Essentials Of Ordinary Differential Equations
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Essential Ordinary Differential Equations
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Author : Robert Magnus
language : en
Publisher: Springer Nature
Release Date : 2022-11-24
Essential Ordinary Differential Equations written by Robert Magnus and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-24 with Mathematics categories.
This textbook offers an engaging account of the theory of ordinary differential equations intended for advanced undergraduate students of mathematics. Informed by the author’s extensive teaching experience, the book presents a series of carefully selected topics that, taken together, cover an essential body of knowledge in the field. Each topic is treated rigorously and in depth. The book begins with a thorough treatment of linear differential equations, including general boundary conditions and Green’s functions. The next chapters cover separable equations and other problems solvable by quadratures, series solutions of linear equations and matrix exponentials, culminating in Sturm–Liouville theory, an indispensable tool for partial differential equations and mathematical physics. The theoretical underpinnings of the material, namely, the existence and uniqueness of solutions and dependence on initial values, are treated at length. A noteworthy feature of this book is the inclusion of project sections, which go beyond the main text by introducing important further topics, guiding the student by alternating exercises and explanations. Designed to serve as the basis for a course for upper undergraduate students, the prerequisites for this book are a rigorous grounding in analysis (real and complex), multivariate calculus and linear algebra. Some familiarity with metric spaces is also helpful. The numerous exercises of the text provide ample opportunities for practice, and the aforementioned projects can be used for guided study. Some exercises have hints to help make the book suitable for independent study.fsfsfsscs
Essentials Of Ordinary Differential Equations
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Author : Ravi P. Agarwal
language : en
Publisher:
Release Date : 1991
Essentials Of Ordinary Differential Equations written by Ravi P. Agarwal and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Differential equations categories.
An Introduction To Ordinary Differential Equations
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Author : Ravi P. Agarwal
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-10
An Introduction To Ordinary Differential Equations written by Ravi P. Agarwal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-10 with Mathematics categories.
Ordinary differential equations serve as mathematical models for many exciting real world problems. Rapid growth in the theory and applications of differential equations has resulted in a continued interest in their study by students in many disciplines. This textbook organizes material around theorems and proofs, comprising of 42 class-tested lectures that effectively convey the subject in easily manageable sections. The presentation is driven by detailed examples that illustrate how the subject works. Numerous exercise sets, with an "answers and hints" section, are included. The book further provides a background and history of the subject.
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.
Fundamentals Of Ordinary Differential Equations
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Author : Uri Elias
language : en
Publisher: Springer Nature
Release Date : 2025-06-21
Fundamentals Of Ordinary Differential Equations written by Uri Elias and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-21 with Mathematics categories.
This textbook offers an introduction to ODEs that focuses on the qualitative behavior of differential equations rather than specialized methods for solving them. The book is organized around this approach with important topics, such as existence, uniqueness, qualitative behaviour, and stability, appearing in early chapters and explicit solution methods covered later. Proofs are included in an approachable manner, which are first motivated by describing the main ideas in a general sense before being written out in detail. A clear and accessible writing style is used, containing numerous examples and calculations throughout the text. Two appendices offer readers further material to explore, with the first using the orbits of the planets as an illustrative example and the second providing insightful historical notes. After reading this book, students will have a strong foundation for a course in PDEs or mathematical modeling. Fundamentals of Ordinary Differential Equations is suitable for an undergraduate course for students who have taken basic calculus and linear algebra courses, and who are able to read and write basic proofs. Because of its detailed approach, it is also conducive to self-study.
Ordinary Differential Equations Basics And Beyond
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Author : David G. Schaeffer
language : en
Publisher: Springer
Release Date : 2016-11-10
Ordinary Differential Equations Basics And Beyond written by David G. Schaeffer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-10 with Mathematics categories.
This book develops the theory of ordinary differential equations (ODEs), starting from an introductory level (with no prior experience in ODEs assumed) through to a graduate-level treatment of the qualitative theory, including bifurcation theory (but not chaos). While proofs are rigorous, the exposition is reader-friendly, aiming for the informality of face-to-face interactions. A unique feature of this book is the integration of rigorous theory with numerous applications of scientific interest. Besides providing motivation, this synthesis clarifies the theory and enhances scientific literacy. Other features include: (i) a wealth of exercises at various levels, along with commentary that explains why they matter; (ii) figures with consistent color conventions to identify nullclines, periodic orbits, stable and unstable manifolds; and (iii) a dedicated website with software templates, problem solutions, and other resources supporting the text (www.math.duke.edu/ode-book). Given its many applications, the book may be used comfortably in science and engineering courses as well as in mathematics courses. Its level is accessible to upper-level undergraduates but still appropriate for graduate students. The thoughtful presentation, which anticipates many confusions of beginning students, makes the book suitable for a teaching environment that emphasizes self-directed, active learning (including the so-called inverted classroom).
Essential Partial Differential Equations
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Author : David F. Griffiths
language : en
Publisher: Springer
Release Date : 2015-09-24
Essential Partial Differential Equations written by David F. Griffiths and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-24 with Mathematics categories.
This volume provides an introduction to the analytical and numerical aspects of partial differential equations (PDEs). It unifies an analytical and computational approach for these; the qualitative behaviour of solutions being established using classical concepts: maximum principles and energy methods. Notable inclusions are the treatment of irregularly shaped boundaries, polar coordinates and the use of flux-limiters when approximating hyperbolic conservation laws. The numerical analysis of difference schemes is rigorously developed using discrete maximum principles and discrete Fourier analysis. A novel feature is the inclusion of a chapter containing projects, intended for either individual or group study, that cover a range of topics such as parabolic smoothing, travelling waves, isospectral matrices, and the approximation of multidimensional advection–diffusion problems. The underlying theory is illustrated by numerous examples and there are around 300 exercises, designed to promote and test understanding. They are starred according to level of difficulty. Solutions to odd-numbered exercises are available to all readers while even-numbered solutions are available to authorised instructors. Written in an informal yet rigorous style, Essential Partial Differential Equations is designed for mathematics undergraduates in their final or penultimate year of university study, but will be equally useful for students following other scientific and engineering disciplines in which PDEs are of practical importance. The only prerequisite is a familiarity with the basic concepts of calculus and linear algebra.
Essential Engineering Equations
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Author : Syed A. Nasar
language : en
Publisher: CRC Press
Release Date : 1991-02-26
Essential Engineering Equations written by Syed A. Nasar and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-02-26 with Technology & Engineering categories.
Linear, simultaneous algebraic equations, ordinary differential equations, partial differential equations; and difference equations are the four most common types of equations encountered in engineering. This book provides methods for solving general equations of all four types and draws examples from the major branches of engineering. Problems illustrating electric circuit theory, linear systems, electromagnetic field theory, mechanics, bending of beams, buckling of columns, twisting of shafts, vibration, fluid flow, heat transfer, and mass transfer are included. Essential Engineering Equations is an excellent book for engineering students and professional engineers.
Essential Differential Equations
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Author : Joseph Previte
language : en
Publisher: Lulu.com
Release Date : 2017-10-05
Essential Differential Equations written by Joseph Previte and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-05 with Technology & Engineering categories.
This is an affordable text that covers the material in a standard one semester differential equations class.
Asymptotic Behavior And Stability Problems In Ordinary Differential Equations
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Author : Lamberto Cesari
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Asymptotic Behavior And Stability Problems In Ordinary Differential Equations written by Lamberto Cesari and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
In the last few decades the theory of ordinary differential equations has grown rapidly under the action of forces which have been working both from within and without: from within, as a development and deepen ing of the concepts and of the topological and analytical methods brought about by LYAPUNOV, POINCARE, BENDIXSON, and a few others at the turn of the century; from without, in the wake of the technological development, particularly in communications, servomechanisms, auto matic controls, and electronics. The early research of the authors just mentioned lay in challenging problems of astronomy, but the line of thought thus produced found the most impressive applications in the new fields. The body of research now accumulated is overwhelming, and many books and reports have appeared on one or another of the multiple aspects of the new line of research which some authors call" qualitative theory of differential equations". The purpose of the present volume is to present many of the view points and questions in a readable short report for which completeness is not claimed. The bibliographical notes in each section are intended to be a guide to more detailed expositions and to the original papers. Some traditional topics such as the Sturm comparison theory have been omitted. Also excluded were all those papers, dealing with special differential equations motivated by and intended for the applications.