A Practical Course In Differential Equations And Mathematical Modelling

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Practical Course In Differential Equations And Mathematical Modelling, A: Classical And New Methods. Nonlinear Mathematical Models. Symmetry And Invariance Principles

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Author : Nail H Ibragimov
Publisher : World Scientific Publishing Company
ISBN 13 : 9813107766
Total Pages : 365 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis Practical Course In Differential Equations And Mathematical Modelling, A: Classical And New Methods. Nonlinear Mathematical Models. Symmetry And Invariance Principles by : Nail H Ibragimov

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.

A Practical Course in Differential Equations and Mathematical Modelling

Author : Nailʹ Khaĭrullovich Ibragimov
Publisher :
ISBN 13 : 9789172959880
Total Pages : 370 pages
Book Rating : 4.9/5 (598 download)

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Book Synopsis A Practical Course in Differential Equations and Mathematical Modelling by : Nailʹ Khaĭrullovich Ibragimov

Download or read book A Practical Course in Differential Equations and Mathematical Modelling written by Nailʹ Khaĭrullovich Ibragimov and published by . This book was released on 2006 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Practical Course in Differential Equations and Mathematical Modeling

Author : Nail H. Ibragimov
Publisher :
ISBN 13 : 9787894236227
Total Pages : 362 pages
Book Rating : 4.2/5 (362 download)

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Book Synopsis A Practical Course in Differential Equations and Mathematical Modeling by : Nail H. Ibragimov

Download or read book A Practical Course in Differential Equations and Mathematical Modeling written by Nail H. Ibragimov and published by . This book was released on with total page 362 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 fundame.

A Practical Course in Differential Equations and Mathematical Modelling

Author : Nail H. Ibragimov
Publisher :
ISBN 13 : 9789172959989
Total Pages : 203 pages
Book Rating : 4.9/5 (599 download)

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Book Synopsis A Practical Course in Differential Equations and Mathematical Modelling by : Nail H. Ibragimov

Download or read book A Practical Course in Differential Equations and Mathematical Modelling written by Nail H. Ibragimov and published by . This book was released on 2004 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Practical Course in Differential Equations and Mathematical Modelling

Author : Nail H. Ibragimov
Publisher : World Scientific
ISBN 13 : 9814291951
Total Pages : 365 pages
Book Rating : 4.8/5 (142 download)

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Book Synopsis A Practical Course in Differential Equations and Mathematical Modelling by : Nail H. Ibragimov

Download or read book A Practical Course in Differential Equations and Mathematical Modelling written by Nail H. Ibragimov and published by World Scientific. This book was released on 2009 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, Collge 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.

A First Course in Differential Equations, Modeling, and Simulation

Author : Carlos A. Smith
Publisher : CRC Press
ISBN 13 : 1439850879
Total Pages : 350 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis A First Course in Differential Equations, Modeling, and Simulation by : Carlos A. Smith

Download or read book A First Course in Differential Equations, Modeling, and Simulation written by Carlos A. Smith and published by CRC Press. This book was released on 2011-05-18 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: Emphasizing a practical approach for engineers and scientists, A First Course in Differential Equations, Modeling, and Simulation avoids overly theoretical explanations and shows readers how differential equations arise from applying basic physical principles and experimental observations to engineering systems. It also covers classical methods for obtaining the analytical solution of differential equations and Laplace transforms. In addition, the authors discuss how these equations describe mathematical systems and how to use software to solve sets of equations where analytical solutions cannot be obtained. Using simple physics, the book introduces dynamic modeling, the definition of differential equations, two simple methods for obtaining their analytical solution, and a method to follow when modeling. It then presents classical methods for solving differential equations, discusses the engineering importance of the roots of a characteristic equation, and describes the response of first- and second-order differential equations. A study of the Laplace transform method follows with explanations of the transfer function and the power of Laplace transform for obtaining the analytical solution of coupled differential equations. The next several chapters present the modeling of translational and rotational mechanical systems, fluid systems, thermal systems, and electrical systems. The final chapter explores many simulation examples using a typical software package for the solution of the models developed in previous chapters. Providing the necessary tools to apply differential equations in engineering and science, this text helps readers understand differential equations, their meaning, and their analytical and computer solutions. It illustrates how and where differential equations develop, how they describe engineering systems, how to obtain the analytical solution, and how to use software to simulate the systems.

Differential Equations with MATLAB

Author : Mark McKibben
Publisher : CRC Press
ISBN 13 : 1466557087
Total Pages : 497 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis Differential Equations with MATLAB by : Mark McKibben

Download or read book Differential Equations with MATLAB written by Mark McKibben and published by CRC Press. This book was released on 2014-09-08 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unique textbook for an undergraduate course on mathematical modeling, Differential Equations with MATLAB: Exploration, Applications, and Theory provides students with an understanding of the practical and theoretical aspects of mathematical models involving ordinary and partial differential equations (ODEs and PDEs). The text presents a unifying

Modelling with Ordinary Differential Equations

Author : T.P. Dreyer
Publisher : Routledge
ISBN 13 : 1351430696
Total Pages : 302 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Modelling with Ordinary Differential Equations by : T.P. Dreyer

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.

Numerical Partial Differential Equations for Environmental Scientists and Engineers

Author : Daniel R. Lynch
Publisher : Springer Science & Business Media
ISBN 13 : 0387236201
Total Pages : 390 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Numerical Partial Differential Equations for Environmental Scientists and Engineers by : Daniel R. Lynch

Download or read book Numerical Partial Differential Equations for Environmental Scientists and Engineers written by Daniel R. Lynch and published by Springer Science & Business Media. This book was released on 2006-06-02 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A First Course in Differential Equations

Author : John David Logan
Publisher : Springer Science & Business Media
ISBN 13 : 0387259635
Total Pages : 297 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis A First Course in Differential Equations by : John David Logan

Download or read book A First Course in Differential Equations written by John David Logan and published by Springer Science & Business Media. This book was released on 2006 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: While the standard sophomore course on elementary differential equations is typically one semester in length, most of the texts currently being used for these courses have evolved into calculus-like presentations that include a large collection of methods and applications, packaged with state-of-the-art color graphics, student solution manuals, the latest fonts, marginal notes, and web-based supplements. All of this adds up to several hundred pages of text and can be very expensive. Many students do not have the time or desire to read voluminous texts and explore internet supplements. Thats what makes the format of this differential equations book unique. It is a one-semester, brief treatment of the basic ideas, models, and solution methods. Its limited coverage places it somewhere between an outline and a detailed textbook. The author writes concisely, to the point, and in plain language. Many worked examples and exercises are included. A student who works through this primer will have the tools to go to the next level in applying ODEs to problems in engineering, science, and applied mathematics. It will also give instructors, who want more concise coverage, an alternative to existing texts. This text also encourages students to use a computer algebra system to solve problems numerically. It can be stated with certainty that the numerical solution of differential equations is a central activity in science and engineering, and it is absolutely necessary to teach students scientific computation as early as possible. Templates of MATLAB programs that solve differential equations are given in an appendix. Maple and Mathematica commands are given as well. The author taught this material on several ocassions to students who have had a standard three-semester calculus sequence. It has been well received by many students who appreciated having a small, definitive parcel of material to learn. Moreover, this text gives students the opportunity to start reading mathematics at a slightly higher level than experienced in pre-calculus and calculus; not every small detail is included. Therefore the book can be a bridge in their progress to study more advanced material at the junior-senior level, where books leave a lot to the reader and are not packaged with elementary formats. J. David Logan is Professor of Mathematics at the University of Nebraska, Lincoln. He is the author of another recent undergraduate textbook, Applied Partial Differential Equations, 2nd Edition (Springer 2004).

A First Course in Differential Equations

Author : J. David Logan
Publisher : Springer
ISBN 13 : 3319178520
Total Pages : 377 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis A First Course in Differential Equations by : J. David Logan

Download or read book A First Course in Differential Equations written by J. David Logan and published by Springer. This book was released on 2015-07-01 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: The third edition of this concise, popular textbook on elementary differential equations gives instructors an alternative to the many voluminous texts on the market. It presents a thorough treatment of the standard topics in an accessible, easy-to-read, format. The overarching perspective of the text conveys that differential equations are about applications. This book illuminates the mathematical theory in the text with a wide variety of applications that will appeal to students in physics, engineering, the biosciences, economics and mathematics. Instructors are likely to find that the first four or five chapters are suitable for a first course in the subject. This edition contains a healthy increase over earlier editions in the number of worked examples and exercises, particularly those routine in nature. Two appendices include a review with practice problems, and a MATLAB® supplement that gives basic codes and commands for solving differential equations. MATLAB® is not required; students are encouraged to utilize available software to plot many of their solutions. Solutions to even-numbered problems are available on springer.com.

Applied Differential Equations

Author : Vladimir A. Dobrushkin
Publisher : CRC Press
ISBN 13 : 0429880480
Total Pages : 731 pages
Book Rating : 4.4/5 (298 download)

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Book Synopsis Applied Differential Equations by : Vladimir A. Dobrushkin

Download or read book Applied Differential Equations written by Vladimir A. Dobrushkin and published by CRC Press. This book was released on 2018-12-07 with total page 731 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Contemporary Approach to Teaching Differential Equations Applied Differential Equations: An Introduction presents a contemporary treatment of ordinary differential equations (ODEs) and an introduction to partial differential equations (PDEs), including their applications in engineering and the sciences. Designed for a two-semester undergraduate course, the text offers a true alternative to books published for past generations of students. It enables students majoring in a range of fields to obtain a solid foundation in differential equations. The text covers traditional material, along with novel approaches to mathematical modeling that harness the capabilities of numerical algorithms and popular computer software packages. It contains practical techniques for solving the equations as well as corresponding codes for numerical solvers. Many examples and exercises help students master effective solution techniques, including reliable numerical approximations. This book describes differential equations in the context of applications and presents the main techniques needed for modeling and systems analysis. It teaches students how to formulate a mathematical model, solve differential equations analytically and numerically, analyze them qualitatively, and interpret the results.

Applied Differential Equations

Author : Vladimir A. Dobrushkin
Publisher : CRC Press
ISBN 13 : 1000606309
Total Pages : 1331 pages
Book Rating : 4.0/5 (6 download)

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Book Synopsis Applied Differential Equations by : Vladimir A. Dobrushkin

Download or read book Applied Differential Equations written by Vladimir A. Dobrushkin and published by CRC Press. This book was released on 2022-09-21 with total page 1331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book started as a collection of lecture notes for a course in differential equations taught by the Division of Applied Mathematics at Brown University. To some extent, it is a result of collective insights given by almost every instructor who taught such a course over the last 15 years. Therefore, the material and its presentation covered in this book were practically tested for many years. This text is designed for a two-semester sophomore or junior level course in differential equations. It offers novel approaches in presentation and utilization of computer capabilities. This text intends to provide a solid background in differential equations for students majoring in a breadth of fields. Differential equations are described in the context of applications. The author stresses differential equations constitute an essential part of modeling by showing their applications, including numerical algorithms and syntax of the four most popular software packages. Students learn how to formulate a mathematical model, how to solve differential equations (analytically or numerically), how to analyze them qualitatively, and how to interpret the results. In writing this textbook, the author aims to assist instructors and students through: Showing a course in differential equations is essential for modeling real-life phenomena Stressing the mastery of traditional solution techniques and presenting effective methods, including reliable numerical approximations Providing qualitative analysis of ordinary differential equations. The reader should get an idea of how all solutions to the given problem behave, what are their validity intervals, whether there are oscillations, vertical or horizontal asymptotes, and what is their long-term behavior The reader will learn various methods of solving, analysis, visualization, and approximation, exploiting the capabilities of computers Introduces and employs MapleTM, Mathematica®, MatLab®, and Maxima This textbook facilitates the development of the student’s skills to model real-world problems Ordinary and partial differential equations is a classical subject that has been studied for about 300 years. The beauty and utility of differential equations and their application in mathematics, biology, chemistry, computer science, economics, engineering, geology, neuroscience, physics, the life sciences, and other fields reaffirm their inclusion in myriad curricula. A great number of examples and exercises make this text well suited for self-study or for traditional use by a lecturer in class. Therefore, this textbook addresses the needs of two levels of audience, the beginning and the advanced.

A First Course in Ordinary Differential Equations

Author : Martin Hermann
Publisher : Springer Science & Business
ISBN 13 : 8132218353
Total Pages : 300 pages
Book Rating : 4.1/5 (322 download)

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Book Synopsis A First Course in Ordinary Differential Equations by : Martin Hermann

Download or read book A First Course in Ordinary Differential Equations written by Martin Hermann and published by Springer Science & Business. This book was released on 2014-04-22 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a modern introduction to analytical and numerical techniques for solving ordinary differential equations (ODEs). Contrary to the traditional format—the theorem-and-proof format—the book is focusing on analytical and numerical methods. The book supplies a variety of problems and examples, ranging from the elementary to the advanced level, to introduce and study the mathematics of ODEs. The analytical part of the book deals with solution techniques for scalar first-order and second-order linear ODEs, and systems of linear ODEs—with a special focus on the Laplace transform, operator techniques and power series solutions. In the numerical part, theoretical and practical aspects of Runge-Kutta methods for solving initial-value problems and shooting methods for linear two-point boundary-value problems are considered. The book is intended as a primary text for courses on the theory of ODEs and numerical treatment of ODEs for advanced undergraduate and early graduate students. It is assumed that the reader has a basic grasp of elementary calculus, in particular methods of integration, and of numerical analysis. Physicists, chemists, biologists, computer scientists and engineers whose work involves solving ODEs will also find the book useful as a reference work and tool for independent study. The book has been prepared within the framework of a German–Iranian research project on mathematical methods for ODEs, which was started in early 2012.

Introduction to Computation and Modeling for Differential Equations

Author : Lennart Edsberg
Publisher : John Wiley & Sons
ISBN 13 : 1119018447
Total Pages : 286 pages
Book Rating : 4.1/5 (19 download)

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Book Synopsis Introduction to Computation and Modeling for Differential Equations by : Lennart Edsberg

Download or read book Introduction to Computation and Modeling for Differential Equations written by Lennart Edsberg and published by John Wiley & Sons. This book was released on 2015-10-05 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uses mathematical, numerical, and programming tools to solve differential equations for physical phenomena and engineering problems Introduction to Computation and Modeling for Differential Equations, Second Edition features the essential principles and applications of problem solving across disciplines such as engineering, physics, and chemistry. The Second Edition integrates the science of solving differential equations with mathematical, numerical, and programming tools, specifically with methods involving ordinary differential equations; numerical methods for initial value problems (IVPs); numerical methods for boundary value problems (BVPs); partial differential equations (PDEs); numerical methods for parabolic, elliptic, and hyperbolic PDEs; mathematical modeling with differential equations; numerical solutions; and finite difference and finite element methods. The author features a unique “Five-M” approach: Modeling, Mathematics, Methods, MATLAB®, and Multiphysics, which facilitates a thorough understanding of how models are created and preprocessed mathematically with scaling, classification, and approximation and also demonstrates how a problem is solved numerically using the appropriate mathematical methods. With numerous real-world examples to aid in the visualization of the solutions, Introduction to Computation and Modeling for Differential Equations, Second Edition includes: New sections on topics including variational formulation, the finite element method, examples of discretization, ansatz methods such as Galerkin’s method for BVPs, parabolic and elliptic PDEs, and finite volume methods Numerous practical examples with applications in mechanics, fluid dynamics, solid mechanics, chemical engineering, heat conduction, electromagnetic field theory, and control theory, some of which are solved with computer programs MATLAB and COMSOL Multiphysics® Additional exercises that introduce new methods, projects, and problems to further illustrate possible applications A related website with select solutions to the exercises, as well as the MATLAB data sets for ordinary differential equations (ODEs) and PDEs Introduction to Computation and Modeling for Differential Equations, Second Edition is a useful textbook for upper-undergraduate and graduate-level courses in scientific computing, differential equations, ordinary differential equations, partial differential equations, and numerical methods. The book is also an excellent self-study guide for mathematics, science, computer science, physics, and engineering students, as well as an excellent reference for practitioners and consultants who use differential equations and numerical methods in everyday situations.

Differential Equations

Author : C. Henry Edwards
Publisher : Pearson
ISBN 13 : 9780134850474
Total Pages : 576 pages
Book Rating : 4.8/5 (54 download)

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Book Synopsis Differential Equations by : C. Henry Edwards

Download or read book Differential Equations written by C. Henry Edwards and published by Pearson. This book was released on 2018-01-15 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: For one-semester sophomore- or junior-level courses in Differential Equations. Fosters the conceptual development and geometric visualization students need--now available with MyLab Math Differential Equations: Computing and Modeling blends traditional algebra problem-solving skills with the conceptual development and geometric visualization of a modern differential equations course that is essential to science and engineering students. It balances traditional manual methods with the new, computer-based methods that illuminate qualitative phenomena--a comprehensive approach that makes accessible a wider range of more realistic applications. The book starts and ends with discussions of mathematical modeling of real-world phenomena, evident in figures, examples, problems, and applications throughout. For the first time, MyLab(tm) Math is available for the 5th Edition, providing online homework with immediate feedback, the complete eText, and more. Also available with MyLab Math MyLab(tm) Math is the teaching and learning platform that empowers instructors to reach every student. By combining trusted author content with digital tools and a flexible platform, MyLab Math personalizes the learning experience and improves results for each student. Note: You are purchasing a standalone product; MyLab Math does not come packaged with this content. Students, if interested in purchasing this title with MyLab Math, ask your instructor to confirm the correct package ISBN and Course ID. Instructors, contact your Pearson representative for more information. If you would like to purchase both the physical text and MyLab Math, search for: 0134996003 / 9780134996004 Differential Equations: Computing and Modeling Media Update and MyLab Math with Pearson eText -- Title-Specific Access Card Package, 5/e Package consists of: 0134850475 / 9780134850474 Differential Equations: Computing and Modeling Media Update 0134873084 / 9780134873084 MyLab Math plus Pearson eText - Standalone Access Card - for Differential Equations: Computing and Modeling Media Update

Differential Dynamical Systems, Revised Edition

Author : James D. Meiss
Publisher : SIAM
ISBN 13 : 1611974631
Total Pages : 410 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Differential Dynamical Systems, Revised Edition by : James D. Meiss

Download or read book Differential Dynamical Systems, Revised Edition written by James D. Meiss and published by SIAM. This book was released on 2017-01-24 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics. Differential Dynamical Systems begins with coverage of linear systems, including matrix algebra; the focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems concepts?flow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. This new edition contains several important updates and revisions throughout the book. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics. Many of the exercises and examples are based on applications and some involve computation; an appendix offers simple codes written in Maple, Mathematica, and MATLAB software to give students practice with computation applied to dynamical systems problems.