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Author: Zdzislaw Trzaska Publisher: Springer Nature ISBN: 3031399854 Category : Technology & Engineering Languages : en Pages : 320
Book Description
This book keeps an eye in the direction of applications of advanced and high performance scientific computing in describing the behavior of natural and constructed systems, e.g. chaos, bifurcation, fractal, Lyapunov exponent, period doubling, Poincaré map, strange attractor etc. With the aid of powerful computers the modem theory of chaos and its geometry, the fractals, and attractors are developed. The concepts of object oriented computing are introduced early in the text and steadily expanded as one progresses through the chapters. The beginning of each chapter is of an introductory nature, followed by practical applications, the discussion of numerical results, theoretical investigations on nonlinear stability and convergence. This is the first complete introduction to process modelling and computing that fully integrates software tools — enabling professionals and students to master critical techniques hands on through computer simulations based on the popular MATLAB environment. The book offers a simple tool for all those oscillations that are travelling through the world, helping them discover its hidden beauty. Many applications as well as results of computer simulations are presented. The center of concern is set on existing as well as emerging continuous methods of investigations useful for researchers, engineers and practitioners active in many and often interdisciplinary fields, where physics, electrochemistry, biology and medicine play a key role. Coverage includes: • Dynamic behavior of nonlinear systems, • Fundamental descriptions of processes exhibiting nonlinear oscillations, • Mechanism and function of structures of nonlinear oscillations’ patterns, • Analysis of dynamical oscillations in electric circuits and systems, • Artificial intelligence models of natural systems, • Nonlinear oscillations in chemistry, biology and medicine, • Oscillations in mechanics and transport systems, • Oscillations in fractional-order systems, • Energy harvesting systems from the surrounding environment. With an insatiable appetite for exploring the surrounding world and doing research, this book can help readers quickly find ways to use new computers and facilitate the quest for greater knowledge and understanding of reality. The reach of novelty of the book ranges from new mathematical ideas to motivating questions and science issues in many subject areas.
Author: Zdzislaw Trzaska Publisher: Springer Nature ISBN: 3031399854 Category : Technology & Engineering Languages : en Pages : 320
Book Description
This book keeps an eye in the direction of applications of advanced and high performance scientific computing in describing the behavior of natural and constructed systems, e.g. chaos, bifurcation, fractal, Lyapunov exponent, period doubling, Poincaré map, strange attractor etc. With the aid of powerful computers the modem theory of chaos and its geometry, the fractals, and attractors are developed. The concepts of object oriented computing are introduced early in the text and steadily expanded as one progresses through the chapters. The beginning of each chapter is of an introductory nature, followed by practical applications, the discussion of numerical results, theoretical investigations on nonlinear stability and convergence. This is the first complete introduction to process modelling and computing that fully integrates software tools — enabling professionals and students to master critical techniques hands on through computer simulations based on the popular MATLAB environment. The book offers a simple tool for all those oscillations that are travelling through the world, helping them discover its hidden beauty. Many applications as well as results of computer simulations are presented. The center of concern is set on existing as well as emerging continuous methods of investigations useful for researchers, engineers and practitioners active in many and often interdisciplinary fields, where physics, electrochemistry, biology and medicine play a key role. Coverage includes: • Dynamic behavior of nonlinear systems, • Fundamental descriptions of processes exhibiting nonlinear oscillations, • Mechanism and function of structures of nonlinear oscillations’ patterns, • Analysis of dynamical oscillations in electric circuits and systems, • Artificial intelligence models of natural systems, • Nonlinear oscillations in chemistry, biology and medicine, • Oscillations in mechanics and transport systems, • Oscillations in fractional-order systems, • Energy harvesting systems from the surrounding environment. With an insatiable appetite for exploring the surrounding world and doing research, this book can help readers quickly find ways to use new computers and facilitate the quest for greater knowledge and understanding of reality. The reach of novelty of the book ranges from new mathematical ideas to motivating questions and science issues in many subject areas.
Author: Leah Edelstein-Keshet Publisher: SIAM ISBN: 9780898719147 Category : Mathematics Languages : en Pages : 629
Book Description
Mathematical Models in Biology is an introductory book for readers interested in biological applications of mathematics and modeling in biology. A favorite in the mathematical biology community, it shows how relatively simple mathematics can be applied to a variety of models to draw interesting conclusions. Connections are made between diverse biological examples linked by common mathematical themes. A variety of discrete and continuous ordinary and partial differential equation models are explored. Although great advances have taken place in many of the topics covered, the simple lessons contained in this book are still important and informative. Audience: the book does not assume too much background knowledge--essentially some calculus and high-school algebra. It was originally written with third- and fourth-year undergraduate mathematical-biology majors in mind; however, it was picked up by beginning graduate students as well as researchers in math (and some in biology) who wanted to learn about this field.
Author: Vladimir Mityushev Publisher: CRC Press ISBN: 1351998757 Category : Mathematics Languages : en Pages : 202
Book Description
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.
Author: Dianne P. O'Leary Publisher: SIAM ISBN: 0898716667 Category : Mathematics Languages : en Pages : 376
Book Description
This book is a practical guide to the numerical solution of linear and nonlinear equations, differential equations, optimization problems, and eigenvalue problems. It treats standard problems and introduces important variants such as sparse systems, differential-algebraic equations, constrained optimization, Monte Carlo simulations, and parametric studies. Stability and error analysis are emphasized, and the Matlab algorithms are grounded in sound principles of software design and understanding of machine arithmetic and memory management. Nineteen case studies provide experience in mathematical modeling and algorithm design, motivated by problems in physics, engineering, epidemiology, chemistry, and biology. The topics included go well beyond the standard first-course syllabus, introducing important problems such as differential-algebraic equations and conic optimization problems, and important solution techniques such as continuation methods. The case studies cover a wide variety of fascinating applications, from modeling the spread of an epidemic to determining truss configurations.
Author: Vitaly Volpert Publisher: MDPI ISBN: 3039434934 Category : Mathematics Languages : en Pages : 224
Book Description
Mathematical modelling in biomedicine is a rapidly developing scientific discipline at the intersection of medicine, biology, mathematics, physics, and computer science. Its progress is stimulated by fundamental scientific questions and by the applications to public health. This book represents a collection of papers devoted to mathematical modelling of various physiological problems in normal and pathological conditions. It covers a broad range of topics including cardiovascular system and diseases, heart and brain modelling, tumor growth, viral infections, and immune response. Computational models of blood circulation are used to study the influence of heart arrhythmias on coronary blood flow and on operating modes for left-ventricle-assisted devices. Wave propagation in the cardiac tissue is investigated in order to show the influence of tissue heterogeneity and fibrosis. The models of tumor growth are used to determine optimal protocols of antiangiogenic and radiotherapy. The models of viral hepatitis kinetics are considered for the parameter identification, and the evolution of viral quasi-species is investigated. The book presents the state-of-the-art in mathematical modelling in biomedicine and opens new perspectives in this passionate field of research.
Author: Edward A. Bender Publisher: Courier Corporation ISBN: 0486137120 Category : Mathematics Languages : en Pages : 273
Book Description
Employing a practical, "learn by doing" approach, this first-rate text fosters the development of the skills beyond the pure mathematics needed to set up and manipulate mathematical models. The author draws on a diversity of fields — including science, engineering, and operations research — to provide over 100 reality-based examples. Students learn from the examples by applying mathematical methods to formulate, analyze, and criticize models. Extensive documentation, consisting of over 150 references, supplements the models, encouraging further research on models of particular interest. The lively and accessible text requires only minimal scientific background. Designed for senior college or beginning graduate-level students, it assumes only elementary calculus and basic probability theory for the first part, and ordinary differential equations and continuous probability for the second section. All problems require students to study and create models, encouraging their active participation rather than a mechanical approach. Beyond the classroom, this volume will prove interesting and rewarding to anyone concerned with the development of mathematical models or the application of modeling to problem solving in a wide array of applications.
Author: Sandip Banerjee Publisher: CRC Press ISBN: 1351022938 Category : Mathematics Languages : en Pages : 419
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: Angela B. Shiflet Publisher: Princeton University Press ISBN: 140085055X Category : Computers Languages : en Pages : 857
Book Description
The essential introduction to computational science—now fully updated and expanded Computational science is an exciting new field at the intersection of the sciences, computer science, and mathematics because much scientific investigation now involves computing as well as theory and experiment. This textbook provides students with a versatile and accessible introduction to the subject. It assumes only a background in high school algebra, enables instructors to follow tailored pathways through the material, and is the only textbook of its kind designed specifically for an introductory course in the computational science and engineering curriculum. While the text itself is generic, an accompanying website offers tutorials and files in a variety of software packages. This fully updated and expanded edition features two new chapters on agent-based simulations and modeling with matrices, ten new project modules, and an additional module on diffusion. Besides increased treatment of high-performance computing and its applications, the book also includes additional quick review questions with answers, exercises, and individual and team projects. The only introductory textbook of its kind—now fully updated and expanded Features two new chapters on agent-based simulations and modeling with matrices Increased coverage of high-performance computing and its applications Includes additional modules, review questions, exercises, and projects An online instructor's manual with exercise answers, selected project solutions, and a test bank and solutions (available only to professors) An online illustration package is available to professors
Author: National Research Council Publisher: National Academies Press ISBN: 030917662X Category : Mathematics Languages : en Pages : 143
Book Description
Computational methods are rapidly becoming major tools of theoretical, pharmaceutical, materials, and biological chemists. Accordingly, the mathematical models and numerical analysis that underlie these methods have an increasingly important and direct role to play in the progress of many areas of chemistry. This book explores the research interface between computational chemistry and the mathematical sciences. In language that is aimed at non-specialists, it documents some prominent examples of past successful cross-fertilizations between the fields and explores the mathematical research opportunities in a broad cross-section of chemical research frontiers. It also discusses cultural differences between the two fields and makes recommendations for overcoming those differences and generally promoting this interdisciplinary work.
Author: Brian P. Ingalls Publisher: MIT Press ISBN: 0262545829 Category : Science Languages : en Pages : 423
Book Description
An introduction to the mathematical concepts and techniques needed for the construction and analysis of models in molecular systems biology. Systems techniques are integral to current research in molecular cell biology, and system-level investigations are often accompanied by mathematical models. These models serve as working hypotheses: they help us to understand and predict the behavior of complex systems. This book offers an introduction to mathematical concepts and techniques needed for the construction and interpretation of models in molecular systems biology. It is accessible to upper-level undergraduate or graduate students in life science or engineering who have some familiarity with calculus, and will be a useful reference for researchers at all levels. The first four chapters cover the basics of mathematical modeling in molecular systems biology. The last four chapters address specific biological domains, treating modeling of metabolic networks, of signal transduction pathways, of gene regulatory networks, and of electrophysiology and neuronal action potentials. Chapters 3–8 end with optional sections that address more specialized modeling topics. Exercises, solvable with pen-and-paper calculations, appear throughout the text to encourage interaction with the mathematical techniques. More involved end-of-chapter problem sets require computational software. Appendixes provide a review of basic concepts of molecular biology, additional mathematical background material, and tutorials for two computational software packages (XPPAUT and MATLAB) that can be used for model simulation and analysis.
Author: Zdzislaw Trzaska
Author: Zdzislaw Trzaska
Author: Leah Edelstein-Keshet
Author: Vladimir Mityushev
Author: Dianne P. O'Leary
Author: Vitaly Volpert
Author: Edward A. Bender
Author: Sandip Banerjee
Author: Angela B. Shiflet
Author: National Research Council
Author: Brian P. Ingalls