Mathematical Modeling for the Solution of Equations and Systems of Equations with Applications. Volume IV PDF Download
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Author: Ioannis K. Argyros
Publisher:
ISBN: 9781536174748
Category :
Languages : en
Pages : 633
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Book Description
The exponential growth of technology forces all disciplines to adjust accordingly, so they can meet the demands of a very dynamic world that heavily depends upon it. Therefore, mathematics cannot be an exception. In fact, mathematics should be the first to adjust and in fact it is. In this volume, which is a continuation of the previous three under the same title, we present state-of-the-art iterative methods for solving equations related to concrete problems from diverse areas such as applied mathematics, mathematical: biology, chemistry, economics, physics and also engineering to mention a few. Most of these methods are new and a few are old but still very popular. One major problem with iterative methods is that the convergence domain is small in general. We have introduced a technique that finds a smaller set than before containing the iterates leading to tighter Lipschitz functions than before. This way and under the same computational effort, we derive: weaker sufficient convergence criteria (leading to a wider choice of initial points); tighter error bounds on the distances involved (i.e., fewer iterates are needed to obtain a desired predetermined accuracy), and a more precise information on the location of the solution. These advantages are considered major achievements in computational disciplines. The volume requires knowledge of linear algebra, numerical functional analysis and familiarity with contemporary computing programing. It can be used by researchers, practitioners, senior undergraduate and graduate students as a source material or as a required textbook in the classroom.
Author: Ioannis K. Argyros
Publisher:
ISBN: 9781536174748
Category :
Languages : en
Pages : 633
Get Book Here
Book Description
The exponential growth of technology forces all disciplines to adjust accordingly, so they can meet the demands of a very dynamic world that heavily depends upon it. Therefore, mathematics cannot be an exception. In fact, mathematics should be the first to adjust and in fact it is. In this volume, which is a continuation of the previous three under the same title, we present state-of-the-art iterative methods for solving equations related to concrete problems from diverse areas such as applied mathematics, mathematical: biology, chemistry, economics, physics and also engineering to mention a few. Most of these methods are new and a few are old but still very popular. One major problem with iterative methods is that the convergence domain is small in general. We have introduced a technique that finds a smaller set than before containing the iterates leading to tighter Lipschitz functions than before. This way and under the same computational effort, we derive: weaker sufficient convergence criteria (leading to a wider choice of initial points); tighter error bounds on the distances involved (i.e., fewer iterates are needed to obtain a desired predetermined accuracy), and a more precise information on the location of the solution. These advantages are considered major achievements in computational disciplines. The volume requires knowledge of linear algebra, numerical functional analysis and familiarity with contemporary computing programing. It can be used by researchers, practitioners, senior undergraduate and graduate students as a source material or as a required textbook in the classroom.
Author: Ioannis K. Argyros
Publisher:
ISBN: 9781536133103
Category : MATHEMATICS
Languages : en
Pages :
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Book Description
Author: Ludmilla A. Uvarova
Publisher: Springer Science & Business Media
ISBN: 1475733976
Category : Mathematics
Languages : en
Pages : 285
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Book Description
This volume contains review articles and original results obtained in various fields of modern science using mathematical simulation methods. The basis of the articles are the plenary and some section reports that were made and discussed at the Fourth International Mathematical Simulation Conference, held in Moscow on June 27 through July 1, 2000. The conference was devoted to the following scientific areas: • mathematical and computer discrete systems models; • non-linear excitation in condensed media; • complex systems evolution; • mathematical models in economics; • non-equilibrium processes kinematics; • dynamics and structure of the molecular and biomolecular systems; • mathematical transfer models in non-linear systems; • numerical simulation and algorithms; • turbulence and determined chaos; • chemical physics of polymer. This conference was supported by the Russian Ministry of Education, Russian foundation for Basic Research and Federal Program "Integration". This volume contains the following sections: 1. models of non-linear phenomena in physics; 2. numerical methods and computer simulations; 3. mathematical computer models of discrete systems; 4. mathematical models in economics; 5. non-linear models in chemical physics and physical chemistry; 6. mathematical models of transport processes in complex systems. In Sections One and Five a number of fundamental and sufficiently general problems, concerning real physical and physical-chemical systems simulation, is discussed.
Author: Mark McKibben
Publisher: CRC Press
ISBN: 1466557079
Category : Mathematics
Languages : en
Pages : 500
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Book Description
A unique textbook for an undergraduate course on mathematical modeling, Differential Equations with MATLAB: Exploration, Applications, and Theory provides students with an understanding of the practical and theoretical aspects of mathematical models involving ordinary and partial differential equations (ODEs and PDEs). The text presents a unifying picture inherent to the study and analysis of more than 20 distinct models spanning disciplines such as physics, engineering, and finance. The first part of the book presents systems of linear ODEs. The text develops mathematical models from ten disparate fields, including pharmacokinetics, chemistry, classical mechanics, neural networks, physiology, and electrical circuits. Focusing on linear PDEs, the second part covers PDEs that arise in the mathematical modeling of phenomena in ten other areas, including heat conduction, wave propagation, fluid flow through fissured rocks, pattern formation, and financial mathematics. The authors engage students by posing questions of all types throughout, including verifying details, proving conjectures of actual results, analyzing broad strokes that occur within the development of the theory, and applying the theory to specific models. The authors’ accessible style encourages students to actively work through the material and answer these questions. In addition, the extensive use of MATLAB® GUIs allows students to discover patterns and make conjectures.
Author: Thomas Witelski
Publisher: Springer
ISBN: 3319230425
Category : Mathematics
Languages : en
Pages : 309
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Book Description
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.
Author: Belinda Barnes
Publisher: CRC Press
ISBN: 9780415298049
Category : Mathematics
Languages : en
Pages : 454
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Book Description
Certain basic modeling skills can be applied to a wide variety of problems. It focuses on those mathematical techniques which are applicable to models involving differential equations. Models in three different areas are considered: growth and decay process, interacting populations and heating/cooling problems. The main mathematical technique is solving differential equations, while the range of applications and mathematical techniques presented provides a broad appreciation of this type of modeling. This book contains three general sections: Compartmental Models, Population Models and Heat Transfer Models. Within each section, the process of constructing a model is presented in full detail. Applications and case studies are integral to this text, and case studies are included throughout. This is a useful course text, and basic calculus and fundamental computing skills are required.
Author: Sandip Banerjee
Publisher: CRC Press
ISBN: 1351022938
Category : Mathematics
Languages : en
Pages : 419
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Book Description
Mathematical Modeling: Models, Analysis and Applications, Second Edition introduces models of both discrete and continuous systems. This book is aimed at newcomers who desires to learn mathematical modeling, especially students taking a first course in the subject. Beginning with the step-by-step guidance of model formulation, this book equips the reader about modeling with difference equations (discrete models), ODE’s, PDE’s, delay and stochastic differential equations (continuous models). This book provides interdisciplinary and integrative overview of mathematical modeling, making it a complete textbook for a wide audience. A unique feature of the book is the breadth of coverage of different examples on mathematical modelling, which include population models, economic models, arms race models, combat models, learning model, alcohol dynamics model, carbon dating, drug distribution models, mechanical oscillation models, epidemic models, tumor models, traffic flow models, crime flow models, spatial models, football team performance model, breathing model, two neuron system model, zombie model and model on love affairs. Common themes such as equilibrium points, stability, phase plane analysis, bifurcations, limit cycles, period doubling and chaos run through several chapters and their interpretations in the context of the model have been highlighted. In chapter 3, a section on estimation of system parameters with real life data for model validation has also been discussed. Features Covers discrete, continuous, spatial, delayed and stochastic models. Over 250 illustrations, 300 examples and exercises with complete solutions. Incorporates MATHEMATICA® and MATLAB®, each chapter contains Mathematica and Matlab codes used to display numerical results (available at CRC website). Separate sections for Projects. Several exercise problems can also be used for projects. Presents real life examples of discrete and continuous scenarios. The book is ideal for an introductory course for undergraduate and graduate students, engineers, applied mathematicians and researchers working in various areas of natural and applied sciences.
Author: Jay Abramson
Publisher:
ISBN: 9789888407439
Category : Mathematics
Languages : en
Pages : 892
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Book Description
College Algebra provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra course. The modular approach and richness of content ensure that the book meets the needs of a variety of courses. College Algebra offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they've learned. Coverage and Scope In determining the concepts, skills, and topics to cover, we engaged dozens of highly experienced instructors with a range of student audiences. The resulting scope and sequence proceeds logically while allowing for a significant amount of flexibility in instruction. Chapters 1 and 2 provide both a review and foundation for study of Functions that begins in Chapter 3. The authors recognize that while some institutions may find this material a prerequisite, other institutions have told us that they have a cohort that need the prerequisite skills built into the course. Chapter 1: Prerequisites Chapter 2: Equations and Inequalities Chapters 3-6: The Algebraic Functions Chapter 3: Functions Chapter 4: Linear Functions Chapter 5: Polynomial and Rational Functions Chapter 6: Exponential and Logarithm Functions Chapters 7-9: Further Study in College Algebra Chapter 7: Systems of Equations and Inequalities Chapter 8: Analytic Geometry Chapter 9: Sequences, Probability and Counting Theory
Author: Achim Ilchmann
Publisher: Springer
ISBN: 3319466186
Category : Mathematics
Languages : en
Pages : 312
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Book Description
The present volume comprises survey articles on various fields of Differential-Algebraic Equations (DAEs) which have widespread applications in controlled dynamical systems, especially in mechanical and electrical engineering and a strong relation to (ordinary) differential equations. The individual chapters provide reviews, presentations of the current state of research and new concepts in - History of DAEs - DAE aspects of mechanical multibody systems - Model reduction of DAEs - Observability for DAEs - Numerical Analysis for DAEs The results are presented in an accessible style, making this book suitable not only for active researchers but also for graduate students (with a good knowledge of the basic principles of DAEs) for self-study.
Author: Pradip Debnath
Publisher: CRC Press
ISBN: 1000967263
Category : Mathematics
Languages : en
Pages : 493
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Book Description
Advanced Mathematical Analysis and its Applications presents state-of-the-art developments in mathematical analysis through new and original contributions and surveys, with a particular emphasis on applications in engineering and mathematical sciences. New research directions are indicated in each of the chapters, and while this book is meant primarily for graduate students, there is content that will be equally useful and stimulating for faculty and researchers. The readers of this book will require minimum knowledge of real, complex, and functional analysis, and topology. Features Suitable as a reference for graduate students, researchers, and faculty Contains the most up-to-date developments at the time of writing.
