Mathematical Modelling Selected Objects And Processes
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Mathematical Modelling Selected Objects And Processes
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Author : Anatoliy A Martynyuk
language : en
Publisher: World Scientific
Release Date : 2025-04-11
Mathematical Modelling Selected Objects And Processes written by Anatoliy A Martynyuk and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-11 with Mathematics categories.
This is the first book on the problems of mathematical modelling that combines a generalised approach to the problem of mathematical modelling processes and phenomena in the real world with developing modelling methods in relation to specific objects and processes. Some of the problems discussed here include the stability and bifurcation of simplified models of supply and demand, and resultants of various approaches, such as standardisation, unification, partial ordering and data packaging.As well as touching upon the general principles of modelling, the book studies the stability of mathematical models using the generalised direct Lyapunov method based on matrix-valued auxiliary functions. It has significant potential for application in the design of new moving objects (nano-robots, manipulators, drones, etc.) and processes related to artificial intelligence (multidimensional interaction of related data arrays) that can be described by differential equations of different types.Written by two respected specialists in the field of the qualitative theory of equations and problems of modelling real-world phenomena, this book is primarily targeted at specialists in the field of engineering sciences, but is also suitable for graduate courses.
Mathematical Modelling
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Author : Anatoliĭ Andreevich Martyni︠u︡k
language : en
Publisher: World Scientific Publishing Company
Release Date : 2024-12
Mathematical Modelling written by Anatoliĭ Andreevich Martyni︠u︡k and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12 with Mathematics categories.
This is the first book on the problems of mathematical modelling that combines a generalised approach to the problem of mathematical modelling processes and phenomena in the real world with developing modelling methods in relation to specific objects and processes. Some of the problems discussed here include the stability and bifurcation of simplified models of supply and demand, and resultants of various approaches, such as standardisation, unification, partial ordering and data packaging. As well as touching upon the general principles of modelling, the book studies the stability of mathematical models using the generalised direct Lyapunov method based on matrix-valued auxiliary functions. It has significant potential for application in the design of new moving objects (nano-robots, manipulators, drones, etc.) and processes related to artificial intelligence (multidimensional interaction of related data arrays) that can be described by differential equations of different types. Written by two respected specialists in the field of the qualitative theory of equations and problems of modelling real-world phenomena, this book is primarily targeted at specialists in the field of engineering sciences, but is also suitable for graduate courses.
Mathematical And Experimental Modeling Of Physical And Biological Processes
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Author : H.T. Banks
language : en
Publisher: CRC Press
Release Date : 2009-01-12
Mathematical And Experimental Modeling Of Physical And Biological Processes written by H.T. Banks and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-12 with Mathematics categories.
Through several case study problems from industrial and scientific research laboratory applications, Mathematical and Experimental Modeling of Physical and Biological Processes provides students with a fundamental understanding of how mathematics is applied to problems in science and engineering. For each case study problem, the authors discuss why a model is needed and what goals can be achieved with the model. Exploring what mathematics can reveal about applications, the book focuses on the design of appropriate experiments to validate the development of mathematical models. It guides students through the modeling process, from empirical observations and formalization of properties to model analysis and interpretation of results. The authors also describe the hardware and software tools used to design the experiments so faculty/students can duplicate them. Integrating real-world applications into the traditional mathematics curriculum, this textbook deals with the formulation and analysis of mathematical models in science and engineering. It gives students an appreciation of the use of mathematics and encourages them to further study the applied topics. Real experimental data for projects can be downloaded from CRC Press Online.
Methods Of Mathematical Modelling
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Author : Thomas Witelski
language : en
Publisher: Springer
Release Date : 2015-09-18
Methods Of Mathematical Modelling written by Thomas Witelski and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-18 with Mathematics categories.
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 Modeling And Simulation
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Author : Kai Velten
language : en
Publisher: John Wiley & Sons
Release Date : 2009-06-01
Mathematical Modeling And Simulation written by Kai Velten and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-01 with Science categories.
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).
Introduction To Mathematical Modeling And Computer Simulations
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Author : Vladimir Mityushev
language : en
Publisher: CRC Press
Release Date : 2018-02-19
Introduction To Mathematical Modeling And Computer Simulations written by Vladimir Mityushev and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-19 with Mathematics categories.
Introduction to Mathematical Modeling and Computer Simulations is written as a textbook for readers who want to understand the main principles of Modeling and Simulations in settings that are important for the applications, without using the profound mathematical tools required by most advanced texts. It can be particularly useful for applied mathematicians and engineers who are just beginning their careers. The goal of this book is to outline Mathematical Modeling using simple mathematical descriptions, making it accessible for first- and second-year students.
Mathematical Modeling And Methods Of Option Pricing
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Author : Lishang Jiang
language : en
Publisher: World Scientific Publishing Company
Release Date : 2005-07-18
Mathematical Modeling And Methods Of Option Pricing written by Lishang Jiang and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-07-18 with Business & Economics categories.
From the unique perspective of partial differential equations (PDE), this self-contained book presents a systematic, advanced introduction to 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. In particular, the qualitative and quantitative analysis of American option pricing is treated based on free boundary problems, and the implied volatility as an inverse problem is solved in the optimal control framework of parabolic equations.
Mathematical Modelling And Applications
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Author : Gloria Ann Stillman
language : en
Publisher: Springer
Release Date : 2017-11-05
Mathematical Modelling And Applications written by Gloria Ann Stillman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-05 with Education categories.
This volume documents on-going research and theorising in the sub-field of mathematics education devoted to the teaching and learning of mathematical modelling and applications. Mathematical modelling provides a way of conceiving and resolving problems in the life world of people whether these range from the everyday individual numeracy level to sophisticated new problems for society at large. Mathematical modelling and real world applications are considered as having potential for multi-disciplinary work that involves knowledge from a variety of communities of practice such as those in different workplaces (e.g., those of educators, designers, construction engineers, museum curators) and in different fields of academic endeavour (e.g., history, archaeology, mathematics, economics). From an educational perspective, researching the development of competency in real world modelling involves research situated in crossing the boundaries between being a student engaged in modelling or mathematical application to real word tasks in the classroom, being a teacher of mathematical modelling (in or outside the classroom or bridging both), and being a modeller of the world outside the classroom. This is the focus of many of the authors of the chapters in this book. All authors of this volume are members of the International Community of Teachers of Mathematical Modelling (ICTMA), the peak research body into researching the teaching and learning of mathematical modelling at all levels of education from the early years to tertiary education as well as in the workplace.
Hydrogeodynamics
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Author : I.K. Gavich
language : en
Publisher: CRC Press
Release Date : 2020-10-07
Hydrogeodynamics written by I.K. Gavich and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-07 with Science categories.
This text focuses particularly on the growing interest in hydrodynamic principles of the study of underground waters, new methods of eco-based hydrogeodynamic analysis, and the estimation of the quantity of infiltration water transfer. The author also discusses aspects of mass transfer by subsurface water flow in the light of molecular kinetics, and examines a new apporach to investigating the slow movements of groundwater at the deep zones of the hydrolithosphere.
Measuring Professional Competence For The Teaching Of Mathematical Modelling
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Author : Raphael Wess
language : en
Publisher: Springer Nature
Release Date : 2021-07-14
Measuring Professional Competence For The Teaching Of Mathematical Modelling written by Raphael Wess and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-14 with Education categories.
This open access book presents a structural model and an associated test instrument designed to provide a detailed analysis of professional competences for teaching mathematical modelling. The conceptualisation is based on the COACTIV model, which describes aspects, areas and facets of professional competences of teachers. The manual provides an overview of the essential teaching skills in application-related contexts and offers the tools needed to capture these aspects. It discusses the objectives and application areas of the instrument, as well as the development of the test. In addition, it describes the implementation and evaluates the quality and results of the structural equation analysis of the model. Teaching mathematical modelling is a cognitively challenging activity for (prospective) teachers. Thus, teacher education requires a detailed analysis of professional competence for teaching mathematical modelling. Measuring this competence requires theoretical models that accurately describe requirements placed upon teachers, as well as appropriate evaluation tools that adequately capture skills and abilities in this field. This book presents an instrument that measures the professional competences in a sample of 349 prospective teachers.