# krainaksiazek the integration theory of linear ordinary differential equations 20045695

- znaleziono 42 produkty w 4 sklepach

### The Integration Theory Of Linear Ordinary Differential Equations

**Książki Obcojęzyczne>Angielskie>Mathematics & science>Mathematics**

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Sklep: Gigant.pl

### The Turning Point Problem In The Asymptotic Integration Of Ordinary Linear Differential Equations (Classic Reprint)

**Książki Obcojęzyczne>Angielskie>Mathematics & science>Mathematics>Calculus & mathematical analysis>CalculusKsiążki Obcojęzyczne>Angi...**

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Sklep: Gigant.pl

### The Qualitative Theory of Ordinary Differential Equations Dover Publications

**Książki / Literatura obcojęzyczna**

Preface Chapter 1. Systems of Differential Equations 1.1 A Simple Mass-Spring System 1.2 Coupled Mass-Spring Systems 1.3 Systems of First-Order Equations 1.4 Vector-Matrix Notation for Systems 1.5 The Need for a Theory 1.6 Existence, Uniqueness, and Continuity 1.7 The Gronwall Inequality Chapter 2. Linear Systems, with an Introduction to Phase Space Analysis 2.1 Introduction 2.2 Existence and Uniqueness for Linear Systems 2.3 Linear Homogeneous Systems 2.4 Linear Nonhomogeneous Systems 2.5 Linear Systems with Constant Coefficients 2.6 Similarity of Matrices and the Jordan Canonical Form 2.7 Asymptotic Behavior of Solutions of Linear Systems with Constant Coefficients 2.8 Autonomous Systems--Phase Space--Two-Dimensional Systems 2.9 Linear Systems with Periodic Coefficients; Miscellaneous Exercises Chapter 3. Existence Theory 3.1 Existence in the Scalar Case 3.2 Existence Theory for Systems of First-Order Equations 3.3 Uniqueness of Solutions 3.4 Continuation of Solutions 3.5 Dependence on Initial Conditions and Parameters; Miscellaneous Exercises Chapter 4. Stability of Linear and Almost Linear Systems 4.1 Introduction 4.2 Definitions of Stability 4.3 Linear Systems 4.4 Almost Linear Systems 4.5 Conditional Stability 4.6 Asymptotic Equivalence 4.7 Stability of Periodic Solutions Chapter 5. Lyapunov's Second Method 5.1 Introductory Remarks 5.2 Lyapunov's Theorems 5.3 Proofs of Lyapunov's Theorems 5.4 Invariant Sets and Stability 5.5 The Extent of Asymptotic Stability--Global Asymptotic Stability 5.6 Nonautonomous Systems Chapter 6. Some Applications 6.1 Introduction 6.2 The Undamped Oscillator 6.3 The Pendulum 6.4 Self-Excited Oscillations--Periodic Solutions of the Liénard Equation 6.5 The Regulator Problem 6.6 Absolute Stability of the Regulator System Appendix 1. Generalized Eigenvectors, Invariant Subspaces, and Canonical Forms of Matrices Appendix 2. Canonical Forms of 2 x 2 Matrices Appendix 3. The Logarithm of a Matrix Appendix 4. Some Results from Matrix Theory Bibliography; Index

Sklep: Libristo.pl

### Basic Theory of Ordinary Differential Equations Springer, Berlin

**Książki / Literatura obcojęzyczna**

The authors' aim is to provide the reader with the very basic knowledge necessary to begin research on differential equations with professional ability. The selection of topics should provide the reader with methods and results that are applicable in a variety of different fields. The text is suitable for a one-year graduate course, as well as a reference book for research mathematicians. The book is divided into four parts. The first covers fundamental existence, uniqueness, smoothness with respect to data, and nonuniqueness. 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 114 illustrations and 206 exercises. Hints and comments for many problems are given.

Sklep: Libristo.pl

### Ordinary Differential Equations Springer-Verlag New York Inc.

**Książki / Literatura obcojęzyczna**

This book develops the theory of ordinary differential equations (ODEs), starting from an introductory level 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 and (ii) a dedicated website with software templates, problem solutions, and other resources supporting the text and (iii) a large number and variety of illustrations.§§Given its many applications, the book is suitable for senior undergraduates and graduate students in mathematics and science and engineering courses. 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).§

Sklep: Libristo.pl

### Ordinary Differential Equations Springer, Berlin

**Książki / Literatura obcojęzyczna**

Ordinary differential equations develops the theory of initial-, boundary-, and eigenvalue problems, real and complex linear systems, asymptotic behavior and stability. Using novel approaches to many subjects, the book emphasizes differential inequalities and treats more advanced topics such as Caratheodory theory, nonlinear boundary value problems and radially symmetric elliptic problems. New proofs are given which use concepts and methods from functional analysis. Applications from mechanics, physics, and biology are included, and exercises, which range from routine to demanding, are dispersed throughout the text. Solutions for selected exercises are included at the end of the book. All required material from functional analysis is developed in the book and is accessible to students with a sound knowledge of calculus and familiarity with notions from linear algebra.

Sklep: Libristo.pl

### A Textbook on Ordinary Differential Equations Springer, Berlin

**Książki / Literatura obcojęzyczna**

This book is a primer for the theory and applications of Ordinary Differential Equations. The presentation is simple, yet thorough and rigorous.§§Each chapter ends with a broad set of exercises that range from the routine to the more challenging and thought provoking. Solutions to selected exercises can be found at the end of the book.§§The book contains many interesting examples on topics such as electric circuits, the pendulum equation, the logistic equation, the Lotka-Volterra system, the Laplace Transform, etc, which introduce students to some interesting aspects of the theory and applications. The work is mainly intended for students of Mathematics, Physics, Engineering, Computer Science and other areas of the sciences and social sciences that use ordinary differential equations, with adequate knowledge of Calculus and a minimal understanding of the basic concepts in Linear Algebra. Included are also a few more advanced topics, such as Stability Theory and Boundary Value Problems, which may be suitable for more advanced undergraduate or first year graduate students.§

Sklep: Libristo.pl

### Stability and Periodic Solutions of Ordinary and Functional Differential Equations Dover Publications

**Książki / Literatura obcojęzyczna**

Preface An Overview 1. Linear Differential and Integrodifferential Equations 2. History, Motivation, Examples 3. Fixed-Point Theory 4. Limit Sets, Periodicity, and Stability References Indexes

Sklep: Libristo.pl

### Introduction to Linear Algebra and Differential Equations Dover Publications

**Książki / Literatura obcojęzyczna**

Preface 1. Complex Numbers 1.1 Introduction 1.2 The Algebra of Complex Numbers 1.3 The Geometry of Complex Numbers 1.4 Two-dimensional Vectors 1.5 Functions of a Complex Variable 1.6 Exponential Function 1.7 Power Series 2. Linear Algebraic Equations 2.1 Introduction 2.2 Matrices 2.3 Elimination Method 2.4 Determinants 2.5 Inverse of a Matrix 2.6 Existence and Uniqueness Theorems 3. Vector Spaces 3.1 Introduction 3.2 Three-dimensional Vectors 3.3 Axioms of a Vector Space 3.4 Dependence and Independence of Vectors 3.5 Basis and Dimension 3.6 Scalar Product 3.7 Orthonormal Bases 3.8 Infinite-dimensional Vector Spaces 4. Linear Transformations 4.1 Introduction 4.2 Definitions and Examples 4.3 Matrix Representations 4.4 Changes of Bases 4.5 Characteristic Values and Characteristic Vectors 4.6 Symmetric and Hermitian Matrices 4.7 Jordan Forms 5. First Order Differential Equations 5.1 Introduction 5.2 An Example 5.3 Basic Definitions 5.4 First Order Linear Equations 5.5 First Order Nonlinear Equations 5.6 Applications of First Order Equations 5.7 Numerical Methods 5.8 Existence and Uniqueness 6. Linear Differential Equations 6.1 Introduction 6.2 General Theorems 6.3 Variation of Parameters 6.4 Equations with Constant Coefficients 6.5 Method of Undetermined Coefficients 6.6 Applications 6.7 Green's Functions 7. Laplace Transforms 7.1 Introduction 7.2 Existence of the Transform 7.3 Transforms of Certain Functions 7.4 Inversion of the Transform 7.5 Solution of Differential Equations 7.6 Applications 7.7 Uniqueness of the Transform 8. Power-Series Methods 8.1 Introduction 8.2 Solution near Ordinary Points 8.3 Solution near Regular Singular Points 8.4 Bessel Functions 8.5 Boundary-value Problems 8.6 Convergence Theorems 9. Systems of Differential Equations 9.1 Introduction 9.2 First Order Systems 9.3 Linear First Order Systems 9.4 Linear First Order Systems with Constant Coefficients 9.5 Higher Order Linear Systems 9.6 Existence and Uniqueness Theorem Answers and Hints for Selected Exercises; Index

Sklep: Libristo.pl

### Theory of Differential Equations Cambridge University Press

**Książki / Literatura obcojęzyczna**

Andrew Russell Forsyth (1858

Sklep: Libristo.pl

### Partial Differential Equations in Action Springer, Berlin

**Książki / Literatura obcojęzyczna**

§The main purpose is on the one hand to train the students to appreciate the interplay between theory and modelling in problems arising in the applied sciences; on the other hand to give them a solid theoretical background for numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first one has a rather elementary character with the goal of developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. Ideas and connections with concrete aspects are emphasized whenever possible, in order to provide intuition and feeling for the subject. For this part, a knowledge of advanced calculus and ordinary differential equations is required. Also, the repeated use of the method of separation of variables assumes some basic results from the theory of Fourier series, which are summarized in an appendix.§§The main topic of the second part is the development of Hilbert space methods for the variational formulation and analysis of linear boundary and initial-boundary value problemsemph{. }%. Given the abstract nature of these chapters, an effort has been made to provide intuition and motivation for the various concepts and results. The understanding of these topics requires some basic knowledge of Lebesgue measure and integration, summarized in another appendix.§§At the end of each chapter, a number of exercises at different level of complexity is included. The most demanding problems are supplied with answers or hints. The exposition if flexible enough to allow substantial changes without compromising the comprehension and to facilitate a selection of topics for a one or two semester course.

Sklep: Libristo.pl

### Techniques of Functional Analysis for Differential and Integral Equations ELSEVIER SCIENCE

**Książki / Literatura obcojęzyczna**

Techniques of Functional Analysis for Differential and Integral Equations describes a variety of powerful and modern tools from mathematical and functional analysis, for graduate study and further research in ordinary differential equations, integral equations and partial differential equations. It is particularly useful as preparation for graduate courses and PhD research in differential equations and numerical analysis, and more specialized topics such as fluid dynamics and control theory. Striking a balance between mathematical rigor and accessibility, proofs involving more technical aspects of measure and integration theory are avoided, but clear statements and precise alternative references are given. The work provides many examples and exercises drawn from the literature. Provides an introduction to mathematical techniques widely used in applied mathematics and needed for advanced research in ordinary and partial differential equations, integral equations, numerical analysis, fluid dynamics and other areasEstablishes the advanced background needed for sophisticated literature review and research in differential equations and integral equationsSuitable for use as a textbook for a two semester graduate level course for M.S. and Ph.D. students in Mathematics and Applied Mathematics

Sklep: Libristo.pl

### Differential Equations with Mathematica ELSEVIER SCIENCE

**Książki / Literatura obcojęzyczna**

Fully updated to version 10 of Mathematica, Differential Equations with Mathematica 4th edition is a supplementing reference which uses the fundamental concepts of the popular platform to solve (analytically, numerically, and / or graphically) differential equations of interest to students, instructors, and scientists. Mathematicaâ

Sklep: Libristo.pl

### A First Course in the Numerical Analysis of Differential Equations Cambridge University Press

**Książki / Literatura obcojęzyczna**

Numerical analysis presents different faces to the world. For mathematicians it is a bona fide mathematical theory with an applicable flavour. For scientists and engineers it is a practical, applied subject, part of the standard repertoire of modelling techniques. For computer scientists it is a theory on the interplay of computer architecture and algorithms for real-number calculations. The tension between these standpoints is the driving force of this book, which presents a rigorous account of the fundamentals of numerical analysis of both ordinary and partial differential equations. The exposition maintains a balance between theoretical, algorithmic and applied aspects. This new edition has been extensively updated, and includes new chapters on emerging subject areas: geometric numerical integration, spectral methods and conjugate gradients. Other topics covered include multistep and Runge-Kutta methods; finite difference and finite elements techniques for the Poisson equation; and a variety of algorithms to solve large, sparse algebraic systems.

Sklep: Libristo.pl

### One-Parameter Semigroups for Linear Evolution Equations Springer, Berlin

**Książki / Literatura obcojęzyczna**

This book gives an up-to-date account of the theory of strongly continuous one-parameter semigroups of linear operators. It includes a systematic discussion of the spectral theory and the long-term behavior of such semigroups. A special feature of the text is an unusually wide range of applications, e.g., to ordinary and partial differential operators, delay and Volterra equations and to control theory, and an emphasis on philosophical motivation and the historical background. The book is written for students, but should also be of value for researchers interested in this field.§

Sklep: Libristo.pl

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t1=0.055, t2=0, t3=0, t4=0.02, t=0.055