Differential Equations as Models in Science and Engineering Book

Differential Equations as Models in Science and Engineering | Download eBook Read Pdf-ePub-Kindle

Download full pdf book Differential Equations as Models in Science and Engineering by Gregory Baker available in full 392 pages, and make sure to check out other latest books Mathematics related to Differential Equations as Models in Science and Engineering below.

Differential Equations as Models in Science and Engineering

By Gregory Baker
  • ISBN Code: : 9814656992
  • Publisher : World Scientific Publishing Company
  • Pages : 392
  • Category : Mathematics
  • Reads : 873
  • Book Compatibility : Pdf, ePub, Mobi, Kindle
  • Pdf : differential-equations-as-models-in-science-and-engineering.pdf

Book Excerpt :

This textbook develops a coherent view of differential equations by progressing through a series of typical examples in science and engineering that arise as mathematical models. All steps of the modeling process are covered: formulation of a mathematical model; the development and use of mathematical concepts that lead to constructive solutions; validation of the solutions; and consideration of the consequences. The volume engages students in thinking mathematically, while emphasizing the power and relevance of mathematics in science and engineering. There are just a few guidelines that bring coherence to the construction of solutions as the book progresses through ordinary to partial differential equations using examples from mixing, electric circuits, chemical reactions and transport processes, among others. The development of differential equations as mathematical models and the construction of their solution is placed center stage in this volume.

Recommended Books For Reading


  • Differential Equation Analysis in Biomedical Science and Engineering
    Differential Equation Analysis in Biomedical Science and Engineering

    A Book written by William E. Schiesser, published by John Wiley & Sons 2014-03-31 - 344 pages - part of Mathematics books.

    Get eBook
  • Differential Equation Analysis in Biomedical Science and Engineering
    Differential Equation Analysis in Biomedical Science and Engineering

    A Book written by William E. Schiesser, published by John Wiley & Sons 2014-02-24 - 440 pages - part of Mathematics books.

    Get eBook
  • Differential Equations
    Differential Equations

    A Book written by Christian Constanda, published by Springer 2017-03-14 - 297 pages - part of Mathematics books.

    Get eBook
  • Numerical Modeling of Coupled Phenomena in Science and Engineering
    Numerical Modeling of Coupled Phenomena in Science and Engineering

    A Book written by Mario César Suárez Arriaga,Jochen Bundschuh,Francisco Javier Dominguez-Mota, published by CRC Press 2008-12-01 - 496 pages - part of Technology & Engineering books.

    Get eBook
  • Introduction to Computation and Modeling for Differential Equations
    Introduction to Computation and Modeling for Differential Equations

    A Book written by Lennart Edsberg, published by John Wiley & Sons 2015-09-16 - 288 pages - part of Mathematics books.

    Get eBook
  • Introduction to Computation and Modeling for Differential Equations
    Introduction to Computation and Modeling for Differential Equations

    A Book written by Lennart Edsberg, published by John Wiley & Sons 2015-10-26 - 288 pages - part of Mathematics books.

    Get eBook
  • The Art of Modeling in Science and Engineering with Mathematica
    The Art of Modeling in Science and Engineering with Mathematica

    A Book written by Diran Basmadjian, published by CRC Press 2019-07-17 - 688 pages - part of Mathematics books.

    Get eBook

Read Also This Books

Integral Methods in Science and Engineering

By Christian Constanda,Paul J. Harris
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Springer Science & Business Media
  • Book Code : 0817682384
  • Total of Pages : 422
  • Category : Mathematics
  • Members : 112
  • Pdf File: integral-methods-in-science-and-engineering.pdf

Book Short Summary:

An enormous array of problems encountered by scientists and engineers are based on the design of mathematical models using many different types of ordinary differential, partial differential, integral, and integro-differential equations. Accordingly, the solutions of these equations are of great interest to practitioners and to science in general. Presenting a wealth of cutting-edge research by a diverse group of experts in the field, Integral Methods in Science and Engineering: Computational and Analytic Aspects gives a vivid picture of both the development of theoretical integral techniques and their use in specific science and engineering problems. This book will be valuable for researchers in applied mathematics, physics, and mechanical and electrical engineering. It will likewise be a useful study guide for graduate students in these disciplines, and for various other professionals who use integration as an essential technique in their work.

Advanced Numerical Methods for Differential Equations

By Harendra Singh,Jagdev Singh,Sunil Dutt Purohit,Devendra Kumar
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : CRC Press
  • Book Code : 1000381080
  • Total of Pages : 336
  • Category : Mathematics
  • Members : 697
  • Pdf File: advanced-numerical-methods-for-differential-equations.pdf

Book Short Summary:

Mathematical models are used to convert real-life problems using mathematical concepts and language. These models are governed by differential equations whose solutions make it easy to understand real-life problems and can be applied to engineering and science disciplines. This book presents numerical methods for solving various mathematical models. This book offers real-life applications, includes research problems on numerical treatment, and shows how to develop the numerical methods for solving problems. The book also covers theory and applications in engineering and science. Engineers, mathematicians, scientists, and researchers working on real-life mathematical problems will find this book useful.

Mathematical Modeling and Simulation

By Kai Velten
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : John Wiley & Sons
  • Book Code : 3527627618
  • Total of Pages : 362
  • Category : Science
  • Members : 809
  • Pdf File: mathematical-modeling-and-simulation.pdf

Book Short Summary:

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).

Ordinary Differential Equations with Applications

By Ali Mason
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Scientific e-Resources
  • Book Code : 1839473282
  • Total of Pages : 284
  • Category :
  • Members : 477
  • Pdf File: ordinary-differential-equations-with-applications.pdf

Book Short Summary:

Ordinary differential equations (ODEs) arise in many contexts of mathematics and science (social as well as natural). Mathematical descriptions of change use differentials and derivatives. Various differentials, derivatives, and functions become related to each other via equations, and thus a differential equation is a result that describes dynamically changing phenomena, evolution, and variation. Often, quantities are defined as the rate of change of other quantities (for example, derivatives of displacement with respect to time), or gradients of quantities, which is how they enter differential equations. Ordinary differential equations are equations to be solved in which the unknown element is a function, rather than a number, and in which the known information relates that function to its derivatives. Few such equations admit an explicit answer, but there is a wealth of qualitative information describing the solutions and their dependence on the defining equation. Systems of differential equations form the basis of mathematical models in a wide range of fields - from engineering and physical sciences to finance and biological sciences. Differential equations are relations between unknown functions and their derivatives. Computing numerical solutions to differential equations is one of the most important tasks in technical computing, and one of the strengths of MATLAB. The book explains the origins of various types of differential equations. The scope of the book is limited to linear differential equations of the first order, linear differential equation of higher order, partial differential equations and special methods of solution of differential equations of second order, keeping in view the requirement of students.

Probability and Partial Differential Equations in Modern Applied Mathematics

By Edward C. Waymire
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Springer Science & Business Media
  • Book Code : 038729371X
  • Total of Pages : 272
  • Category : Mathematics
  • Members : 698
  • Pdf File: probability-and-partial-differential-equations-in-modern-applied-mathematics.pdf

Book Short Summary:

"Probability and Partial Differential Equations in Modern Applied Mathematics" is devoted to the role of probabilistic methods in modern applied mathematics from the perspectives of both a tool for analysis and as a tool in modeling. There is a recognition in the applied mathematics research community that stochastic methods are playing an increasingly prominent role in the formulation and analysis of diverse problems of contemporary interest in the sciences and engineering. A probabilistic representation of solutions to partial differential equations that arise as deterministic models allows one to exploit the power of stochastic calculus and probabilistic limit theory in the analysis of deterministic problems, as well as to offer new perspectives on the phenomena for modeling purposes. There is also a growing appreciation of the role for the inclusion of stochastic effects in the modeling of complex systems. This has led to interesting new mathematical problems at the interface of probability, dynamical systems, numerical analysis, and partial differential equations. This volume will be useful to researchers and graduate students interested in probabilistic methods, dynamical systems approaches and numerical analysis for mathematical modeling in the sciences and engineering.

Integral Methods in Science and Engineering

By M. Zuhair Nashed,D. Rollins
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Springer Science & Business Media
  • Book Code : 0817644504
  • Total of Pages : 312
  • Category : Mathematics
  • Members : 901
  • Pdf File: integral-methods-in-science-and-engineering.pdf

Book Short Summary:

The quantitative and qualitative study of the physical world makes use of many mathematical models governed by a great diversity of ordinary, partial differential, integral, and integro-differential equations. An essential step in such investigations is the solution of these types of equations, which sometimes can be performed analytically, while at other times only numerically. This edited, self-contained volume presents a series of state-of-the-art analytic and numerical methods of solution constructed for important problems arising in science and engineering, all based on the powerful operation of (exact or approximate) integration. The volume may be used as a reference guide and a practical resource. It is suitable for researchers and practitioners in applied mathematics, physics, and mechanical and electrical engineering, as well as graduate students in these disciplines.

New Paradigms in Computational Modeling and Its Applications

By Snehashish Chakraverty
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Academic Press
  • Book Code : 0128221682
  • Total of Pages : 278
  • Category : Science
  • Members : 839
  • Pdf File: new-paradigms-in-computational-modeling-and-its-applications.pdf

Book Short Summary:

In general, every problem of science and engineering is governed by mathematical models. There is often a need to model, solve and interpret the problems one encounters in the world of practical problems. Models of practical application problems usually need to be handled by efficient computational models. New Paradigms in Computational Modeling and Its Applications deals with recent developments in mathematical methods, including theoretical models as well as applied science and engineering. The book focuses on subjects that can benefit from mathematical methods with concepts of simulation, waves, dynamics, uncertainty, machine intelligence, and applied mathematics. The authors bring together leading-edge research on mathematics combining various fields of science and engineering. This perspective acknowledges the inherent characteristic of current research on mathematics operating in parallel over different subject fields. New Paradigms in Computational Modeling and Its Applications meets the present and future needs for the interaction between various science and technology/engineering areas on the one hand and different branches of mathematics on the other. As such, the book contains 13 chapters covering various aspects of computational modeling from theoretical to application problems. The first six chapters address various problems of structural and fluid dynamics. The next four chapters include solving problems where the governing parameters are uncertain regarding fuzzy, interval, and affine. The final three chapters will be devoted to the use of machine intelligence in artificial neural networks. Presents a self-contained and up to date review of modelling real life scientific and engineering application problems Introduces new concepts of various computing techniques to handle different engineering and science problems Demonstrates the efficiency and power of the various algorithms and models in a simple and easy to follow style, including numerous examples to illustrate concepts and algorithms

Numerical Partial Differential Equations for Environmental Scientists and Engineers

By Daniel R. Lynch
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Springer Science & Business Media
  • Book Code : 0387236201
  • Total of Pages : 388
  • Category : Science
  • Members : 928
  • Pdf File: numerical-partial-differential-equations-for-environmental-scientists-and-engineers.pdf

Book Short Summary:

For readers with some competence in PDE solution properties, this book offers an interdisciplinary approach to problems occurring in natural environmental media: the hydrosphere, atmosphere, cryosphere, lithosphere, biosphere and ionosphere. It presents two major discretization methods: Finite Difference and Finite Element, plus a section on practical approaches to ill-posed problems. The blend of theory, analysis, and implementation practicality supports solving and understanding complicated problems.

Mathematics in Science and Technology

By A H Siddiqi,R C Singh,P Manchanda
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : World Scientific
  • Book Code : 9814462144
  • Total of Pages : 556
  • Category : Mathematics
  • Members : 639
  • Pdf File: mathematics-in-science-and-technology.pdf

Book Short Summary:

This unique volume presents reviews of research in several important areas of applications of mathematical concepts to science and technology, for example applications of inverse problems and wavelets to real world systems. The book provides a comprehensive overview of current research of several outstanding scholars engaged in diverse fields such as complexity theory, vertex coupling in quantum graphs, mixing of substances by turbulence, network dynamics and architecture, processes with rate — independent hysteresis, numerical analysis of Hamilton Jacobi — Bellman equations, simulations of complex stochastic differential equations, optimal flow control, shape optimal flow control, shape optimization and aircraft designing, mathematics of brain, nanotechnology and DNA structure and mathematical models of environmental problems. The volume also contains contributory talks based on current researches of comparatively young researchers participating in the conference. Contents:Part A Invited Talk:In Appreciation of Dr Zakir Husain Award (M Zuhair Nashed)Kinematical Conservation Laws (KCL): Equations of Evolution of Curves and Surfaces (K R Arun and P Prasad)Systematic Discretization of Input/Output Maps and Control of Partial Differential Equations (J Heiland, V Mehrmann and M Schmidt)Vertex Couplings in Quantum Graphs: Approximations by Scaled Schrödinger Operators (P Exner)Complexity Leads to Randomness in Chaotic Systems (R Lozi)Mathematical Modeling for Unifying Different Branches of Science, Engineering and Technology (N Rudraiah)On Equivalence Transformations and Exact Solutions of a Helmholtz Type Equation (O P Bhutani and L R Chowdhury)Cognitive Radio: State-of-the-Art and Mathematical Challenges (T Nadkar, V Thumar, A Patel, Md Z Ali Khan, U B Desai and S N Merchant)Part B Thematic Reviews:Inverse Problems of Parameter Identification in Partial Differential Equations (B Jadamba, A A Khan and M Sama)Finite Element Methods for HJB Equations (M Boulbrachene)Dynamics and Control of Underactuated Space Systems (K D Kumar and Godard)Some New Classes of Inverse Coefficient Problems in Engineering Mechanics and Computational Material Science Based on Boundary Measured Data (A Hasanov)Some Recent Developments on Mathematical Aspect of Wavelets (P Manchanda and Meenakshi)Relevance of Wavelets and Inverse Problems to Brain (A H Siddiqi, H K Sevindir, Z Aslan and C Yazici)Wavelets and Inverse Problems (K Goyal and M Mehra)Optimization Models for a Class of Structured Stochastic Games (S K Neogy, S Sinha, A K Das and A Gupta)Part C Contributory Talks:Predator-Prey Relations for Mammals where Prey Suppress Breeding (Q J Khan and M Al-Lawatia)SEI Model with Varying Transmission and Mortality Rates (G Rost)Trajectories and Stability Regions of the Lagrangian Points in the Generalized Chermnykh-Like Problem (B S Kushvah)MHD Flow Past an Infinite Plate Under the Effect of Gravity Modulation (S Wasu and S C Rajvanshi) Readership: Researchers in mathematical modeling, numerical analysis and computational mathematics. Keywords:Complexity Theory;Vertex Coupling in Quantum Graphs;Hamilton-Jacobi–Bellman Equation;Prey and Predator Model;Inverse Problems and Wavelets;Dynamics and Control of Under Actuated Space Systems

Elementary Differential Equations

By Charles Roberts
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : CRC Press
  • Book Code : 1498776094
  • Total of Pages : 536
  • Category : Mathematics
  • Members : 564
  • Pdf File: elementary-differential-equations.pdf

Book Short Summary:

Elementary Differential Equations, Second Edition is written with the knowledge that there has been a dramatic change in the past century in how solutions to differential equations are calculated. However, the way the topic has been taught in introductory courses has barely changed to reflect these advances, which leaves students at a disadvantage. This second edition has been created to address these changes and help instructors facilitate new teaching methods and the latest tools, which includes computers. The text is designed to help instructors who want to use computers in their classrooms. It accomplishes this by emphasizing and integrating computers in teaching elementary or ordinary differential equations. Many examples and exercises included in the text require the use of computer software to solve problems. It should be noted that since instructors use their own preferred software, this book has been written to be independent of any specific software package. Features: Focuses on numerical methods and computing to generate solutions Features extensive coverage of nonlinear differential equations and nonlinear systems Includes software programs to solve problems in the text which are located on the author's website Contains a wider variety of non-mathematical models than any competing textbook This second edition is a valuable, up-to-date tool for instructors teaching courses about differential equations. It serves as an excellent introductory textbook for undergraduate students majoring in applied mathematics, computer science, various engineering disciplines and other sciences. They also will find that the textbook will aide them greatly in their professional careers because of its instructions on how to use computers to solve equations.

Methods of Mathematical Modelling

By Thomas Witelski,Mark Bowen
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Springer
  • Book Code : 3319230425
  • Total of Pages : 305
  • Category : Mathematics
  • Members : 323
  • Pdf File: methods-of-mathematical-modelling.pdf

Book Short Summary:

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.

Computational Partial Differential Equations

By Hans Petter Langtangen
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Springer Science & Business Media
  • Book Code : 3662011700
  • Total of Pages : 685
  • Category : Mathematics
  • Members : 750
  • Pdf File: computational-partial-differential-equations.pdf

Book Short Summary:

Targeted at students and researchers in computational sciences who need to develop computer codes for solving PDEs, the exposition here is focused on numerics and software related to mathematical models in solid and fluid mechanics. The book teaches finite element methods, and basic finite difference methods from a computational point of view, with the main emphasis on developing flexible computer programs, using the numerical library Diffpack. Diffpack is explained in detail for problems including model equations in applied mathematics, heat transfer, elasticity, and viscous fluid flow. All the program examples, as well as Diffpack for use with this book, are available on the Internet. XXXXXXX NEUER TEXT This book is for researchers who need to develop computer code for solving PDEs. Numerical methods and the application of Diffpack are explained in detail. Diffpack is a modern C++ development environment that is widely used by industrial scientists and engineers working in areas such as oil exploration, groundwater modeling, and materials testing. All the program examples, as well as a test version of Diffpack, are available for free over the Internet.

Using R for Numerical Analysis in Science and Engineering

By Victor A. Bloomfield
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : CRC Press
  • Book Code : 1439884498
  • Total of Pages : 359
  • Category : Mathematics
  • Members : 399
  • Pdf File: using-r-for-numerical-analysis-in-science-and-engineering.pdf

Book Short Summary:

Instead of presenting the standard theoretical treatments that underlie the various numerical methods used by scientists and engineers, Using R for Numerical Analysis in Science and Engineering shows how to use R and its add-on packages to obtain numerical solutions to the complex mathematical problems commonly faced by scientists and engineers. This practical guide to the capabilities of R demonstrates Monte Carlo, stochastic, deterministic, and other numerical methods through an abundance of worked examples and code, covering the solution of systems of linear algebraic equations and nonlinear equations as well as ordinary differential equations and partial differential equations. It not only shows how to use R’s powerful graphic tools to construct the types of plots most useful in scientific and engineering work, but also: Explains how to statistically analyze and fit data to linear and nonlinear models Explores numerical differentiation, integration, and optimization Describes how to find eigenvalues and eigenfunctions Discusses interpolation and curve fitting Considers the analysis of time series Using R for Numerical Analysis in Science and Engineering provides a solid introduction to the most useful numerical methods for scientific and engineering data analysis using R.

Methods of Mathematical Modelling

By Harendra Singh,Devendra Kumar,Dumitru Baleanu
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : CRC Press
  • Book Code : 1000596788
  • Total of Pages : 238
  • Category : Technology & Engineering
  • Members : 622
  • Pdf File: methods-of-mathematical-modelling.pdf

Book Short Summary:

This book features original research articles on the topic of mathematical modelling and fractional differential equations. The contributions, written by leading researchers in the field, consist of chapters on classical and modern dynamical systems modelled by fractional differential equations in physics, engineering, signal processing, fluid mechanics, and bioengineering, manufacturing, systems engineering, and project management. The book offers theory and practical applications for the solutions of real-life problems and will be of interest to graduate level students, educators, researchers, and scientists interested in mathematical modelling and its diverse applications. Features Presents several recent developments in the theory and applications of fractional calculus Includes chapters on different analytical and numerical methods dedicated to several mathematical equations Develops methods for the mathematical models which are governed by fractional differential equations Provides methods for models in physics, engineering, signal processing, fluid mechanics, and bioengineering Discusses real-world problems, theory, and applications

Integral Methods in Science and Engineering

By Mario Paul Ahues,Alain R. Largillier
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Springer Science & Business Media
  • Book Code : 0817681841
  • Total of Pages : 280
  • Category : Mathematics
  • Members : 654
  • Pdf File: integral-methods-in-science-and-engineering.pdf

Book Short Summary:

* Good reference text; clusters well with other Birkhauser integral equations & integral methods books (Estrada and Kanwal, Kythe/Puri, Constanda, et al). * Includes many practical applications/techniques for applied mathematicians, physicists, engineers, grad students. * The contributors to the volume draw from a number of physical domains and propose diverse treatments for various mathematical models through the use of integration as an essential solution tool. * Physically meaningful problems in areas related to finite and boundary element techniques, conservation laws, hybrid approaches, ordinary and partial differential equations, and vortex methods are explored in a rigorous, accessible manner. * The new results provided are a good starting point for future exploitation of the interdisciplinary potential of integration as a unifying methodology for the investigation of mathematical models.

Numerical Methods for Evolutionary Differential Equations

By Uri M. Ascher
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : SIAM
  • Book Code : 0898718910
  • Total of Pages : 395
  • Category : Evolution equations
  • Members : 287
  • Pdf File: numerical-methods-for-evolutionary-differential-equations.pdf

Book Short Summary:

Methods for the numerical simulation of dynamic mathematical models have been the focus of intensive research for well over 60 years, and the demand for better and more efficient methods has grown as the range of applications has increased. Mathematical models involving evolutionary partial differential equations (PDEs) as well as ordinary differential equations (ODEs) arise in diverse applications such as fluid flow, image processing and computer vision, physics-based animation, mechanical systems, relativity, earth sciences, and mathematical finance. This textbook develops, analyzes, and applies numerical methods for evolutionary, or time-dependent, differential problems. Both PDEs and ODEs are discussed from a unified viewpoint. The author emphasizes finite difference and finite volume methods, specifically their principled derivation, stability, accuracy, efficient implementation, and practical performance in various fields of science and engineering. Smooth and nonsmooth solutions for hyperbolic PDEs, parabolic-type PDEs, and initial value ODEs are treated, and a practical introduction to geometric integration methods is included as well. Audience: suitable for researchers and graduate students from a variety of fields including computer science, applied mathematics, physics, earth and ocean sciences, and various engineering disciplines. Researchers who simulate processes that are modeled by evolutionary differential equations will find material on the principles underlying the appropriate method to use and the pitfalls that accompany each method.

Contributions to Partial Differential Equations and Applications

By B. N. Chetverushkin,W. Fitzgibbon,Y.A. Kuznetsov,P. Neittaanmäki,J. Periaux,O. Pironneau
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Springer
  • Book Code : 3319783254
  • Total of Pages : 452
  • Category : Technology & Engineering
  • Members : 938
  • Pdf File: contributions-to-partial-differential-equations-and-applications.pdf

Book Short Summary:

This book treats Modelling of CFD problems, Numerical tools for PDE, and Scientific Computing and Systems of ODE for Epidemiology, topics that are closely related to the scientific activities and interests of Prof. William Fitzgibbon, Prof. Yuri Kuznetsov, and Prof. O. Pironneau, whose outstanding achievements are recognised in this volume. It contains 20 contributions from leading scientists in applied mathematics dealing with partial differential equations and their applications to engineering, ab-initio chemistry and life sciences. It includes the mathematical and numerical contributions to PDE for applications presented at the ECCOMAS thematic conference "Contributions to PDE for Applications" held at Laboratoire Jacques Louis Lions in Paris, France, August 31- September 1, 2015, and at the Department of Mathematics, University of Houston, Texas, USA, February 26-27, 2016. This event brought together specialists from universities and research institutions who are developing or applying numerical PDE or ODE methods with an emphasis on industrial and societal applications. This volume is of interest to researchers and practitioners as well as advanced students or engineers in applied and computational mathematics. All contributions are written at an advanced scientific level with no effort made by the editors to make this volume self-contained. It is assumed that the reader is a specialist already who knows the basis of this field of research and has the capability of understanding and appreciating the latest developments in this field.

The Art of Modeling in Science and Engineering with Mathematica

By Diran Basmadjian,Ramin Farnood
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : CRC Press
  • Book Code : 1482286033
  • Total of Pages : 509
  • Category : Mathematics
  • Members : 228
  • Pdf File: the-art-of-modeling-in-science-and-engineering-with-mathematica.pdf

Book Short Summary:

Thoroughly revised and updated, The Art of Modeling in Science and Engineering with Mathematica®, Second Edition explores the mathematical tools and procedures used in modeling based on the laws of conservation of mass, energy, momentum, and electrical charge. The authors have culled and consolidated the best from the first edition and expanded the range of applied examples to reach a wider audience. The text proceeds, in measured steps, from simple models of real-world problems at the algebraic and ordinary differential equations (ODE) levels to more sophisticated models requiring partial differential equations. The traditional solution methods are supplemented with Mathematica , which is used throughout the text to arrive at solutions for many of the problems presented. The text is enlivened with a host of illustrations and practice problems drawn from classical and contemporary sources. They range from Thomson’s famous experiment to determine e/m and Euler’s model for the buckling of a strut to an analysis of the propagation of emissions and the performance of wind turbines. The mathematical tools required are first explained in separate chapters and then carried along throughout the text to solve and analyze the models. Commentaries at the end of each illustration draw attention to the pitfalls to be avoided and, perhaps most important, alert the reader to unexpected results that defy conventional wisdom. These features and more make the book the perfect tool for resolving three common difficulties: the proper choice of model, the absence of precise solutions, and the need to make suitable simplifying assumptions and approximations. The book covers a wide range of physical processes and phenomena drawn from various disciplines and clearly illuminates the link between the physical system being modeled and the mathematical expression that results.

Mathematical Modelling

By J. Caldwell,Y.M. Ram
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Springer Science & Business Media
  • Book Code : 9401722013
  • Total of Pages : 288
  • Category : Mathematics
  • Members : 489
  • Pdf File: mathematical-modelling.pdf

Book Short Summary:

Over the past decade there has been an increasing demand for suitable material in the area of mathematical modelling as applied to science and engineering. There has been a constant movement in the emphasis from developing proficiency in purely mathematical techniques to an approach which caters for industrial and scientific applications in emerging new technologies. In this textbook we have attempted to present the important fundamental concepts of mathematical modelling and to demonstrate their use in solving certain scientific and engineering problems. This text, which serves as a general introduction to the area of mathematical modelling, is aimed at advanced undergraduate students in mathematics or closely related disciplines, e.g., students who have some prerequisite knowledge such as one-variable calculus, linear algebra and ordinary differential equations. Some prior knowledge of computer programming would be useful but is not considered essential. The text also contains some more challenging material which could prove attractive to graduate students in engineering or science who are involved in mathematical modelling. In preparing the text we have tried to use our experience of teaching mathematical modelling to undergraduate students in a wide range of areas including mathematics and computer science and disciplines in engineering and science. An important aspect of the text is the use made of scientific computer software packages such as MAPLE for symbolic algebraic manipulations and MA TLAB for numerical simulation.

Mathematical Modeling

By Stefan Heinz
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Springer Science & Business Media
  • Book Code : 3642203116
  • Total of Pages : 460
  • Category : Technology & Engineering
  • Members : 493
  • Pdf File: mathematical-modeling.pdf

Book Short Summary:

The whole picture of Mathematical Modeling is systematically and thoroughly explained in this text for undergraduate and graduate students of mathematics, engineering, economics, finance, biology, chemistry, and physics. This textbook gives an overview of the spectrum of modeling techniques, deterministic and stochastic methods, and first-principle and empirical solutions. Complete range: The text continuously covers the complete range of basic modeling techniques: it provides a consistent transition from simple algebraic analysis methods to simulation methods used for research. Such an overview of the spectrum of modeling techniques is very helpful for the understanding of how a research problem considered can be appropriately addressed. Complete methods: Real-world processes always involve uncertainty, and the consideration of randomness is often relevant. Many students know deterministic methods, but they do hardly have access to stochastic methods, which are described in advanced textbooks on probability theory. The book develops consistently both deterministic and stochastic methods. In particular, it shows how deterministic methods are generalized by stochastic methods. Complete solutions: A variety of empirical approximations is often available for the modeling of processes. The question of which assumption is valid under certain conditions is clearly relevant. The book provides a bridge between empirical modeling and first-principle methods: it explains how the principles of modeling can be used to explain the validity of empirical assumptions. The basic features of micro-scale and macro-scale modeling are discussed – which is an important problem of current research.

Applied Mathematical Modelling of Engineering Problems

By N.V. Hritonenko,Yuri P. Yatsenko
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Springer Science & Business Media
  • Book Code : 1441991603
  • Total of Pages : 286
  • Category : Mathematics
  • Members : 221
  • Pdf File: applied-mathematical-modelling-of-engineering-problems.pdf

Book Short Summary:

The subject of the book is the "know-how" of applied mathematical modelling: how to construct specific models and adjust them to a new engineering environment or more precise realistic assumptions; how to analyze models for the purpose of investigating real life phenomena; and how the models can extend our knowledge about a specific engineering process. Two major sources of the book are the stock of classic models and the authors' wide experience in the field. The book provides a theoretical background to guide the development of practical models and their investigation. It considers general modelling techniques, explains basic underlying physical laws and shows how to transform them into a set of mathematical equations. The emphasis is placed on common features of the modelling process in various applications as well as on complications and generalizations of models. The book covers a variety of applications: mechanical, acoustical, physical and electrical, water transportation and contamination processes; bioengineering and population control; production systems and technical equipment renovation. Mathematical tools include partial and ordinary differential equations, difference and integral equations, the calculus of variations, optimal control, bifurcation methods, and related subjects.

Solving Differential Equations in R

By Karline Soetaert,Jeff Cash,Francesca Mazzia
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Springer Science & Business Media
  • Book Code : 3642280706
  • Total of Pages : 248
  • Category : Computers
  • Members : 154
  • Pdf File: solving-differential-equations-in-r.pdf

Book Short Summary:

Mathematics plays an important role in many scientific and engineering disciplines. This book deals with the numerical solution of differential equations, a very important branch of mathematics. Our aim is to give a practical and theoretical account of how to solve a large variety of differential equations, comprising ordinary differential equations, initial value problems and boundary value problems, differential algebraic equations, partial differential equations and delay differential equations. The solution of differential equations using R is the main focus of this book. It is therefore intended for the practitioner, the student and the scientist, who wants to know how to use R for solving differential equations. However, it has been our goal that non-mathematicians should at least understand the basics of the methods, while obtaining entrance into the relevant literature that provides more mathematical background. Therefore, each chapter that deals with R examples is preceded by a chapter where the theory behind the numerical methods being used is introduced. In the sections that deal with the use of R for solving differential equations, we have taken examples from a variety of disciplines, including biology, chemistry, physics, pharmacokinetics. Many examples are well-known test examples, used frequently in the field of numerical analysis.

Approximation Methods in Science and Engineering

By Reza N. Jazar
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Springer Nature
  • Book Code : 1071604805
  • Total of Pages : 537
  • Category : Technology & Engineering
  • Members : 946
  • Pdf File: approximation-methods-in-science-and-engineering.pdf

Book Short Summary:

Approximation Methods in Engineering and Science covers fundamental and advanced topics in three areas: Dimensional Analysis, Continued Fractions, and Stability Analysis of the Mathieu Differential Equation. Throughout the book, a strong emphasis is given to concepts and methods used in everyday calculations. Dimensional analysis is a crucial need for every engineer and scientist to be able to do experiments on scaled models and use the results in real world applications. Knowing that most nonlinear equations have no analytic solution, the power series solution is assumed to be the first approach to derive an approximate solution. However, this book will show the advantages of continued fractions and provides a systematic method to develop better approximate solutions in continued fractions. It also shows the importance of determining stability chart of the Mathieu equation and reviews and compares several approximate methods for that. The book provides the energy-rate method to study the stability of parametric differential equations that generates much better approximate solutions.

Simulation and Inference for Stochastic Differential Equations

By Stefano M. Iacus
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Springer Science & Business Media
  • Book Code : 0387758399
  • Total of Pages : 285
  • Category : Computers
  • Members : 441
  • Pdf File: simulation-and-inference-for-stochastic-differential-equations.pdf

Book Short Summary:

This book covers a highly relevant and timely topic that is of wide interest, especially in finance, engineering and computational biology. The introductory material on simulation and stochastic differential equation is very accessible and will prove popular with many readers. While there are several recent texts available that cover stochastic differential equations, the concentration here on inference makes this book stand out. No other direct competitors are known to date. With an emphasis on the practical implementation of the simulation and estimation methods presented, the text will be useful to practitioners and students with minimal mathematical background. What’s more, because of the many R programs, the information here is appropriate for many mathematically well educated practitioners, too.

Random Fields for Spatial Data Modeling

By Dionissios T. Hristopulos
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Springer Nature
  • Book Code : 9402419187
  • Total of Pages : 867
  • Category : Science
  • Members : 522
  • Pdf File: random-fields-for-spatial-data-modeling.pdf

Book Short Summary:

This book provides an inter-disciplinary introduction to the theory of random fields and its applications. Spatial models and spatial data analysis are integral parts of many scientific and engineering disciplines. Random fields provide a general theoretical framework for the development of spatial models and their applications in data analysis. The contents of the book include topics from classical statistics and random field theory (regression models, Gaussian random fields, stationarity, correlation functions) spatial statistics (variogram estimation, model inference, kriging-based prediction) and statistical physics (fractals, Ising model, simulated annealing, maximum entropy, functional integral representations, perturbation and variational methods). The book also explores links between random fields, Gaussian processes and neural networks used in machine learning. Connections with applied mathematics are highlighted by means of models based on stochastic partial differential equations. An interlude on autoregressive time series provides useful lower-dimensional analogies and a connection with the classical linear harmonic oscillator. Other chapters focus on non-Gaussian random fields and stochastic simulation methods. The book also presents results based on the author’s research on Spartan random fields that were inspired by statistical field theories originating in physics. The equivalence of the one-dimensional Spartan random field model with the classical, linear, damped harmonic oscillator driven by white noise is highlighted. Ideas with potentially significant computational gains for the processing of big spatial data are presented and discussed. The final chapter concludes with a description of the Karhunen-Loève expansion of the Spartan model. The book will appeal to engineers, physicists, and geoscientists whose research involves spatial models or spatial data analysis. Anyone with background in probability and statistics can read at least parts of the book. Some chapters will be easier to understand by readers familiar with differential equations and Fourier transforms.

Introduction to Mathematical Modeling and Chaotic Dynamics

By Ranjit Kumar Upadhyay,Satteluri R. K. Iyengar
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : CRC Press
  • Book Code : 1439898871
  • Total of Pages : 363
  • Category : Mathematics
  • Members : 283
  • Pdf File: introduction-to-mathematical-modeling-and-chaotic-dynamics.pdf

Book Short Summary:

Introduction to Mathematical Modeling and Chaotic Dynamics focuses on mathematical models in natural systems, particularly ecological systems. Most of the models presented are solved using MATLAB®. The book first covers the necessary mathematical preliminaries, including testing of stability. It then describes the modeling of systems from natural science, focusing on one- and two-dimensional continuous and discrete time models. Moving on to chaotic dynamics, the authors discuss ways to study chaos, types of chaos, and methods for detecting chaos. They also explore chaotic dynamics in single and multiple species systems. The text concludes with a brief discussion on models of mechanical systems and electronic circuits. Suitable for advanced undergraduate and graduate students, this book provides a practical understanding of how the models are used in current natural science and engineering applications. Along with a variety of exercises and solved examples, the text presents all the fundamental concepts and mathematical skills needed to build models and perform analyses.

Differential Equations - Geometry, Symmetries and Integrability

By Boris Kruglikov,Valentin Lychagin,Eldar Straume
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Springer Science & Business Media
  • Book Code : 3642008739
  • Total of Pages : 386
  • Category : Mathematics
  • Members : 512
  • Pdf File: differential-equations-geometry-symmetries-and-integrability.pdf

Book Short Summary:

The Abel Symposium 2008 focused on the modern theory of differential equations and their applications in geometry, mechanics, and mathematical physics. Following the tradition of Monge, Abel and Lie, the scientific program emphasized the role of algebro-geometric methods, which nowadays permeate all mathematical models in natural and engineering sciences. The ideas of invariance and symmetry are of fundamental importance in the geometric approach to differential equations, with a serious impact coming from the area of integrable systems and field theories. This volume consists of original contributions and broad overview lectures of the participants of the Symposium. The papers in this volume present the modern approach to this classical subject.

Fourier Series and Numerical Methods for Partial Differential Equations

By Richard Bernatz
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : John Wiley & Sons
  • Book Code : 9780470651377
  • Total of Pages : 332
  • Category : Mathematics
  • Members : 470
  • Pdf File: fourier-series-and-numerical-methods-for-partial-differential-equations.pdf

Book Short Summary:

The importance of partial differential equations (PDEs) in modeling phenomena in engineering as well as in the physical, natural, and social sciences is well known by students and practitioners in these fields. Striking a balance between theory and applications, Fourier Series and Numerical Methods for Partial Differential Equations presents an introduction to the analytical and numerical methods that are essential for working with partial differential equations. Combining methodologies from calculus, introductory linear algebra, and ordinary differential equations (ODEs), the book strengthens and extends readers' knowledge of the power of linear spaces and linear transformations for purposes of understanding and solving a wide range of PDEs. The book begins with an introduction to the general terminology and topics related to PDEs, including the notion of initial and boundary value problems and also various solution techniques. Subsequent chapters explore: The solution process for Sturm-Liouville boundary value ODE problems and a Fourier series representation of the solution of initial boundary value problems in PDEs The concept of completeness, which introduces readers to Hilbert spaces The application of Laplace transforms and Duhamel's theorem to solve time-dependent boundary conditions The finite element method, using finite dimensional subspaces The finite analytic method with applications of the Fourier series methodology to linear version of non-linear PDEs Throughout the book, the author incorporates his own class-tested material, ensuring an accessible and easy-to-follow presentation that helps readers connect presented objectives with relevant applications to their own work. Maple is used throughout to solve many exercises, and a related Web site features Maple worksheets for readers to use when working with the book's one- and multi-dimensional problems. Fourier Series and Numerical Methods for Partial Differential Equations is an ideal book for courses on applied mathematics and partial differential equations at the upper-undergraduate and graduate levels. It is also a reliable resource for researchers and practitioners in the fields of mathematics, science, and engineering who work with mathematical modeling of physical phenomena, including diffusion and wave aspects.

Applied Mathematics And Modeling For Chemical Engineers

By Richard G. Rice,Duong D. Do
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : John Wiley & Sons
  • Book Code : 1118343026
  • Total of Pages : 396
  • Category : Technology & Engineering
  • Members : 258
  • Pdf File: applied-mathematics-and-modeling-for-chemical-engineers.pdf

Book Short Summary:

This Second Edition of the go-to reference combines the classical analysis and modern applications of applied mathematics for chemical engineers. The book introduces traditional techniques for solving ordinary differential equations (ODEs), adding new material on approximate solution methods such as perturbation techniques and elementary numerical solutions. It also includes analytical methods to deal with important classes of finite-difference equations. The last half discusses numerical solution techniques and partial differential equations (PDEs). The reader will then be equipped to apply mathematics in the formulation of problems in chemical engineering. Like the first edition, there are many examples provided as homework and worked examples.

Systems Performance Modeling

By Adarsh Anand,Mangey Ram
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Walter de Gruyter GmbH & Co KG
  • Book Code : 3110619059
  • Total of Pages : 192
  • Category : Technology & Engineering
  • Members : 244
  • Pdf File: systems-performance-modeling.pdf

Book Short Summary:

This book describes methods to improve software performance and safety using advanced mathematical and computational analytics. The main focus is laid on the increase of software reliability by preventive and predictive maintenance with efficient usage of modern testing resources. The editors collect contributions from international researchers in the field.

Principles of Mathematical Modeling

By Clive Dym
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Elsevier
  • Book Code : 0080470289
  • Total of Pages : 303
  • Category : Mathematics
  • Members : 901
  • Pdf File: principles-of-mathematical-modeling.pdf

Book Short Summary:

Science and engineering students depend heavily on concepts of mathematical modeling. In an age where almost everything is done on a computer, author Clive Dym believes that students need to understand and "own" the underlying mathematics that computers are doing on their behalf. His goal for Principles of Mathematical Modeling, Second Edition, is to engage the student reader in developing a foundational understanding of the subject that will serve them well into their careers. The first half of the book begins with a clearly defined set of modeling principles, and then introduces a set of foundational tools including dimensional analysis, scaling techniques, and approximation and validation techniques. The second half demonstrates the latest applications for these tools to a broad variety of subjects, including exponential growth and decay in fields ranging from biology to economics, traffic flow, free and forced vibration of mechanical and other systems, and optimization problems in biology, structures, and social decision making. Prospective students should have already completed courses in elementary algebra, trigonometry, and first-year calculus and have some familiarity with differential equations and basic physics. Serves as an introductory text on the development and application of mathematical models Focuses on techniques of particular interest to engineers, scientists, and others who model continuous systems Offers more than 360 problems, providing ample opportunities for practice Covers a wide range of interdisciplinary topics--from engineering to economics to the sciences Uses straightforward language and explanations that make modeling easy to understand and apply New to this Edition: A more systematic approach to mathematical modeling, outlining ten specific principles Expanded and reorganized chapters that flow in an increasing level of complexity Several new problems and updated applications Expanded figure captions that provide more information Improved accessibility and flexibility for teaching