Ordinary and Partial Differential Equations

Ordinary and Partial Differential Equations

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  • Author: Ravi P. Agarwal
  • Publisher: Springer Science & Business Media
  • ISBN: 0387791469
  • Category : Mathematics
  • Languages : en
  • Pages : 422

In this undergraduate/graduate textbook, the authors introduce ODEs and PDEs through 50 class-tested lectures. Mathematical concepts are explained with clarity and rigor, using fully worked-out examples and helpful illustrations. Exercises are provided at the end of each chapter for practice. The treatment of ODEs is developed in conjunction with PDEs and is aimed mainly towards applications. The book covers important applications-oriented topics such as solutions of ODEs in form of power series, special functions, Bessel functions, hypergeometric functions, orthogonal functions and polynomials, Legendre, Chebyshev, Hermite, and Laguerre polynomials, theory of Fourier series. Undergraduate and graduate students in mathematics, physics and engineering will benefit from this book. The book assumes familiarity with calculus.


Differential Equations

Differential Equations

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  • Author: Viorel Barbu
  • Publisher: Springer
  • ISBN: 3319452614
  • Category : Mathematics
  • Languages : en
  • Pages : 230

This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner. Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations. Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.


Formal Power Series and Linear Systems of Meromorphic Ordinary Differential Equations

Formal Power Series and Linear Systems of Meromorphic Ordinary Differential Equations

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  • Author: Werner Balser
  • Publisher: Springer Science & Business Media
  • ISBN: 0387986901
  • Category : Mathematics
  • Languages : en
  • Pages : 314

Simple Ordinary Differential Equations may have solutions in terms of power series whose coefficients grow at such a rate that the series has a radius of convergence equal to zero. In fact, every linear meromorphic system has a formal solution of a certain form, which can be relatively easily computed, but which generally involves such power series diverging everywhere. In this book the author presents the classical theory of meromorphic systems of ODE in the new light shed upon it by the recent achievements in the theory of summability of formal power series.


Differential Equations

Differential Equations

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  • Author: George Finlay Simmons
  • Publisher:
  • ISBN:
  • Category : Differential equations
  • Languages : en
  • Pages : 465


Introduction to Ordinary Differential Equations

Introduction to Ordinary Differential Equations

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  • Author: Albert L. Rabenstein
  • Publisher: Academic Press
  • ISBN: 1483226220
  • Category : Mathematics
  • Languages : en
  • Pages : 444

Introduction to Ordinary Differential Equations is a 12-chapter text that describes useful elementary methods of finding solutions using ordinary differential equations. This book starts with an introduction to the properties and complex variable of linear differential equations. Considerable chapters covered topics that are of particular interest in applications, including Laplace transforms, eigenvalue problems, special functions, Fourier series, and boundary-value problems of mathematical physics. Other chapters are devoted to some topics that are not directly concerned with finding solutions, and that should be of interest to the mathematics major, such as the theorems about the existence and uniqueness of solutions. The final chapters discuss the stability of critical points of plane autonomous systems and the results about the existence of periodic solutions of nonlinear equations. This book is great use to mathematicians, physicists, and undergraduate students of engineering and the science who are interested in applications of differential equation.


Ordinary Differential Equations, with Applications

Ordinary Differential Equations, with Applications

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  • Author: Larry C. Andrews
  • Publisher: Pearson Scott Foresman
  • ISBN:
  • Category : Differential equations
  • Languages : en
  • Pages : 360


Differential Equations

Differential Equations

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  • Author: H. S. Bear
  • Publisher: Courier Corporation
  • ISBN: 0486143643
  • Category : Mathematics
  • Languages : en
  • Pages : 226

First-rate introduction for undergraduates examines first order equations, complex-valued solutions, linear differential operators, the Laplace transform, Picard's existence theorem, and much more. Includes problems and solutions.


Theory and Examples of Ordinary Differential Equations

Theory and Examples of Ordinary Differential Equations

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  • Author: Chin-Yuan Lin
  • Publisher: World Scientific
  • ISBN: 9814307122
  • Category : Mathematics
  • Languages : en
  • Pages : 555

This book presents a complete theory of ordinary differential equations, with many illustrative examples and interesting exercises. A rigorous treatment is offered in this book with clear proofs for the theoretical results and with detailed solutions for the examples and problems. This book is intended for undergraduate students who major in mathematics and have acquired a prerequisite knowledge of calculus and partly the knowledge of a complex variable, and are now reading advanced calculus and linear algebra. Additionally, the comprehensive coverage of the theory with a wide array of examples and detailed solutions, would appeal to mathematics graduate students and researchers as well as graduate students in majors of other disciplines. As a handy reference, advanced knowledge is provided in this book with details developed beyond the basics; optional sections, where main results are extended, offer an understanding of further applications of ordinary differential equations.


Ordinary Differential Equations

Ordinary Differential Equations

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  • Author: William A. Adkins
  • Publisher: Springer Science & Business Media
  • ISBN: 1461436184
  • Category : Mathematics
  • Languages : en
  • Pages : 807

Unlike most texts in differential equations, this textbook gives an early presentation of the Laplace transform, which is then used to motivate and develop many of the remaining differential equation concepts for which it is particularly well suited. For example, the standard solution methods for constant coefficient linear differential equations are immediate and simplified, and solution methods for constant coefficient systems are streamlined. By introducing the Laplace transform early in the text, students become proficient in its use while at the same time learning the standard topics in differential equations. The text also includes proofs of several important theorems that are not usually given in introductory texts. These include a proof of the injectivity of the Laplace transform and a proof of the existence and uniqueness theorem for linear constant coefficient differential equations. Along with its unique traits, this text contains all the topics needed for a standard three- or four-hour, sophomore-level differential equations course for students majoring in science or engineering. These topics include: first order differential equations, general linear differential equations with constant coefficients, second order linear differential equations with variable coefficients, power series methods, and linear systems of differential equations. It is assumed that the reader has had the equivalent of a one-year course in college calculus.


Elementary Differential Equations

Elementary Differential Equations

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  • Author: William E. Boyce
  • Publisher: John Wiley & Sons
  • ISBN: 1119443636
  • Category : Mathematics
  • Languages : en
  • Pages : 512

With Wiley's Enhanced E-Text, you get all the benefits of a downloadable, reflowable eBook with added resources to make your study time more effective, including: Embedded & searchable equations, figures & tables Math XML Index with linked pages numbers for easy reference Redrawn full color figures to allow for easier identification Elementary Differential Equations, 11th Edition is written from the viewpoint of the applied mathematician, whose interest in differential equations may sometimes be quite theoretical, sometimes intensely practical, and often somewhere in between. The authors have sought to combine a sound and accurate (but not abstract) exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and approximation that have proved useful in a wide variety of applications. While the general structure of the book remains unchanged, some notable changes have been made to improve the clarity and readability of basic material about differential equations and their applications. In addition to expanded explanations, the 11th edition includes new problems, updated figures and examples to help motivate students. The program is primarily intended for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year of study. The main prerequisite for engaging with the program is a working knowledge of calculus, gained from a normal two ] or three ] semester course sequence or its equivalent. Some familiarity with matrices will also be helpful in the chapters on systems of differential equations.