Methods of Mathematical Modelling

Author: Thomas Witelski
Publisher: Springer
ISBN: 3319230425
Format: PDF, ePub, Docs
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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.

Methods in Approximation

Author: N.D. Bellman
Publisher: Springer Science & Business Media
ISBN: 9400946007
Format: PDF
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Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Mathematical Modelling Techniques

Author: Rutherford Aris
Publisher: Courier Corporation
ISBN: 0486138895
Format: PDF, Kindle
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Highly useful volume discusses the types of models, how to formulate and manipulate them for best results. Numerous examples.

Mathematical Modelling and Numerical Methods in Finance

Author:
Publisher: Elsevier
ISBN: 0080931006
Format: PDF, Kindle
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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

Principles of Mathematical Modelling

Author: Alexander A. Samarskii
Publisher: CRC Press
ISBN: 9780415272803
Format: PDF, Mobi
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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..

Modelling Mathematical Methods and Scientific Computation

Author: Nicola Bellomo
Publisher: CRC Press
ISBN: 9780849383311
Format: PDF, Kindle
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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

Author: Jagat Narain Kapur
Publisher: New Age International
ISBN: 9788122400069
Format: PDF, Docs
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Each Chapter Of The Book Deals With Mathematical Modelling Through One Or More Specified Techniques. Thus There Are Chapters On Mathematical Modelling Through Algebra, Geometry, Trigonometry And Calculus, Through Ordinary Differential Equations Of First And Second Order, Through Systems Of Differential Equations, Through Difference Equations, Through Partial Differential Equations, Through Functional Equations And Integral Equations, Through Delay-Differential, Differential-Difference And Integro-Differential Equations, Through Calculus Of Variations And Dynamic Programming, Through Graphs, Through Mathematical Programming, Maximum Principle And Maximum Entropy Principle.Each Chapter Contains Mathematical Models From Physical, Biological, Social, Management Sciences And Engineering And Technology And Illustrates Unity In Diversity Of Mathematical Sciences.The Book Contains Plenty Of Exercises In Mathematical Modelling And Is Aimed To Give A Panoramic View Of Applications Of Modelling In All Fields Of Knowledge. It Contains Both Probabilistic And Deterministic Models.The Book Presumes Only The Knowledge Of Undergraduate Mathematics And Can Be Used As A Textbook At Senior Undergraduate Or Post-Graduate Level For A One Or Two- Semester Course For Students Of Mathematics, Statistics, Physical, Social And Biological Sciences And Engineering. It Can Also Be Useful For All Users Of Mathematics And For All Mathematical Modellers.

An Introduction to Mathematical Modeling

Author: Edward A. Bender
Publisher: Courier Corporation
ISBN: 0486137120
Format: PDF
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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.

Principles of Mathematical Modeling

Author: Clive Dym
Publisher: Elsevier
ISBN: 0080470289
Format: PDF, Docs
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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

Author: Matti Heiliƶ
Publisher: Springer
ISBN: 3319278363
Format: PDF, ePub, Mobi
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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.