Aspects of Mathematical Modelling

This book demonstrates the application of mathematics to research topics in ecology and environmental science, health and medicine, phylogenetics and neural networks, theoretical chemistry, economics and management.

Author: Roger J. Hosking

Publisher: Birkhäuser

ISBN: 3764385901

Category: Mathematics

Page: 375

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The construction of mathematical models is an essential scientific activity. Mathematics is associated with developments in science and engineering, but more recently mathematical modelling has been used to investigate complex systems that arise in other fields. This book demonstrates the application of mathematics to research topics in ecology and environmental science, health and medicine, phylogenetics and neural networks, theoretical chemistry, economics and management.
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Mathematical Models in Natural Science and Engineering

This book has come into being as a result ofthe author's lectures on mathematical modelling rendered to the students, BS and MS degree holders specializing in applied mathematics and computer science and to post-graduate students in exact ...

Author: Juri I. Neimark

Publisher: Springer Science & Business Media

ISBN: 9783540478782

Category: Technology & Engineering

Page: 572

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This book has come into being as a result ofthe author's lectures on mathematical modelling rendered to the students, BS and MS degree holders specializing in applied mathematics and computer science and to post-graduate students in exact sciences of the Nizhny Novgorod State University after N.!. Lobatchevsky. These lectures are adapted and presented as a single whole ab out mathematical models and modelling. This new course of lectures appeared because the contemporary Russian educational system in applied mathematics rested upon a combination of fundamental and applied mathematics training; this way of training oriented students upon solving only the exactly stated mathematical problems, and thus there was created a certain estrangement to the most essential stages and sides of real solutions for applied problems, such as thinking over and deeply piercing the essence of a specific problem and its mathematical statement. This statement embraces simplifications, adopted idealizations and creating a mathematical model, its correction and matching the results obtained against a real system. There also existed another main objective, namely to orient university graduates in their future research not only upon purely mathematical issues but also upon comprehending and widely applying mathematics as a universal language of contemporary exact science, and mathematical modelling as a powerful me ans for studying nature, engineering and human society.
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Mathematical Modeling for the Life Sciences

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

Author: Jacques Istas

Publisher: Springer Science & Business Media

ISBN: 354025305X

Category: Mathematics

Page: 168

View: 294

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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
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Mathematical Models In Science

From this point, the author shows how to extract reasonable models for both General Relativity and Quantum Theory. This book concludes that the universe turns out to be the 6-dimensional Hilbert scheme of pairs of points in affine 3-space.

Author: Olav Arnfinn Laudal

Publisher: World Scientific

ISBN: 9781800610293

Category: Science

Page: 320

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Mathematical Models in Science treats General Relativity and Quantum Mechanics in a non-commutative Algebraic Geometric framework.Based on ideas first published in Geometry of Time-Spaces: Non-commutative Algebraic Geometry Applied to Quantum Theory (World Scientific, 2011), Olav Arnfinn Laudal proposes a Toy Model as a Theory of Everything, starting with the notion of the Big Bang in Cosmology, modeled as the non-commutative deformation of a thick point. From this point, the author shows how to extract reasonable models for both General Relativity and Quantum Theory. This book concludes that the universe turns out to be the 6-dimensional Hilbert scheme of pairs of points in affine 3-space. With this in place, one may develop within the model much of the physics known to the reader. In particular, this theory is applicable to the concept of Dark Matter and its effects on our visual universe.Hence, Mathematical Models in Science proves the dependency of deformation theory in Mathematical Physics and summarizes the development of physical applications of pure mathematics developed in the twentieth century.
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Mathematical Modeling in Science and Engineering

This text guides students and professionals through the axiomatic approach, a powerful method that will enable them to easily master the principle types of mathematical and computational models used in engineering and science.

Author: Ismael Herrera

Publisher: John Wiley & Sons

ISBN: 9781118087572

Category: Mathematics

Page: 243

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"Mathematical and computational modeling (MCM) can be used in a diverse set of applications making it a very appealing and potent modeling tool. This book uses a novel and powerful procedural approach to teaching MCM, the Axiomatic Approach, which permits incorporating in a single model, systems that occur in many different branches of science and engineering.This book focuses on the mathematical models, in which processes to be modeled are expressed as a system of partial differential equations. It introduces a systematic method for constructing such models, which can be applied to any macroscopic physical system. This latter feature of the Axiomatic Approach is very valuable when treating new systems, since it permits formulating the models of previously unknown systems. Using it, many of the systems of most common occurrence in engineering practice are introduced and discussed. The effectiveness of this approach is reflected in the broadness and importance of the subjects treated; they cover a great diversity of topics that are basic in many branches of engineering including: Civil Engineering, Mechanical Engineering, Petroleum Engineering, and Water Resources.These topics include: Flow of fluids and transport of solutes which are free to move in the physical space and where fluids may be restricted to move in a porous medium. The transport of solutes is fundamental in Environmental Engineering Water Resources and Petroleum Engineering since it is the means of predicting contaminant behavior. The porous medium based equations are also used to model Enhanced Oil Recovery which is very important for sustaining the oil supply of the world. Model of static and dynamic elasticity are used in several branches of engineering including Foundation and Seismic Engineering"--
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Mathematical Modeling in Optical Science

This volume addresses recent developments in mathematical modeling in three areas of optical science: diffractive optics, photonic band gap structures, and waveguides.

Author: Gang Bao

Publisher: SIAM

ISBN: 0898717590

Category: Optics

Page: 334

View: 282

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This volume addresses recent developments in mathematical modeling in three areas of optical science: diffractive optics, photonic band gap structures, and waveguides. Particular emphasis is on the formulation of mathematical models and the design and analysis of new computational approaches. The book contains cutting-edge discourses on emerging technology in optics that provides significant challenges and opportunities for applied mathematicians, researchers, and engineers.
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Mathematical Modeling and Simulation

This concise and clear introduction to the topic requires only basic knowledge of calculus and linear algebra - all other concepts and ideas are developed in the course of the book.

Author: Kai Velten

Publisher: John Wiley & Sons

ISBN: 9783527627615

Category: Science

Page: 362

View: 368

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This concise and clear introduction to the topic requires only basic knowledge of calculus and linear algebra - all other concepts and ideas are developed in the course of the book. Lucidly written so as to appeal to undergraduates and practitioners alike, it enables readers to set up simple mathematical models on their own and to interpret their results and those of others critically. To achieve this, many examples have been chosen from various fields, such as biology, ecology, economics, medicine, agricultural, chemical, electrical, mechanical and process engineering, which are subsequently discussed in detail. Based on the author`s modeling and simulation experience in science and engineering and as a consultant, the book answers such basic questions as: What is a mathematical model? What types of models do exist? Which model is appropriate for a particular problem? What are simulation, parameter estimation, and validation? The book relies exclusively upon open-source software which is available to everybody free of charge. The entire book software - including 3D CFD and structural mechanics simulation software - can be used based on a free CAELinux-Live-DVD that is available in the Internet (works on most machines and operating systems).
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An Introduction to Mathematical Modeling

Accessible text features over 100 reality-based examples pulled from the science, engineering and operations research fields.

Author: Edward A. Bender

Publisher: Courier Corporation

ISBN: 9780486411804

Category: Mathematics

Page: 256

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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.
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Limits Of Mathematical Modeling In The Social Sciences The The Significance Of Godel s Incompleteness Phenomenon

Can we model them? This book investigates and attempts to answer these questions through Gödel's two incompleteness theorems, and in doing so demonstrates how influential Gödel is in modern logical and mathematical thinking.

Author: Doria Francisco Antonio

Publisher: World Scientific

ISBN: 9781786343178

Category: Mathematics

Page: 288

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Current mathematical models are notoriously unreliable in describing the time evolution of unexpected social phenomena, from financial crashes to revolution. Can such events be forecast? Can we compute probabilities about them? Can we model them? This book investigates and attempts to answer these questions through Gödel's two incompleteness theorems, and in doing so demonstrates how influential Gödel is in modern logical and mathematical thinking. Many mathematical models are applied to economics and social theory, while Gödel's theorems are able to predict their limitations for more accurate analysis and understanding of national and international events. This unique discussion is written for graduate level mathematicians applying their research to the social sciences, including economics, social studies and philosophy, and also for formal logicians and philosophers of science.
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Mathematical Modeling of Complex Biological Systems

The book may be used for advanced graduate courses and seminars in biological systems modeling. This book describes the evolution of several socio-biological systems using mathematical kinetic theory.

Author: Abdelghani Bellouquid

Publisher: Springer Science & Business Media

ISBN: 9780817643959

Category: Science

Page: 188

View: 927

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This book describes the evolution of several socio-biological systems using mathematical kinetic theory. Specifically, it deals with modeling and simulations of biological systems whose dynamics follow the rules of mechanics as well as rules governed by their own ability to organize movement and biological functions. It proposes a new biological model focused on the analysis of competition between cells of an aggressive host and cells of a corresponding immune system. Proposed models are related to the generalized Boltzmann equation. The book may be used for advanced graduate courses and seminars in biological systems modeling.
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