Modelling With Ordinary Differential Equations

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Modelling With Ordinary Differential Equations

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Author : T.P. Dreyer
language : en
Publisher: Routledge
Release Date : 2017-09-06

Modelling With Ordinary Differential Equations written by T.P. Dreyer and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-06 with Mathematics categories.

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.

Modelling With Ordinary Differential Equations

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Author : T.P. Dreyer
language : en
Publisher: Routledge
Release Date : 2017-09-06

Modelling With Ordinary Differential Equations written by T.P. Dreyer and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-06 with Mathematics categories.

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.

Mathematical Modelling

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Author : Jagat Narain Kapur
language : en
Publisher: New Age International
Release Date : 1988

Mathematical Modelling written by Jagat Narain Kapur and has been published by New Age International this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.

Each Chapter Of The Book Deals With Mathematical Modelling Through One Or More Specified Techniques. Thus There Are Chapters On Mathematical Modelling Through Algebra, Geometry, Trigonometry And Calculus, Through Ordinary Differential Equations Of First And Second Order, Through Systems Of Differential Equations, Through Difference Equations, Through Partial Differential Equations, Through Functional Equations And Integral Equations, Through Delay-Differential, Differential-Difference And Integro-Differential Equations, Through Calculus Of Variations And Dynamic Programming, Through Graphs, Through Mathematical Programming, Maximum Principle And Maximum Entropy Principle.Each Chapter Contains Mathematical Models From Physical, Biological, Social, Management Sciences And Engineering And Technology And Illustrates Unity In Diversity Of Mathematical Sciences.The Book Contains Plenty Of Exercises In Mathematical Modelling And Is Aimed To Give A Panoramic View Of Applications Of Modelling In All Fields Of Knowledge. It Contains Both Probabilistic And Deterministic Models.The Book Presumes Only The Knowledge Of Undergraduate Mathematics And Can Be Used As A Textbook At Senior Undergraduate Or Post-Graduate Level For A One Or Two- Semester Course For Students Of Mathematics, Statistics, Physical, Social And Biological Sciences And Engineering. It Can Also Be Useful For All Users Of Mathematics And For All Mathematical Modellers.

Modelling With Ordinary Differential Equations

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Author : Alfio Borzì
language : en
Publisher: CRC Press
Release Date : 2020-04-13

Modelling With Ordinary Differential Equations written by Alfio Borzì and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-13 with Mathematics categories.

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

Modeling With Differential Equations In Chemical Engineering

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Author : Stanley M. Walas
language : en
Publisher: Boston : Butterworth-Heinemann
Release Date : 1991

Modeling With Differential Equations In Chemical Engineering written by Stanley M. Walas and has been published by Boston : Butterworth-Heinemann this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.

'Modelling with Differential Equations in Chemical Engineering' covers the modelling of rate processes of engineering in terms of differential equations. While it includes the purely mathematical aspects of the solution of differential equations, the main emphasis is on the derivation and solution of major equations of engineering and applied science. Methods of solving differential equations by analytical and numerical means are presented in detail with many solved examples, and problems for solution by the reader. Emphasis is placed on numerical and computer methods of solution. A key chapter in the book is devoted to the principles of mathematical modelling. These principles are applied to the equations in important engineering areas. The major disciplines covered are thermodynamics, diffusion and mass transfer, heat transfer, fluid dynamics, chemical reactions, and automatic control. These topics are of particular value to chemical engineers, but also are of interest to mechanical, civil, and environmental engineers, as well as applied scientists. The material is also suitable for undergraduate and beginning graduate students, as well as for review by practising engineers.

Nonstandard Finite Difference Models Of Differential Equations

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Author : Ronald E Mickens
language : en
Publisher: World Scientific
Release Date : 1993-12-23

Nonstandard Finite Difference Models Of Differential Equations written by Ronald E Mickens and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-12-23 with Mathematics categories.

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.

Ordinary Differential Equations

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Author : Radu Precup
language : en
Publisher: de Gruyter
Release Date : 2017-10-15

Ordinary Differential Equations written by Radu Precup and has been published by de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-15 with categories.

Precup's introduction into Ordinary Differential Equations combines models arising in physics and biology for motivation with rigorous reasoning in describing the theory of ODEs and applications and computer simulations with Maple. While offering a concise course of the theory of ODEs it enables the reader to enter thie field of computer simulations. Thus, it is a valuable read for students of mathematics as well as physics and engineering.

Fundamentals Of Ordinary Differential Equations

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Author : Mohit Chatterjee
language : en
Publisher: Educohack Press
Release Date : 2025-02-20

Fundamentals Of Ordinary Differential Equations written by Mohit Chatterjee and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.

"Fundamentals of Ordinary Differential Equations" is a comprehensive guide designed for students, researchers, and professionals to master ODE theory and applications. We cover essential principles, advanced techniques, and practical applications, providing a well-rounded resource for understanding differential equations and their real-world impact. The book offers a multifaceted approach, from basic principles to advanced concepts, catering to fields like physics, engineering, biology, and economics. Mathematical ideas are broken down with step-by-step explanations, examples, and illustrations, making complex concepts accessible. Real-world examples throughout each chapter show how ODEs model and analyze systems in diverse disciplines. We also explain numerical methods such as Euler’s method, Runge-Kutta, and finite differences, equipping readers with computational tools for solving ODEs. Advanced topics include bifurcation, chaos theory, Hamiltonian systems, and singular perturbations, providing an in-depth grasp of ODE topics. With chapter summaries, exercises, glossaries, and additional resources, "Fundamentals of Ordinary Differential Equations" is an essential reference for students, professionals, and practitioners across science and engineering fields.

A Practical Course In Differential Equations And Mathematical Modelling

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Author : Nail H. Ibragimov
language : en
Publisher: World Scientific
Release Date : 2009

A Practical Course In Differential Equations And Mathematical Modelling written by Nail H. Ibragimov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.

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, CollŠge 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.

Mathematical Modelling In Science And Technology

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Author : Xavier J.R. Avula
language : en
Publisher: Elsevier
Release Date : 2014-05-09

Mathematical Modelling In Science And Technology written by Xavier J.R. Avula and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-09 with Mathematics categories.

Mathematical Modelling in Science and Technology: The Fourth International Conference covers the proceedings of the Fourth International Conference by the same title, held at the Swiss Federal Institute of Technology, Zurich, Switzerland on August 15-17, 1983. Mathematical modeling is a powerful tool to solve many complex problems presented by scientific and technological developments. This book is organized into 20 parts encompassing 180 chapters. The first parts present the basic principles, methodology, systems theory, parameter estimation, system identification, and optimization of mathematical modeling. The succeeding parts discuss the features of stochastic and numerical modeling and simulation languages. Considerable parts deal with the application areas of mathematical modeling, such as in chemical engineering, solid and fluid mechanics, water resources, medicine, economics, transportation, and industry. The last parts tackle the application of mathematical modeling in student management and other academic cases. This book will prove useful to researchers in various science and technology fields.