Download or read book Modelling with Ordinary Differential Equations written by Alfio Borzì and published by CRC Press. This book was released on 2020-04-13 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modelling with Ordinary Differential Equations: A Comprehensive Approach aims to provide a broad and self-contained introduction to the mathematical tools necessary to investigate and apply ODE models. The book starts by establishing the existence of solutions in various settings and analysing their stability properties. The next step is to illustrate modelling issues arising in the calculus of variation and optimal control theory that are of interest in many applications. This discussion is continued with an introduction to inverse problems governed by ODE models and to differential games. The book is completed with an illustration of stochastic differential equations and the development of neural networks to solve ODE systems. Many numerical methods are presented to solve the classes of problems discussed in this book. Features: Provides insight into rigorous mathematical issues concerning various topics, while discussing many different models of interest in different disciplines (biology, chemistry, economics, medicine, physics, social sciences, etc.) Suitable for undergraduate and graduate students and as an introduction for researchers in engineering and the sciences Accompanied by codes which allow the reader to apply the numerical methods discussed in this book in those cases where analytical solutions are not available

Download or read book Modelling with Ordinary Differential Equations written by T.P. Dreyer and published by Routledge. This book was released on 2017-09-06 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modelling with Ordinary Differential Equations integrates standard material from an elementary course on ordinary differential equations with the skills of mathematical modeling in a number of diverse real-world situations. Each situation highlights a different aspect of the theory or modeling. Carefully selected exercises and projects present excellent opportunities for tutorial sessions and self-study.This text/reference addresses common types of first order ordinary differential equations and the basic theory of linear second order equations with constant coefficients. It also explores the elementary theory of systems of differential equations, Laplace transforms, and numerical solutions. Theorems on the existence and uniqueness of solutions are a central feature. Topics such as curve fitting, time-delay equations, and phase plane diagrams are introduced. The book includes algorithms for computer programs as an integral part of the answer-finding process. Professionals and students in the social and biological sciences, as well as those in physics and mathematics will find this text/reference indispensable for self-study.

Download or read book Modelling with Ordinary Differential Equations written by T.P. Dreyer and published by Routledge. This book was released on 2017-09-06 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modelling with Ordinary Differential Equations integrates standard material from an elementary course on ordinary differential equations with the skills of mathematical modeling in a number of diverse real-world situations. Each situation highlights a different aspect of the theory or modeling. Carefully selected exercises and projects present excellent opportunities for tutorial sessions and self-study.This text/reference addresses common types of first order ordinary differential equations and the basic theory of linear second order equations with constant coefficients. It also explores the elementary theory of systems of differential equations, Laplace transforms, and numerical solutions. Theorems on the existence and uniqueness of solutions are a central feature. Topics such as curve fitting, time-delay equations, and phase plane diagrams are introduced. The book includes algorithms for computer programs as an integral part of the answer-finding process. Professionals and students in the social and biological sciences, as well as those in physics and mathematics will find this text/reference indispensable for self-study.

Download or read book Differential Equations written by Courtney Brown and published by SAGE. This book was released on 2007-05-18 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Differential Equations: A Modeling Approach' explains the mathematics and theory of differential equations. Graphical methods of analysis are emphasized over formal proofs, making the text even more accessible for newcomers to the subject matter.

Download or read book Modelling with Ordinary Differential Equations written by Alfio Borzì and published by CRC Press. This book was released on 2020-04-13 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modelling with Ordinary Differential Equations: A Comprehensive Approach aims to provide a broad and self-contained introduction to the mathematical tools necessary to investigate and apply ODE models. The book starts by establishing the existence of solutions in various settings and analysing their stability properties. The next step is to illustrate modelling issues arising in the calculus of variation and optimal control theory that are of interest in many applications. This discussion is continued with an introduction to inverse problems governed by ODE models and to differential games. The book is completed with an illustration of stochastic differential equations and the development of neural networks to solve ODE systems. Many numerical methods are presented to solve the classes of problems discussed in this book. Features: Provides insight into rigorous mathematical issues concerning various topics, while discussing many different models of interest in different disciplines (biology, chemistry, economics, medicine, physics, social sciences, etc.) Suitable for undergraduate and graduate students and as an introduction for researchers in engineering and the sciences Accompanied by codes which allow the reader to apply the numerical methods discussed in this book in those cases where analytical solutions are not available

Download or read book Scaling of Differential Equations written by Hans Petter Langtangen and published by Springer. This book was released on 2016-06-15 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book serves both as a reference for various scaled models with corresponding dimensionless numbers, and as a resource for learning the art of scaling. A special feature of the book is the emphasis on how to create software for scaled models, based on existing software for unscaled models. Scaling (or non-dimensionalization) is a mathematical technique that greatly simplifies the setting of input parameters in numerical simulations. Moreover, scaling enhances the understanding of how different physical processes interact in a differential equation model. Compared to the existing literature, where the topic of scaling is frequently encountered, but very often in only a brief and shallow setting, the present book gives much more thorough explanations of how to reason about finding the right scales. This process is highly problem dependent, and therefore the book features a lot of worked examples, from very simple ODEs to systems of PDEs, especially from fluid mechanics. The text is easily accessible and example-driven. The first part on ODEs fits even a lower undergraduate level, while the most advanced multiphysics fluid mechanics examples target the graduate level. The scientific literature is full of scaled models, but in most of the cases, the scales are just stated without thorough mathematical reasoning. This book explains how the scales are found mathematically. This book will be a valuable read for anyone doing numerical simulations based on ordinary or partial differential equations.

Download or read book Practical Course In Differential Equations And Mathematical Modelling A Classical And New Methods Nonlinear Mathematical Models Symmetry And Invariance Principles written by Nail H Ibragimov and published by World Scientific Publishing Company. This book was released on 2009-11-19 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Practical Course in Differential Equations and Mathematical Modelling is a unique blend of the traditional methods of ordinary and partial differential equations with Lie group analysis enriched by the author's own theoretical developments. The book — which aims to present new mathematical curricula based on symmetry and invariance principles — is tailored to develop analytic skills and “working knowledge” in both classical and Lie's methods for solving linear and nonlinear equations. This approach helps to make courses in differential equations, mathematical modelling, distributions and fundamental solution, etc. easy to follow and interesting for students. The book is based on the author's extensive teaching experience at Novosibirsk and Moscow universities in Russia, Collège de France, Georgia Tech and Stanford University in the United States, universities in South Africa, Cyprus, Turkey, and Blekinge Institute of Technology (BTH) in Sweden. The new curriculum prepares students for solving modern nonlinear problems and will essentially be more appealing to students compared to the traditional way of teaching mathematics.

Download or read book Modelling with Differential and Difference Equations written by Glenn Fulford and published by Cambridge University Press. This book was released on 1997-06-12 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Any student wishing to solve problems via mathematical modelling will find that this book provides an excellent introduction to the subject.

Download or read book Computational Immunology written by Josep Bassaganya-Riera and published by Academic Press. This book was released on 2015-10-21 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Immunology: Models and Tools encompasses the methodological framework and application of cutting-edge tools and techniques to study immunological processes at a systems level, along with the concept of multi-scale modeling. The book's emphasis is on selected cases studies and application of the most updated technologies in computational modeling, discussing topics such as computational modeling and its usage in immunological research, bioinformatics infrastructure, ODE based modeling, agent based modeling, and high performance computing, data analytics, and multiscale modeling. There are also modeling exercises using recent tools and models which lead the readers to a thorough comprehension and applicability. The book is a valuable resource for immunologists, computational biologists, bioinformaticians, biotechnologists, and computer scientists, as well as all those who wish to broaden their knowledge in systems modeling. - Offers case studies with different levels of complexity - Provides a detailed view on cutting-edge tools for modeling that are useful to experimentalists with limited computational skills - Explores the usage of simulation for hypothesis generation, helping the reader to understand the most valuable points on experimental setting

Download or read book Dynamical Modeling And Analysis Of Epidemics written by Zhien Ma and published by World Scientific. This book was released on 2009-05-22 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: This timely book covers the basic concepts of the dynamics of epidemic disease, presenting various kinds of models as well as typical research methods and results. It introduces the latest results in the current literature, especially those obtained by highly rated Chinese scholars. A lot of attention is paid to the qualitative analysis of models, the sheer variety of models, and the frontiers of mathematical epidemiology. The process and key steps in epidemiological modeling and prediction are highlighted, using transmission models of HIV/AIDS, SARS, and tuberculosis as application examples.

Download or read book Modelling with Differential Equations written by David N. Burghes and published by . This book was released on 1981 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Motivated by the authors' combined ability and experience, this book is about the concepts of mathematical modelling with the use of differential equations, as a powerful technique of mathematical analysis. It is both enjoyable to read, and informative. The reader's mind is continually exercised by enlightenment, or recollection, or enquiry; either something new is to be learned, or something known is to be re-examined. It is with mathematical clarity that the authors explain the theory of ordinary differential equations and introduce their manifold applications. They show a skillful and imaginative succession of applications introducing such instances as accident risk or fish population; forgery detection in old masters or kidney life-support machines; and many others. They show the influence of these mathematical probes into problems occurring in biology, economics, geography, medicine, planning, psychology, or sociology.

Download or read book Ordinary Differential Equations and Mechanical Systems written by Jan Awrejcewicz and published by Springer. This book was released on 2014-09-17 with total page 621 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book applies a step-by-step treatment of the current state-of-the-art of ordinary differential equations used in modeling of engineering systems/processes and beyond. It covers systematically ordered problems, beginning with first and second order ODEs, linear and higher-order ODEs of polynomial form, theory and criteria of similarity, modeling approaches, phase plane and phase space concepts, stability optimization and ending on chaos and synchronization. Presenting both an overview of the theory of the introductory differential equations in the context of applicability and a systematic treatment of modeling of numerous engineering and physical problems through linear and non-linear ODEs, the volume is self-contained, yet serves both scientific and engineering interests. The presentation relies on a general treatment, analytical and numerical methods, concrete examples and engineering intuition. The scientific background used is well balanced between elementary and advanced level, making it as a unique self-contained source for both theoretically and application oriented graduate and doctoral students, university teachers, researchers and engineers of mechanical, civil and mechatronic engineering.

Download or read book Mathematical Modeling of Biological Processes written by Avner Friedman and published by Springer. This book was released on 2014-09-19 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on mathematical modeling of biological processes includes a wide selection of biological topics that demonstrate the power of mathematics and computational codes in setting up biological processes with a rigorous and predictive framework. Topics include: enzyme dynamics, spread of disease, harvesting bacteria, competition among live species, neuronal oscillations, transport of neurofilaments in axon, cancer and cancer therapy, and granulomas. Complete with a description of the biological background and biological question that requires the use of mathematics, this book is developed for graduate students and advanced undergraduate students with only basic knowledge of ordinary differential equations and partial differential equations; background in biology is not required. Students will gain knowledge on how to program with MATLAB without previous programming experience and how to use codes in order to test biological hypothesis.

Download or read book Partial Differential Equations Modeling Analysis and Numerical Approximation written by Hervé Le Dret and published by Birkhäuser. This book was released on 2016-02-11 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the study of partial differential equation problems both from the theoretical and numerical points of view. After presenting modeling aspects, it develops the theoretical analysis of partial differential equation problems for the three main classes of partial differential equations: elliptic, parabolic and hyperbolic. Several numerical approximation methods adapted to each of these examples are analyzed: finite difference, finite element and finite volumes methods, and they are illustrated using numerical simulation results. Although parts of the book are accessible to Bachelor students in mathematics or engineering, it is primarily aimed at Masters students in applied mathematics or computational engineering. The emphasis is on mathematical detail and rigor for the analysis of both continuous and discrete problems.

Download or read book A Compendium of Partial Differential Equation Models written by William E. Schiesser and published by Cambridge University Press. This book was released on 2009-03-16 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents numerical methods and computer code in Matlab for the solution of ODEs and PDEs with detailed line-by-line discussion.

Download or read book Methods of Mathematical Modelling written by Thomas Witelski and published by Springer. This book was released on 2015-09-18 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Nonstandard Finite Difference Models of Differential Equations written by Ronald E. Mickens and published by World Scientific. This book was released on 1994 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a clear summary of the work of the author on the construction of nonstandard finite difference schemes for the numerical integration of differential equations. The major thrust of the book is to show that discrete models of differential equations exist such that the elementary types of numerical instabilities do not occur. A consequence of this result is that in general bigger step-sizes can often be used in actual calculations and/or finite difference schemes can be constructed that are conditionally stable in many instances whereas in using standard techniques no such schemes exist. The theoretical basis of this work is centered on the concepts of ?exact? and ?best? finite difference schemes. In addition, a set of rules is given for the discrete modeling of derivatives and nonlinear expressions that occur in differential equations. These rules often lead to a unique nonstandard finite difference model for a given differential equation.