Applying Power Series To Differential Equations

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Applying Power Series To Differential Equations

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Author : James Sochacki
language : en
Publisher: Springer Nature
Release Date : 2023-03-15

Applying Power Series To Differential Equations written by James Sochacki and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-15 with Mathematics categories.

This book is aimed to undergraduate STEM majors and to researchers using ordinary differential equations. It covers a wide range of STEM-oriented differential equation problems that can be solved using computational power series methods. Many examples are illustrated with figures and each chapter ends with discovery/research questions most of which are accessible to undergraduate students, and almost all of which may be extended to graduate level research. Methodologies implemented may also be useful for researchers to solve their differential equations analytically or numerically. The textbook can be used as supplementary for undergraduate coursework, graduate research, and for independent study.

Notes On Diffy Qs

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Author : Jiri Lebl
language : en
Publisher:
Release Date : 2013

Notes On Diffy Qs written by Jiri Lebl and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Boundary value problems categories.

Annotation An introductory course on differential equations aimed at engineers. The book covers first order ODEs, higher order linear ODEs, systems of ODEs, Fourier series and PDEs, eigenvalue problems, the Laplace transform, and power series methods. The book originated as class notes for Math 286 at the University of Illinois at Urbana-Champaign in the Fall 2008 and Spring 2009 semesters. It has since been successfully used in many university classrooms as the main textbook. See http: //www.jirka.org/diffyqs/ for more information, updates, errata, and a list of classroom adoptions.

500 Examples And Problems Of Applied Differential Equations

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Author : Ravi P. Agarwal
language : en
Publisher: Springer
Release Date : 2021-01-21

500 Examples And Problems Of Applied Differential Equations written by Ravi P. Agarwal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-21 with Mathematics categories.

This book highlights an unprecedented number of real-life applications of differential equations together with the underlying theory and techniques. The problems and examples presented here touch on key topics in the discipline, including first order (linear and nonlinear) differential equations, second (and higher) order differential equations, first order differential systems, the Runge–Kutta method, and nonlinear boundary value problems. Applications include growth of bacterial colonies, commodity prices, suspension bridges, spreading rumors, modeling the shape of a tsunami, planetary motion, quantum mechanics, circulation of blood in blood vessels, price-demand-supply relations, predator-prey relations, and many more. Upper undergraduate and graduate students in Mathematics, Physics and Engineering will find this volume particularly useful, both for independent study and as supplementary reading. While many problems can be solved at the undergraduate level, a number of challenging real-life applications have also been included as a way to motivate further research in this vast and fascinating field.

Introduction To Differential Equations

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Author : Michael Eugene Taylor
language : en
Publisher: American Mathematical Soc.
Release Date : 2011

Introduction To Differential Equations written by Michael Eugene Taylor and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.

The mathematical formulations of problems in physics, economics, biology, and other sciences are usually embodied in differential equations. The analysis of the resulting equations then provides new insight into the original problems. This book describes the tools for performing that analysis. The first chapter treats single differential equations, emphasizing linear and nonlinear first order equations, linear second order equations, and a class of nonlinear second order equations arising from Newton's laws. The first order linear theory starts with a self-contained presentation of the exponential and trigonometric functions, which plays a central role in the subsequent development of this chapter. Chapter 2 provides a mini-course on linear algebra, giving detailed treatments of linear transformations, determinants and invertibility, eigenvalues and eigenvectors, and generalized eigenvectors. This treatment is more detailed than that in most differential equations texts, and provides a solid foundation for the next two chapters. Chapter 3 studies linear systems of differential equations. It starts with the matrix exponential, melding material from Chapters 1 and 2, and uses this exponential as a key tool in the linear theory. Chapter 4 deals with nonlinear systems of differential equations. This uses all the material developed in the first three chapters and moves it to a deeper level. The chapter includes theoretical studies, such as the fundamental existence and uniqueness theorem, but also has numerous examples, arising from Newtonian physics, mathematical biology, electrical circuits, and geometrical problems. These studies bring in variational methods, a fertile source of nonlinear systems of differential equations. The reader who works through this book will be well prepared for advanced studies in dynamical systems, mathematical physics, and partial differential equations.

Applied Stochastic Differential Equations

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Author : Simo Särkkä
language : en
Publisher: Cambridge University Press
Release Date : 2019-05-02

Applied Stochastic Differential Equations written by Simo Särkkä and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-02 with Business & Economics categories.

With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.

Applied Differential Equations

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Author : Vladimir A. Dobrushkin
language : en
Publisher: CRC Press
Release Date : 2022-09-21

Applied Differential Equations written by Vladimir A. Dobrushkin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-21 with Mathematics categories.

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.

Generatingfunctionology

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Author : Herbert S. Wilf
language : en
Publisher: CRC Press
Release Date : 2005-12-20

Generatingfunctionology written by Herbert S. Wilf and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-20 with Computers categories.

Generating functions, one of the most important tools in enumerative combinatorics, are a bridge between discrete mathematics and continuous analysis. Generating functions have numerous applications in mathematics, especially in - Combinatorics - Probability Theory - Statistics - Theory of Markov Chains - Number Theory One of the most important and relevant recent applications of combinatorics lies in the development of Internet search engines whose incredible capabilities dazzle even the mathematically trained user.

Differential Equations Workbook For Dummies

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Author : Steven Holzner
language : en
Publisher: John Wiley & Sons
Release Date : 2009-06-29

Differential Equations Workbook For Dummies written by Steven Holzner and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-29 with Mathematics categories.

Make sense of these difficult equations Improve your problem-solving skills Practice with clear, concise examples Score higher on standardized tests and exams Get the confidence and the skills you need to master differential equations! Need to know how to solve differential equations? This easy-to-follow, hands-on workbook helps you master the basic concepts and work through the types of problems you'll encounter in your coursework. You get valuable exercises, problem-solving shortcuts, plenty of workspace, and step-by-step solutions to every equation. You'll also memorize the most-common types of differential equations, see how to avoid common mistakes, get tips and tricks for advanced problems, improve your exam scores, and much more! More than 100 Problems! Detailed, fully worked-out solutions to problems The inside scoop on first, second, and higher order differential equations A wealth of advanced techniques, including power series THE DUMMIES WORKBOOK WAY Quick, refresher explanations Step-by-step procedures Hands-on practice exercises Ample workspace to work out problems Online Cheat Sheet A dash of humor and fun

Exploring Odes

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Author : Lloyd N. Trefethen
language : en
Publisher: SIAM
Release Date : 2017-12-21

Exploring Odes written by Lloyd N. Trefethen and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-21 with Mathematics categories.

Exploring ODEs is a textbook of ordinary differential equations for advanced undergraduates, graduate students, scientists, and engineers. It is unlike other books in this field in that each concept is illustrated numerically via a few lines of Chebfun code. There are about 400 computer-generated figures in all, and Appendix B presents 100 more examples as templates for further exploration.?

Essential Mathematics For The Physical Sciences Volume 1

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Author : Brett Borden
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2017-10-31

Essential Mathematics For The Physical Sciences Volume 1 written by Brett Borden and has been published by Morgan & Claypool Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-31 with Science categories.

Physics is expressed in the language of mathematics; it is deeply ingrained in how physics is taught and how it's practiced. A study of the mathematics used in science is thus asound intellectual investment for training as scientists and engineers. This first volume of two is centered on methods of solving partial differential equations (PDEs) and the special functions introduced. Solving PDEs can't be done, however, outside of the context in which they apply to physical systems. The solutions to PDEs must conform to boundary conditions, a set of additional constraints in space or time to be satisfied at the boundaries of the system, that small part of the universe under study. The first volume is devoted to homogeneous boundary-value problems (BVPs), homogeneous implying a system lacking a forcing function, or source function. The second volume takes up (in addition to other topics) inhomogeneous problems where, in addition to the intrinsic PDE governing a physical field, source functions are an essential part of the system. This text is based on a course offered at the Naval Postgraduate School (NPS) and while produced for NPS needs, it will serve other universities well. It is based on the assumption that it follows a math review course, and was designed to coincide with the second quarter of student study, which is dominated by BVPs but also requires an understanding of special functions and Fourier analysis.