Methods of Mathematical Modelling

Continuous Systems and Differential Equations

Author: Thomas Witelski,Mark Bowen

Publisher: Springer

ISBN: 3319230425

Category: Mathematics

Page: 305

View: 2946

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: 6311

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

The Nature of Mathematical Modeling

Author: Neil A. Gershenfeld

Publisher: Cambridge University Press

ISBN: 9780521570954

Category: Mathematics

Page: 344

View: 9450

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.

Principles of Mathematical Modelling

Ideas, Methods, Examples

Author: Alexander A. Samarskii,Alexander P. Mikhailov

Publisher: CRC Press

ISBN: 9780415272803

Category: Mathematics

Page: 360

View: 6858

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: 1808

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.

Methods of Mathematical Finance

Author: Ioannis Karatzas,Steven E. Shreve

Publisher: Springer Science & Business Media

ISBN: 0387948392

Category: Business & Economics

Page: 407

View: 2628

Written by two of the best-known researchers in mathematical finance, Methods of Mathematical Finance will appeal to theorists and practitioners in this very active research area. It is the sequel to Brownian Motion and Stochastic Calculus by the same authors, and includes much material that has not appeared before in book form. From the reviews:"Constitutes a valuable research-level text which should be consulted by anyone interested in the area." --MATHEMATICAL REVIEWS

Mathematical Modelling and Numerical Methods in Finance

Special Volume

Author: N.A

Publisher: Elsevier

ISBN: 0080931006

Category: Mathematics

Page: 684

View: 955

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: 7344

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.

Mathematical Modelling

A Graduate Textbook

Author: Seyed M. Moghadas,Majid Jaberi-Douraki

Publisher: John Wiley & Sons

ISBN: 1119484022

Category: Mathematics

Page: 192

View: 5894

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.

Mathematical Modelling

Author: Matti Heiliö,Timo Lähivaara,Erkki Laitinen,Timo Mantere,Jorma Merikoski,Kimmo Raivio,Risto Silvennoinen,Antti Suutala,Tanja Tarvainen,Timo Tiihonen,Jukka Tuomela,Esko Turunen,Marko Vauhkonen

Publisher: Springer

ISBN: 3319278363

Category: Mathematics

Page: 242

View: 4454

This book provides a thorough introduction to the challenge of applying mathematics in real-world scenarios. Modelling tasks rarely involve well-defined categories, and they often require multidisciplinary input from mathematics, physics, computer sciences, or engineering. In keeping with this spirit of modelling, the book includes a wealth of cross-references between the chapters and frequently points to the real-world context. The book combines classical approaches to modelling with novel areas such as soft computing methods, inverse problems, and model uncertainty. Attention is also paid to the interaction between models, data and the use of mathematical software. The reader will find a broad selection of theoretical tools for practicing industrial mathematics, including the analysis of continuum models, probabilistic and discrete phenomena, and asymptotic and sensitivity analysis.

Mathematical Modelling

Case Studies and Projects

Author: J. Caldwell,Douglas K.S. Ng

Publisher: Springer Science & Business Media

ISBN: 1402019939

Category: Mathematics

Page: 253

View: 7152

Over the past decade there has been an increasing demand for suitable material in the area of mathematical modelling as applied to science, engineering, business and management. Recent developments in computer technology and related software have provided the necessary tools of increasing power and sophistication which have significant implications for the use and role of mathematical modelling in the above disciplines. In the past, traditional methods have relied heavily on expensive experimentation and the building of scaled models, but now a more flexible and cost effective approach is available through greater use of mathematical modelling and computer simulation. In particular, developments in computer algebra, symbolic manipulation packages and user friendly software packages for large scale problems, all have important implications in both the teaching of mathematical modelling and, more importantly, its use in the solution of real world problems. Many textbooks have been published which cover the art and techniques of modelling as well as specific mathematical modelling techniques in specialist areas within science and business. In most of these books the mathematical material tends to be rather tailor made to fit in with a one or two semester course for teaching students at the undergraduate or postgraduate level, usually the former. This textbook is quite different in that it is intended to build on and enhance students’ modelling skills using a combination of case studies and projects.

Mathematical Modeling and Methods of Option Pricing

Author: Lishang Jiang,Canguo Li

Publisher: World Scientific

ISBN: 9812563695

Category: Science

Page: 329

View: 3995

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: 878

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

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: 764

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.

Mathematical Modelling of Zombies

Author: Robert Smith?

Publisher: University of Ottawa Press

ISBN: 0776621688

Category: Mathematics

Page: 468

View: 5625

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 One Dimension

An Introduction Via Difference and Differential Equations

Author: Jacek Banasiak

Publisher: Cambridge University Press

ISBN: 1107654688

Category: Mathematics

Page: 118

View: 9551

Uses a wide variety of applications to demonstrate the universality of mathematical techniques in describing and analysing natural phenomena.

Modelling Methodology for Physiology and Medicine

Author: Ewart Carson,Claudio Cobelli

Publisher: Elsevier

ISBN: 9780080511900

Category: Technology & Engineering

Page: 421

View: 9697

Modelling Methodology for Physiology and Medicine offers a unique approach and an unprecedented range of coverage of the state-of-the-art, advanced modelling methodology that is widely applicable to physiology and medicine. The book opens with a clear and integrated treatment of advanced methodology for developing mathematical models of physiology and medical systems. Readers are then shown how to apply this methodology beneficially to real-world problems in physiology and medicine, such as circulation and respiration. Builds upon and enhances the readers existing knowledge of modelling methodology and practice Editors are internationally renowned leaders in their respective fields

Mathematical Modelling

A Case Studies Approach

Author: Reinhard Illner

Publisher: American Mathematical Soc.

ISBN: 0821836501

Category: Mathematics

Page: 196

View: 890

Mathematical modelling is a subject without boundaries. It is the means by which mathematics becomes useful to virtually any subject. Moreover, modelling has been and continues to be a driving force for the development of mathematics itself. This book explains the process of modelling real situations to obtain mathematical problems that can be analyzed, thus solving the original problem. The presentation is in the form of case studies, which are developed much as they would be in true applications. In many cases, an initial model is created, then modified along the way. Some cases are familiar, such as the evaluation of an annuity. Others are unique, such as the fascinating situation in which an engineer, armed only with a slide rule, had 24 hours to compute whether a valve would hold when a temporary rock plug was removed from a water tunnel. Each chapter ends with a set of exercises and some suggestions for class projects.Some projects are extensive, as with the explorations of the predator-prey model; others are more modest. The text was designed to be suitable for a one-term course for advanced undergraduates. The selection of topics and the style of exposition reflect this choice. The authors have also succeeded in demonstrating just how enjoyable the subject can be. This is an ideal text for classes on modelling. It can also be used in seminars or as preparation for mathematical modelling competitions.

Guide to Mathematical Modelling

Author: Dilwyn Edwards,Mike Hamson

Publisher: Macmillan International Higher Education

ISBN: 1349100420

Category: Applied mathematics

Page: 277

View: 5234

The authors' enthusiasm for their subject is eloquently conveyed in this book, and draws the reader very quickly into active investigation of the problems posed. By providing plenty of modelling examples from a wide variety of fields - most of which are familiar from everyday life - the book shows how to apply mathematical ideas to situations which would not previously have been considered to be 'mathematical' in character.