Introduction to Mathematical Modeling

Author: Edward A. Bender

Publisher: Courier Corporation

ISBN: 9780486411804

Category: Mathematics

Page: 256

View: 3095

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 Modelling

A Graduate Textbook

Author: Seyed M. Moghadas,Majid Jaberi-Douraki

Publisher: John Wiley & Sons

ISBN: 1119484022

Category: Mathematics

Page: 192

View: 1246

An important resource that provides an overview of mathematical modelling Mathematical Modelling offers a comprehensive guide to both analytical and computational aspects of mathematical modelling that encompasses a wide range of subjects. The authors provide an overview of the basic concepts of mathematical modelling and review the relevant topics from differential equations and linear algebra. The text explores the various types of mathematical models, and includes a range of examples that help to describe a variety of techniques from dynamical systems theory. The book’s analytical techniques examine compartmental modelling, stability, bifurcation, discretization, and fixed-point analysis. The theoretical analyses involve systems of ordinary differential equations for deterministic models. The text also contains information on concepts of probability and random variables as the requirements of stochastic processes. In addition, the authors describe algorithms for computer simulation of both deterministic and stochastic models, and review a number of well-known models that illustrate their application in different fields of study. This important resource: Includes a broad spectrum of models that fall under deterministic and stochastic classes and discusses them in both continuous and discrete forms Demonstrates the wide spectrum of problems that can be addressed through mathematical modelling based on fundamental tools and techniques in applied mathematics and statistics Contains an appendix that reveals the overall approach that can be taken to solve exercises in different chapters Offers many exercises to help better understand the modelling process Written for graduate students in applied mathematics, instructors, and professionals using mathematical modelling for research and training purposes, Mathematical Modelling: A Graduate Textbook covers a broad range of analytical and computational aspects of mathematical modelling.

The Nature of Mathematical Modeling

Author: Neil A. Gershenfeld

Publisher: Cambridge University Press

ISBN: 9780521570954

Category: Mathematics

Page: 344

View: 6950

This book first covers exact and approximate analytical techniques (ordinary differential and difference equations, partial differential equations, variational principles, stochastic processes); numerical methods (finite differences for ODE's and PDE's, finite elements, cellular automata); model inference based on observations (function fitting, data transforms, network architectures, search techniques, density estimation); as well as the special role of time in modeling (filtering and state estimation, hidden Markov processes, linear and nonlinear time series). 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, providing an orientation to what they can (and cannot) do, enough background to use them to solve typical problems, and pointers to access the literature for particular applications.

Mathematical Modeling and Methods of Option Pricing

Author: Lishang Jiang,Canguo Li

Publisher: World Scientific

ISBN: 9812563695

Category: Science

Page: 329

View: 8857

From the perspective of partial differential equations (PDE), this book introduces the Black-Scholes-Merton's option pricing theory. A unified approach is used to model various types of option pricing as PDE problems, to derive pricing formulas as their solutions, and to design efficient algorithms from the numerical calculation of PDEs.

Principles of Mathematical Modeling

Author: Clive Dym

Publisher: Elsevier

ISBN: 0080470289

Category: Mathematics

Page: 303

View: 5688

Science and engineering students depend heavily on concepts of mathematical modeling. In an age where almost everything is done on a computer, author Clive Dym believes that students need to understand and "own" the underlying mathematics that computers are doing on their behalf. His goal for Principles of Mathematical Modeling, Second Edition, is to engage the student reader in developing a foundational understanding of the subject that will serve them well into their careers. The first half of the book begins with a clearly defined set of modeling principles, and then introduces a set of foundational tools including dimensional analysis, scaling techniques, and approximation and validation techniques. The second half demonstrates the latest applications for these tools to a broad variety of subjects, including exponential 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. Prospective students should have already completed courses in elementary algebra, trigonometry, and first-year calculus and have some familiarity with differential equations and basic physics. Serves as an introductory text on the development and application of mathematical models Focuses on techniques of particular interest to engineers, scientists, and others who model continuous systems Offers more than 360 problems, providing ample opportunities for practice Covers a wide range of interdisciplinary topics--from engineering to economics to the sciences Uses straightforward language and explanations that make modeling easy to understand and apply New to this Edition: A more systematic approach to mathematical modeling, outlining ten specific principles Expanded and reorganized chapters that flow in an increasing level of complexity Several new problems and updated applications Expanded figure captions that provide more information Improved accessibility and flexibility for teaching

Mathematical Modelling and Numerical Methods in Finance

Special Volume

Author: N.A

Publisher: Elsevier

ISBN: 0080931006

Category: Mathematics

Page: 684

View: 7898

Mathematical finance is a prolific scientific domain in which there exists a particular characteristic of developing both advanced theories and practical techniques simultaneously. Mathematical Modelling and Numerical Methods in Finance addresses the three most important aspects in the field: mathematical models, computational methods, and applications, and provides a solid overview of major new ideas and results in the three domains. Coverage of all aspects of quantitative finance including models, computational methods and applications Provides an overview of new ideas and results Contributors are leaders of the field

Modelling Mathematical Methods and Scientific Computation

Author: Nicola Bellomo,Luigi Preziosi

Publisher: CRC Press

ISBN: 9780849383311

Category: Mathematics

Page: 512

View: 5834

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

A Practical Course in Differential Equations and Mathematical Modelling

Classical and New Methods. Nonlinear Mathematical Models. Symmetry and Invariance Principles

Author: Nail H Ibragimov

Publisher: World Scientific Publishing Company

ISBN: 9813107766

Category: Mathematics

Page: 364

View: 7172

A Practical Course in Differential Equations and Mathematical Modelling is a unique blend of the traditional methods of ordinary and partial differential equations with Lie group analysis enriched by the author's own theoretical developments. The book — which aims to present new mathematical curricula based on symmetry and invariance principles — is tailored to develop analytic skills and “working knowledge” in both classical and Lie's methods for solving linear and nonlinear equations. This approach helps to make courses in differential equations, mathematical modelling, distributions and fundamental solution, etc. easy to follow and interesting for students. The book is based on the author's extensive teaching experience at Novosibirsk and Moscow universities in Russia, Collège de France, Georgia Tech and Stanford University in the United States, universities in South Africa, Cyprus, Turkey, and Blekinge Institute of Technology (BTH) in Sweden. The new curriculum prepares students for solving modern nonlinear problems and will essentially be more appealing to students compared to the traditional way of teaching mathematics.

Applied Mathematical Modelling of Engineering Problems

Author: N.V. Hritonenko,Yuri P. Yatsenko

Publisher: Springer Science & Business Media

ISBN: 1441991603

Category: Mathematics

Page: 286

View: 1897

The subject of the book is the "know-how" of applied mathematical modelling: how to construct specific models and adjust them to a new engineering environment or more precise realistic assumptions; how to analyze models for the purpose of investigating real life phenomena; and how the models can extend our knowledge about a specific engineering process. Two major sources of the book are the stock of classic models and the authors' wide experience in the field. The book provides a theoretical background to guide the development of practical models and their investigation. It considers general modelling techniques, explains basic underlying physical laws and shows how to transform them into a set of mathematical equations. The emphasis is placed on common features of the modelling process in various applications as well as on complications and generalizations of models. The book covers a variety of applications: mechanical, acoustical, physical and electrical, water transportation and contamination processes; bioengineering and population control; production systems and technical equipment renovation. Mathematical tools include partial and ordinary differential equations, difference and integral equations, the calculus of variations, optimal control, bifurcation methods, and related subjects.

Mathematical Modelling in Education and Culture


Author: Q-X Ye,W Blum,S K Houston,Q-Y Jiang

Publisher: Elsevier

ISBN: 0857099558

Category: Mathematics

Page: 342

View: 9309

The mathematical modelling movement in mathematics education at school and university level has been influencing curricula for about 25 years. Lecturers will find material to enhance their teaching and extracurricular activities and educators will find innovative ideas to inform their course design and focus their research, while students will find interesting problems to explore. Helps lecturers enhance their teaching and extracurricular activities Provides educators with innovative ideas to inform their course design and focus their research Students will find interesting problems to explore

Mining Modelling

Author: V. Ehrenberger,A. Fajkoš

Publisher: Elsevier

ISBN: 0444597441

Category: Technology & Engineering

Page: 217

View: 7925

The main aim of this book is to offer an exposition of the principles and applications of an original method which was introduced by the authors, developed gradually in the course of time, and applied extensively in the most diverse fields of management in the mining industry and power engineering. It is a relatively universal method of mathematical model construction and application intended to aid managerial personnel at various management levels in decision-making situations, which are frequently characterized by complicated relations of a quantitative as well as logical character. The method, called by the authors simply the ``method of mathematical-logical modelling'' (MLM for short), is based upon an interesting and effective combination of tools from mathematical logic, Boolean algebra and computer programming. From the mathematical point of view it is based primarily on the construction and solution of systems of pseudo-Boolean equations and inequalities with a generalized logical structure. The principal features of the method are its universality, iterativity, interactivity, and advanced and broadly applicable software, coded in FORTRAN 77. Due in particular to these properties, MLM is a powerful tool for modelling real-life situations in the mining industry (and, naturally, in other fields of human activity as well). The exposition is illustrated by a considerable number of examples. Some of these are rather simple and aimed at helping the reader verify his correct understanding of the text. Other examples, especially in the second part of the book (Chapters 6, 7 and 8), are more complicated and extensive. In some instances they have the character of case studies and demonstrate typical approaches applied when modelling mining situations. The book will be of interest to a broad range of specialists working in the mining industry - research workers, designers, computer personnel, system analysts, management personnel at all managerial levels, and also undergraduate as well as graduate students.

Methods of Mathematical Finance

Author: Ioannis Karatzas,Steven Shreve

Publisher: Springer

ISBN: 1493968459

Category: Mathematics

Page: 415

View: 6506

This sequel to Brownian Motion and Stochastic Calculus by the same authors develops contingent claim pricing and optimal consumption/investment in both complete and incomplete markets, within the context of Brownian-motion-driven asset prices. The latter topic is extended to a study of equilibrium, providing conditions for existence and uniqueness of market prices which support trading by several heterogeneous agents. Although much of the incomplete-market material is available in research papers, these topics are treated for the first time in a unified manner. The book contains an extensive set of references and notes describing the field, including topics not treated in the book. This book will be of interest to researchers wishing to see advanced mathematics applied to finance. The material on optimal consumption and investment, leading to equilibrium, is addressed to the theoretical finance community. The chapters on contingent claim valuation present techniques of practical importance, especially for pricing exotic options.

Practical Applied Mathematics

Modelling, Analysis, Approximation

Author: Sam Howison

Publisher: Cambridge University Press

ISBN: 9780521842747

Category: Mathematics

Page: 326

View: 4592

Drawing from a wide variety of mathematical subjects, this book aims to show how mathematics is realised in practice in the everyday world. Dozens of applications are used to show that applied mathematics is much more than a series of academic calculations. Mathematical topics covered include distributions, ordinary and partial differential equations, and asymptotic methods as well as basics of modelling. The range of applications is similarly varied, from the modelling of hair to piano tuning, egg incubation and traffic flow. The style is informal but not superficial. In addition, the text is supplemented by a large number of exercises and sideline discussions, assisting the reader's grasp of the material. Used either in the classroom by upper-undergraduate students, or as extra reading for any applied mathematician, this book illustrates how the reader's knowledge can be used to describe the world around them.

Trends in Teaching and Learning of Mathematical Modelling


Author: Gabriele Kaiser,Werner Blum,Rita Borromeo Ferri,Gloria Stillman

Publisher: Springer Science & Business Media

ISBN: 9789400709102

Category: Education

Page: 734

View: 1357

This book contains suggestions for and reflections on the teaching, learning and assessing of mathematical modelling and applications in a rapidly changing world, including teaching and learning environments. It addresses all levels of education from universities and technical colleges to secondary and primary schools. Sponsored by the International Community of Teachers of Mathematical Modelling and Applications (ICTMA), it reflects recent ideas and methods contributed by specialists from 30 countries in Africa, the Americas, Asia, Australia and Europe. Inspired by contributions to the Fourteenth Conference on the Teaching of Mathematical Modelling and Applications (ICTMA14) in Hamburg, 2009, the book describes the latest trends in the teaching and learning of mathematical modelling at school and university including teacher education. The broad and versatile range of topics will stress the international state-of-the-art on the following issues: Theoretical reflections on the teaching and learning of modelling Modelling competencies Cognitive perspectives on modelling Modelling examples for all educational levels Practice of modelling in school and at university level Practices in Engineering and Applications

Mathematical Modelling of Zombies

Author: Robert Smith?

Publisher: University of Ottawa Press

ISBN: 0776621688

Category: Mathematics

Page: 468

View: 8689

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.

Mathematical Modelling in Science and Technology

The Fourth International Conference, Zurich, Switzerland, August 1983

Author: Xavier J.R. Avula,Rudolf E. Kalman,Anthanasios I. Liapis

Publisher: Elsevier

ISBN: 1483190595

Category: Mathematics

Page: 1022

View: 559

Mathematical Modelling in Science and Technology: The Fourth International Conference covers the proceedings of the Fourth International Conference by the same title, held at the Swiss Federal Institute of Technology, Zurich, Switzerland on August 15-17, 1983. Mathematical modeling is a powerful tool to solve many complex problems presented by scientific and technological developments. This book is organized into 20 parts encompassing 180 chapters. The first parts present the basic principles, methodology, systems theory, parameter estimation, system identification, and optimization of mathematical modeling. The succeeding parts discuss the features of stochastic and numerical modeling and simulation languages. Considerable parts deal with the application areas of mathematical modeling, such as in chemical engineering, solid and fluid mechanics, water resources, medicine, economics, transportation, and industry. The last parts tackle the application of mathematical modeling in student management and other academic cases. This book will prove useful to researchers in various science and technology fields.