1 edition of **Theory and examples of ordinary differential equations** found in the catalog.

Theory and examples of ordinary differential equations

Chin-Yuan Lin

- 80 Want to read
- 33 Currently reading

Published
**2011** by World Scientific in Singapore, Hackensack, N J .

Written in English

- Differential equations

**Edition Notes**

Includes bibliographical references (p. 537) and index.

Statement | Chin-Yuan Lin |

Series | Series on concrete and applicable mathematics -- v. 10, Series on concrete and applicable mathematics -- v. 10. |

Classifications | |
---|---|

LC Classifications | QA372 .L56 2011 |

The Physical Object | |

Pagination | xiii, 540 p. : |

Number of Pages | 540 |

ID Numbers | |

Open Library | OL25027431M |

ISBN 10 | 9814307122 |

ISBN 10 | 9789814307123 |

LC Control Number | 2011381523 |

OCLC/WorldCa | 696115825 |

An ordinary differential equation (ODE) is an equation containing an unknown function of one real or complex variable x, its derivatives, and some given functions of unknown function is generally represented by a variable (often denoted y), which, therefore, depends on x is often called the independent variable of the equation. The term "ordinary" is used in contrast . The Fuchsian theory of linear differential equations, which is named after Lazarus Immanuel Fuchs, provides a characterization of various types of singularities and the relations among them.. At any ordinary point of a homogeneous linear differential equation of order there exists a fundamental system of linearly independent power series solutions. A non-ordinary points is . The second part describes the basic results concerning linear differential equations, the third deals with nonlinear equations. In the last part the authors write about the basic results concerning power series solutions. Each chapter begins with a brief discussion of its contents and history. The book has illustrations and exercises.

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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 : Chin-Yuan Lin.

“The Theory and examples of ordinary differential equations book is an introduction to the theory of ordinary differential equations and intended for first- or second-year graduate students. The main feature of this book is its comprehensive structure, many examples and illustrations, and complementary electronic by: A book with usable contents ranging from undergraduates to researchers.

Coddington and Levinson's book Theory of Ordinary Differential Equations is definitely not recommended as a first reading on the subject but I am sure this is the best one of them by: Theory and Examples of Ordinary Differential Equations.

This book presents a complete theory of ordinary differential equations, with many illustrative examples and interesting exercises. A rigorous treatment is offered with clear proofs for the theoretical results and with detailed solutions for the examples and problems.

The book provides a comprehensive introduction to the theory of ordinary differential equations at the graduate level and includes applications to Newtonian and Theory and examples of ordinary differential equations book mechanics.

It not only has a large number of examples and computer graphics, but also has a complete collection Brand: Springer-Verlag New York. Presents the theory of ordinary differential equations, with illustrative examples and interesting exercises. This book is suitable for undergraduate students who major in mathematics and have acquired a Theory and examples of ordinary differential equations book knowledge of calculus and partly the knowledge of a complex variable, and are now reading advanced calculus and linear algebra.

All terms related to differential equations used in the textbook are introduced in a form of a definition. Many examples are assisted by pictures which significantly improve the clarity of Theory and examples of ordinary differential equations book exposition.

Notation, terminology and appearance are consistent throughout the book/5(1). Fundamental Theory ODEs and Dynamical Systems Ordinary Differential Equations An ordinary differential equation (or ODE) is an equation involving derivatives of an unknown quantity with respect to a single variable.

More precisely, suppose j;n2 N, Eis a Euclidean space, and FW dom.F/ R nC 1copies ‚ „ ƒ E E. Rj: ()File Size: KB. SOME BASICS 3 Example Show that the diﬀerential equation x0 = x2/3 has inﬁnitely many solutions satisfying x(0) = 0 on every interval [0,b].

Solution Deﬁne xc(t)= 0, if 0 ≤ tFile Size: KB. models by ordinary differential equations: population dynamics in biology dynamics in classical mechanics. The ﬁrst one studies behaviors of population of species. It can also be applied to economics, chemical reactions, etc.

The second one include many important examples such File Size: 1MB. Theory and examples of ordinary differential equations. Lin, Chin-Yuan. World Scientific pages $ Hardcover Series on concrete and applicable mathematics; v QA This text is for undergraduate math majors whose work is.

This concept is usually called a classical solution of a diﬀerential equation. The domain for ODE is usually an interval or a union of intervals.

Next we are going to deal with an example of Theory and examples of ordinary differential equations book that has rather a more real world ﬂavor than a theoretical one as the ones we have encountered so far.

Problem File Size: 1MB. Abstract The Handbook of Ordinary Differential Equations: Exact Solutions, Methods, and Problems, is an exceptional and complete reference for. The book is also intended to serve as a bridge to important topics that are often left out of a course on ordinary differential equations.

In particular, it provides brief introductions to bifurcation theory, center manifolds, normal forms and Hamiltonian by: 8. Ordinary diﬀerential equations serve as mathematical models for many exciting “real-world” problems, not only in science and technology, but also in such diverse ﬁelds as economics, psychology, defense, and demography.

Rapid growth in the theory of diﬀerential equations and in its applicationsCited by: (source: Nielsen Book Data) Summary 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. Ordinary Differential Equations. Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order.4/5(1).

The book comprises a rigorous and self-contained treatment of initial-value problems for ordinary differential equations. It additionally develops the basics of control theory, which is a unique feature in current textbook following topics are particularly emphasised:• existence.

8CHAPTER 2. FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS Theorem If F and G are functions that are continuously diﬀerentiable throughout a simply connected region, then F dx+Gdy is exact if and only if ∂G/∂x = ∂F/∂y.

Proof. Proof is given in MATB Example Consider 2 +,File Size: 1MB. Ordinary Differential Equations. and Dynamical Systems.

Gerald Teschl. This is a preliminary version of the book Ordinary Differential Equations and Dynamical Systems. published by the American Mathematical Society (AMS). This preliminary version is made available with.

Some examples of simple differential equations. The book covers separation of variables, linear differential equation of first order, the existence and uniqueness theorem, the Bernoulli differential equation, and the setup of model equations. (views)Ordinary Differential Equations and Dynamical Systems by Gerald Teschl- Universitaet Wien, In Introduction we will be concerned with various examples and speci ﬁc classes of ODEs of the ﬁrst and second order, postponing the general theory to the next Chapters.

Consider the diﬀerential equation of the ﬁrst order y0 = f(x,y), () where y= y(x) is the unknown real-valued function of a real argument x,andf(x,y) is. Fundamental Theory ODEs and Dynamical Systems Ordinary Diﬀerential Equations An ordinary diﬀerential equation (or ODE) is an equation involving derivatives of an unknown quantity with respect to a single variable.

More precisely, suppose j,n∈ N, Eis a Euclidean space, and F: dom(F)⊆ R× n+1 copies z }| {E× ×E→ Rj. ()File Size: KB. The present book describes the state-of-art in the middle of the 20th century, concerning first order differential equations of known solution formulæ.

Among the topics can be found exact differential forms, homogeneous differential forms, integrating factors, separation of the variables, and linear differential equations, Bernoulli's equation. an introductory course of ordinary diﬀerential equations (ODE): existence theory, ﬂows, invariant manifolds, linearization, omega limit sets, phase plane analysis, and stability.

These topics, covered in Sections – of Chapter 1 of this book File Size: 3MB. Most astpects of theory are illustrated by examples. The main areas covered in the book are existence theorems, transformation group (Lie group) methods of solution, linear systems of equations, boundary eigenvalue problems, nature and methods of solution of regular, singular and nonlinear equation in.

This elementary text-book on Ordinary Differential Equations, is an attempt to present as much of the subject as is necessary for the beginner in Differential Equations, or, perhaps, for the student of Technology who will not make a specialty of pure Mathematics.

Ordinary Differential Equations: An Introduction to the Fundamentals (Textbooks in Mathematics) by Kenneth B. Howell | Dec 8, out of 5 stars 3. The book is also intended to serve as a bridge to important topics that are often left out of a course on ordinary differential equations.

In particular, it provides brief introductions to bifurcation theory, center manifolds, normal forms and Hamiltonian systems. Ordinary Differential Equations Lecture Notes by Eugen J. Ionascu. This note explains the following topics: Solving various types of differential equations, Analytical Methods, Second and n-order Linear Differential Equations, Systems of Differential Equations, Nonlinear Systems and Qualitative Methods, Laplace Transform, Power Series Methods, Fourier Series.

Ordinary differential equations an elementary text book with an introduction to Lie's theory of the group of one parameter. This elementary text-book on Ordinary Differential Equations, is an attempt to present as much of the subject as is necessary for the beginner in Differential Equations, or, perhaps, for the student of Technology who will not make a specialty of pure.

Differential equations are among the most important mathematical tools used in pro-ducing models in the physical sciences, biological sciences, and engineering. In this text, we consider numerical methods for solving ordinary differential equations, that is, those differential equations that have only one independent variable.

This book provides an introduction to ordinary differential equations and dynamical systems. We start with some simple examples of explicitly solvable equations. Then we prove the fundamental results concerning the initial value problem: existence, uniqueness, extensibility, dependence on initial conditions.

Coddington’s book (An Introduction to Ordinary Differential Equations) is a cheap book that does a good job of introducing the basic theory of ordinary differential equations. It talks a lot about linear equations and the existence and uniqueness.

The book is a primer of the theory of Ordinary Differential Equations. Each chapter is completed by a broad set of exercises; the reader will also find a set of solutions of selected exercises.

The book contains many interesting examples as well (like the equations for the electric circuits, the. Sturm–Liouville theory is a theory of a special type of second order linear ordinary differential equation.

Their solutions are based on eigenvalues and corresponding eigenfunctions of linear operators defined via second-order homogeneous linear equations. used textbook “Elementary differential equations and boundary value problems” by Boyce & DiPrima (John Wiley & Sons, Inc., Seventh Edition, c ).

Many of the examples presented in these notes may be found in this book. The material of Chapter 7 is adapted from the textbook “Nonlinear dynamics and chaos” by Steven. Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order.

The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a. Theory of Ordinary Differential Equations book. Read reviews from world’s largest community for readers. Reprint. Originally published: New York: McGraw- 4/5.

Theory of ordinary differential equations Earl A. Coddington, Norman Levinson. The prerequisite for the study of this book is a knowledge of matrices and the essentials of functions of a complex variable.

It has been developed from courses given by the authors and probably contains more material than will ordinarily be covered in a one-year course. Ordinary differential equations, and second-order equations pdf particular, are at the heart of many mathematical descriptions of physical systems, as used by engineers, physicists and applied mathematicians/5(26).This book, together with the linked YouTube videos, reviews a first course on differential equations.

The main purpose is to help students prepare for their university exams. Theory is summarized, and the solutions of typical exam questions are demonstrated in YouTube videos/5(30).In mathematics, delay ebook equations (DDEs) are a type of differential equation in which the derivative of the ebook function at a certain time is given in terms of the values of the function at previous times.

DDEs are also called time-delay systems, systems with aftereffect or dead-time, hereditary systems, equations with deviating argument, or differential-difference equations.