Worldwide Differential Calculus
Author: David B. Massey
Publisher:
Published: 2009-01-01
Total Pages: 565
ISBN-13: 9780984207190
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Global Properties of Linear Ordinary Differential Equations
Author: Frantisek Neuman
Publisher: Springer
Published: 1991
Total Pages: 344
ISBN-13:
DOWNLOAD EBOOKThis volume presents an authoritative, unified overview of the methods and results concerning the global properties of linear differential equations of order n (n>=2). It does not, however, seek to be comprehensive. Rather, it contains a selection of results which richly illustrate the unified approach presented. By making use of recent methods and results from many different areas of mathematics and by introducing several original methods, global solutions of problems previously studied only locally are given. The structure of global transformations is described algebraically, and a new geometrical approach is introduced which leads to global canonical forms suitable for Cartan's moving frame-of-reference method. The theory discussed also provides effective tools for solving some open problems, especially relating to the distribution of zeros of solutions. In addition, the theory of functional equations plays an important role in studying the asymptotic behaviour of solutions. Applications to differential geometry and functional equations are also described. The volume is largely self-contained. This book is for mathematicians, computer scientists, physicists, chemists, engineers, and others whose work involves the use of linear differential equations.
Ordinary Differential Equations
Author: William A. Adkins
Publisher: Springer Science & Business Media
Published: 2012-07-01
Total Pages: 807
ISBN-13: 1461436184
DOWNLOAD EBOOKUnlike 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.
Ordinary Differential Equations and Dynamical Systems
Author: Thomas C. Sideris
Publisher: Springer Science & Business Media
Published: 2013-10-17
Total Pages: 230
ISBN-13: 9462390215
DOWNLOAD EBOOKThis book is a mathematically rigorous introduction to the beautiful subject of ordinary differential equations for beginning graduate or advanced undergraduate students. Students should have a solid background in analysis and linear algebra. The presentation emphasizes commonly used techniques without necessarily striving for completeness or for the treatment of a large number of topics. The first half of the book is devoted to the development of the basic theory: linear systems, existence and uniqueness of solutions to the initial value problem, flows, stability, and smooth dependence of solutions upon initial conditions and parameters. Much of this theory also serves as the paradigm for evolutionary partial differential equations. The second half of the book is devoted to geometric theory: topological conjugacy, invariant manifolds, existence and stability of periodic solutions, bifurcations, normal forms, and the existence of transverse homoclinic points and their link to chaotic dynamics. A common thread throughout the second part is the use of the implicit function theorem in Banach space. Chapter 5, devoted to this topic, the serves as the bridge between the two halves of the book.
Handbook of Exact Solutions for Ordinary Differential Equations
Author: Valentin F. Zaitsev
Publisher: CRC Press
Published: 2002-10-28
Total Pages: 815
ISBN-13: 1420035339
DOWNLOAD EBOOKExact solutions of differential equations continue to play an important role in the understanding of many phenomena and processes throughout the natural sciences in that they can verify the correctness of or estimate errors in solutions reached by numerical, asymptotic, and approximate analytical methods. The new edition of this bestselling handboo
Differential and Difference Equations with Applications
Author: Sandra Pinelas
Publisher: Springer Science & Business Media
Published: 2013-09-21
Total Pages: 639
ISBN-13: 1461473330
DOWNLOAD EBOOKThe volume contains carefully selected papers presented at the International Conference on Differential & Difference Equations and Applications held in Ponta Delgada – Azores, from July 4-8, 2011 in honor of Professor Ravi P. Agarwal. The objective of the gathering was to bring together researchers in the fields of differential & difference equations and to promote the exchange of ideas and research. The papers cover all areas of differential and difference equations with a special emphasis on applications.
Ordinary Differential Equations: Basics and Beyond
Author: David G. Schaeffer
Publisher: Springer
Published: 2016-11-10
Total Pages: 565
ISBN-13: 1493963899
DOWNLOAD EBOOKThis 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).
Differential Equations
Author: Allan Struthers
Publisher: Springer
Published: 2019-07-31
Total Pages: 522
ISBN-13: 3030205061
DOWNLOAD EBOOKThis book is designed to serve as a textbook for a course on ordinary differential equations, which is usually a required course in most science and engineering disciplines and follows calculus courses. The book begins with linear algebra, including a number of physical applications, and goes on to discuss first-order differential equations, linear systems of differential equations, higher order differential equations, Laplace transforms, nonlinear systems of differential equations, and numerical methods used in solving differential equations. The style of presentation of the book ensures that the student with a minimum of assistance may apply the theorems and proofs presented. Liberal use of examples and homework problems aids the student in the study of the topics presented and applying them to numerous applications in the real scientific world. This textbook focuses on the actual solution of ordinary differential equations preparing the student to solve ordinary differential equations when exposed to such equations in subsequent courses in engineering or pure science programs. The book can be used as a text in a one-semester core course on differential equations, alternatively it can also be used as a partial or supplementary text in intensive courses that cover multiple topics including differential equations.
Existence Theory for Nonlinear Ordinary Differential Equations
Author: Donal O'Regan
Publisher: Springer Science & Business Media
Published: 2013-04-17
Total Pages: 207
ISBN-13: 9401715173
DOWNLOAD EBOOKWe begin our applications of fixed point methods with existence of solutions to certain first order initial initial value problems. This problem is relatively easy to treat, illustrates important methods, and in the end will carry us a good deal further than may first meet the eye. Thus, we seek solutions to Y'. = I(t,y) (1. 1 ) { yeO) = r n where I: I X R n ---+ R and I = [0, b]. We shall seek solutions that are de fined either locally or globally on I, according to the assumptions imposed on I. Notice that (1. 1) is a system of first order equations because I takes its values in Rn. In section 3. 2 we will first establish some basic existence theorems which guarantee that a solution to (1. 1) exists for t > 0 and near zero. Familiar examples show that the interval of existence can be arbi trarily short, depending on the initial value r and the nonlinear behaviour of I. As a result we will also examine in section 3. 2 the dependence of the interval of existence on I and r. We mention in passing that, in the results which follow, the interval I can be replaced by any bounded interval and the initial value can be specified at any point in I. The reasoning needed to cover this slightly more general situation requires minor modifications on the arguments given here.
Introduction to Partial Differential Equations
Author: David Borthwick
Publisher: Springer
Published: 2017-01-12
Total Pages: 293
ISBN-13: 3319489364
DOWNLOAD EBOOKThis modern take on partial differential equations does not require knowledge beyond vector calculus and linear algebra. The author focuses on the most important classical partial differential equations, including conservation equations and their characteristics, the wave equation, the heat equation, function spaces, and Fourier series, drawing on tools from analysis only as they arise. Within each section the author creates a narrative that answers the five questions: What is the scientific problem we are trying to understand? How do we model that with PDE? What techniques can we use to analyze the PDE? How do those techniques apply to this equation? What information or insight did we obtain by developing and analyzing the PDE? The text stresses the interplay between modeling and mathematical analysis, providing a thorough source of problems and an inspiration for the development of methods.
