# krainaksiazek the integration theory of linear ordinary differential equations 20045695

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### Ordinary Differential Equations Springer, Berlin

**Książki / Literatura obcojęzyczna**

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 literature.§The following topics are particularly emphasised:§ existence, uniqueness and continuation of solutions,§ continuous dependence on initial data,§ flows,§ qualitative behaviour of solutions,§ limit sets,§ stability theory,§ invariance principles,§ introductory control theory,§ feedback and stabilization.§The last two items cover classical control theoretic material such as linear control theory and absolute stability of nonlinear feedback systems. It also includes an introduction to the more recent concept of input-to-state stability.§Only a basic grounding in linear algebra and analysis is assumed. Ordinary Differential Equations will be suitable for final year undergraduate students of mathematics and appropriate for beginning postgraduates in mathematics and in mathematically oriented engineering and science.§

Sklep: Libristo.pl

### Ordinary Differential Equations

**Książki Obcojęzyczne>Angielskie>Mathematics & science>Mathematics>Calculus & mathematical analysis>Calculus of variationsKsiążki Obcoję...**

Develops The Theory Of Initial-, Boundary-, And Eigen Value Problems, Real And Complex Linear Systems, Asymptotic Behavior And Stability. This Book Emphasizes Differential Inequalities And Treats More Advanced Topics Such As Caratheodory Theory, Nonlinear Boundary Value Problems And Radially Symmetric Elliptic Problems.

Sklep: Gigant.pl

### Contribution to the Theory of Linear Homogeneous Geometric Difference Equations (Q-Difference Equations) (Classic Reprint) Forgotten Books

**Książki / Literatura obcojęzyczna**

Excerpt from A Contribution to the Theory of Linear Homogeneous Geometric Difference Equations (Q-Difference Equations) Introduction. A functional relation of the following type i= nA.(a:).u(a:q ) = 0, (1) 1 = 0 where Af(x), A(x),. -(0:)are known functions of the complex variable Xand where qis a real or imaginary constant while u(x) is the function to be determined, may be termed a linear homogeneous geometric difference equation (or 7-difference equation) of the n-th order. The aim of the present paper is to bring the theory of these equations, at least on some points, to the same degree of perfection as the theories of the corresponding differential equations and arithmetic (ordinary) difference equations as they have been built up the former principally by Fuchs and Frobenius (1)the latter by Norlund (1).This equation(1) is a particular case of a general class of functional relations considered by Grevy (1), following ideas set forth by Ka-nigs (1), (2), (3).The equation(1) has then been treated in detail by Carmichael(1), who employs the method of successive approximations. He also indicates a possibility of solving the equation by aid of power series, which idea has then been worked out in a particular case by Mason(1). In a still more particular case power series have been used already by Heine(1) and Thomae (1), (2)and later on by Jackson(4) and Smith(1), It is, however, possible to replace the power series by another class of series, which may be termed geometric factorial series. These series appear in many respects to be more natural to the problem in question, just as arithmetic (ordinary) Such a number placed in a parenthesis close by a name refers to the list of literature p.43. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Sklep: Libristo.pl

### Treatise on Linear Differential Equations, Vol. 1 (Classic Reprint) Forgotten Books

**Książki / Literatura obcojęzyczna**

Excerpt from A Treatise on Linear Differential Equations, Vol. 1 The theory of linear differential equations may almost be said to find its origin in Fuchs's two memoirs published in 1866 and 1868 in volumes 66 and 68 of Crelle's Journal. Previous to this the only class of linear differential equations for which a general method of integration was known was the class of equations with constant coefficients, including of course Legendre's well-known equation which is immediately transformable into one with constant coefficients. After the appearance of Fuchs's second memoir many mathematicians, particularly in France and Germany, including Fuchs himself, took up the subject which, though still in its infancy, now possesses a very large literature. This literature, however, is so scattered among the different mathematical journals and publications of learned societies that it is extremely difficult for students to read up the subject properly. I have endeavored in the present treatise to give a by no means complete but, I trust, a sufficient account of the theory as it stands to-day, to meet the needs of students. Full references to original sources arc given in every case. Most of the results in the first two chapters, which deal with the general properties of linear differential equations and with equations having constant coefficients, arc of course old, but the presentation of these properties is comparatively new and is due to such mathematicians as Hermite, Jordan, Darboux, and others. All that follows these two chapters is quite new and constitutes the essential part of the modern theory of linear differential equations. The present volume deals principally with Fuchs's type of equations, i.e. equations whose integrals are all regular: a sufficient account has been given, however, of the researches of Frobenius and Thomé on equations whose integrals arc not all regular. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

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

### Introduction to Partial Differential Equations Dover Publications

**Książki / Literatura obcojęzyczna**

Chapter 1. Fourier series 1.1 Basic concepts 1.2 Fourier series and Fourier coefficients 1.3 A mimimizing property of the Fourier coefficients. The Riemann-Lebesgue theorem 1.4 Convergence of Fourier series 1.5 The Parseval formula 1.6 Determination of the sum of certain trigonemetric series Chapter 2. Orthogonal systems 2.1 Integration of complex-valued functions of a real variable 2.2 Orthogonal systems 2.3 Complete orthogonal systems 2.4 Integration of Fourier series 2.5 The Gram-Schmidt orthogonalization process 2.6 Sturm-Liouville problems Chapter 3. Orthogonal polynomials 3.1 The Legendre polynomials 3.2 Legendre series 3.3 The Legendre differential equation. The generating function of the Legendre polynomials 3.4 The Tchebycheff polynomials 3.5 Tchebycheff series 3.6 The Hermite polynomials. The Laguerre polynomials Chapter 4. Fourier transforms 4.1 Infinite interval of integration 4.2 The Fourier integral formula: a heuristic introduction 4.3 Auxiliary theorems 4.4 Proof of the Fourier integral formula. Fourier transforms 4.5 The convention theorem. The Parseval formula Chapter 5. Laplace transforms 5.1 Definition of the Laplace transform. Domain. Analyticity 5.2 Inversion formula 5.3 Further properties of Laplace transforms. The convolution theorem 5.4 Applications to ordinary differential equations Chapter 6. Bessel functions 6.1 The gamma function 6.2 The Bessel differential equation. Bessel functions 6.3 Some particular Bessel functions 6.4 Recursion formulas for the Bessel functions 6.5 Estimation of Bessel functions for large values of x. The zeros of the Bessel functions 6.6 Bessel series 6.7 The generating function of the Bessel functions of integral order 6.8 Neumann functions Chapter 7. Partial differential equations of first order 7.1 Introduction 7.2 The differential equation of a family of surfaces 7.3 Homogeneous differential equations 7.4 Linear and quasilinear differential equations Chapter 8. Partial differential equations of second order 8.1 Problems in physics leading to partial differential equations 8.2 Definitions 8.3 The wave equation 8.4 The heat equation 8.5 The Laplace equation Answers to exercises; Bibliography; Conventions; Symbols; Index

Sklep: Libristo.pl

### Theory Of Differential Equations

**Książki Obcojęzyczne>Angielskie>Mathematics & science>Mathematics>Calculus & mathematical analysis>Differential calculus & equations**

The Fourth Of Six Volumes In Forsyth's Theory Of Differential Equations Series, Concentrating Specifically On Ordinary Linear Equations.

Sklep: Gigant.pl

### A First Course in Partial Differential Equations with Complex Variables and Transform Methods Dover Publications

**Książki / Literatura obcojęzyczna**

I. The one-dimensional wave equation 1. A physical problem and its mathematical models: the vibrating string 2. The one-dimensional wave equation 3. Discussion of the solution: characteristics 4. Reflection and the free boundary problem 5. The nonhomogeneous wave equation II. Linear second-order partial differential equations in two variables 6. Linearity and superposition 7. Uniqueness for the vibrating string problem 8. Classification of second-order equations with constant coefficients 9. Classification of general second-order operators III. Some properties of elliptic and parabolic equations 10. Laplace's equation 11. Green's theorem and uniqueness for the Laplace's equation 12. The maximum principle 13. The heat equation IV. Separation of variables and Fourier series 14. The method of separation of variables 15. Orthogonality and least square approximation 16. Completeness and the Parseval equation 17. The Riemann-Lebesgue lemma 18. Convergence of the trigonometric Fourier series 19. "Uniform convergence, Schwarz's inequality, and completeness" 20. Sine and cosine series 21. Change of scale 22. The heat equation 23. Laplace's equation in a rectangle 24. Laplace's equation in a circle 25. An extension of the validity of these solutions 26. The damped wave equation V. Nonhomogeneous problems 27. Initial value problems for ordinary differential equations 28. Boundary value problems and Green's function for ordinary differential equations 29. Nonhomogeneous problems and the finite Fourier transform 30. Green's function VI. Problems in higher dimensions and multiple Fourier series 31. Multiple Fourier series 32. Laplace's equation in a cube 33. Laplace's equation in a cylinder 34. The three-dimensional wave equation in a cube 35. Poisson's equation in a cube VII. Sturm-Liouville theory and general Fourier expansions 36. Eigenfunction expansions for regular second-order ordinary differential equations 37. Vibration of a variable string 38. Some properties of eigenvalues and eigenfunctions 39. Equations with singular endpoints 40. Some properties of Bessel functions 41. Vibration of a circular membrane 42. Forced vibration of a circular membrane: natural frequencies and resonance 43. The Legendre polynomials and associated Legendre functions 44. Laplace's equation in the sphere 45. Poisson's equation and Green's function for the sphere VIII. Analytic functions of a complex variable 46. Complex numbers 47. Complex power series and harmonic functions 48. Analytic functions 49. Contour integrals and Cauchy's theorem 50. Composition of analytic functions 51. Taylor series of composite functions 52. Conformal mapping and Laplace's equation 53. The bilinear transformation 54. Laplace's equation on unbounded domains 55. Some special conformal mappings 56. The Cauchy integral representation and Liouville's theorem IX. Evaluation of integrals by complex variable methods 57. Singularities of analytic functions 58. The calculus of residues 59. Laurent series 60. Infinite integrals 61. Infinite series of residues 62. Integrals along branch cuts X. The Fourier transform 63. The Fourier transform 64. Jordan's lemma 65. Schwarz's inequality and the triangle inequality for infinite integrals 66. Fourier transforms of square integrable functions: the Parseval equation 67. Fourier inversion theorems 68. Sine and cosine transforms 69. Some operational formulas 70. The convolution product 71. Multiple Fourier transforms: the heat equation in three dimensions 72. The three-dimensional wave equation 73. The Fourier transform with complex argument XI. The Laplace transform 74. The Laplace transform 75. Initial value problems for ordinary differential equations 76. Initial value problems for the one-dimensional heat equation 77. A diffraction problem 78. The Stokes rule and Duhamel's principle XII. Approximation methods 79. "Exact" and approximate solutions" 80. The method of finite differences for initial-boundary value problems 81. The finite difference method for Laplace's equation 82. The method of successive approximations 83. The Raleigh-Ritz method SOLUTIONS TO THE EXERCISES INDEX

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### Linear Integral Equations Dover Publications

**Książki / Literatura obcojęzyczna**

I. Introductory II. Solution of Integral Equation of Second Kind by Successive Substitutions III. Solution of Fredholm

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### From Elementary Probability to Stochastic Differential Equations with MAPLE Springer, Berlin

**Książki / Literatura obcojęzyczna**

The authors provide a fast introduction to probabilistic and statistical concepts necessary to understand the basic ideas andmethods of stochastic differential equations. The book is based on measure theory which is introduced as smoothly as possible. It is intended for advanced undergraduate students or graduates, not necessarily in mathematics, providing an overview and intuitive background for more advanced studies as well as some practical skills in the use of MAPLE in the context of probability and its applications. As prerequisites the authors assume a familiarity with basic calculus and linear algebra, as well as with elementary ordinary differential equations and, in the final chapter, simple numerical methods for such ODEs. Although statistics is not systematically treated, they introduce statistical concepts such as sampling, estimators, hypothesis testing, confidence intervals, significance levels and p-values and use them in a large number of examples, problems and simulations.

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### Surveys in Differential-Algebraic Equations I Springer, Berlin

**Książki / Literatura obcojęzyczna**

The need for a rigorous mathematical theory for Differential-Algebraic Equations (DAEs) has its roots in the widespread applications of controlled dynamical systems, especially in mechanical and electrical engineering. Due to the strong relation to (ordinary) differential equations, the literature for DAEs mainly started out from introductory textbooks.§As such, the present monograph is new in the sense that it comprises survey articles on various fields of DAEs, providing reviews, presentations of the current state of research and new concepts in§- Controllability for linear DAEs§- Port-Hamiltonian differential-algebraic systems§- Robustness of DAEs§- Solution concepts for DAEs§- DAEs in circuit modeling.§The results in the individual chapters are presented in an accessible style, making this book suitable not only for active researchers but also for graduate students (with a good knowledge of the basic principles of DAEs) for self-study.

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### Introduction to Partial Differential Equations Springer, Berlin

**Książki / Literatura obcojęzyczna**

This is the softcover reprint of a popular book teaching the basic analytical and computational methods of partial differential equations. Standard topics such as separation of variables, Fourier analysis, maximum principles, and energy estimates are included. Prerequisites for this text are the very basics of calculus, linear algebra and ordinary differential equations. Numerical methods are included in the book to show the significance of computations in partial differential equations, and to illustrate the strong interaction between mathematical theory and numerical methods. Great care has been taken throughout the book to seek a sound balance between the analytical and numerical techniques. The authors present the material at an easy pace with exercises and projects ranging from the straightforward to the challenging. The text would be suitable for advanced undergraduate and graduate courses in mathematics and engineering, and it develops basic tools of computational science.

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### Difference Equations in Normed Spaces Elsevier Science Ltd

**Książki / Literatura obcojęzyczna**

Difference equations appear as natural descriptions of observed evolution phenomena because most measurements of time evolving variables are discrete. They also appear in the applications of discretization methods for differential, integral and integro-differential equations. The application of the theory of difference equations is rapidly increasing to various fields, such as numerical analysis, control theory, finite mathematics, and computer sciences. This book is devoted to linear and nonlinear difference equations in a normed space. The main methodology presented in this book is based on a combined use of recent norm estimates for operator-valued functions with the following methods and results: * The freezing method* The Liapunov type equation* The method of majorants* The multiplicative representation of solutions * Deals systematically with difference equations in normed spaces * Considers new classes of equations that could not be studied in the frameworks of ordinary and partial difference equations* Develops the freezing method and presents recent results on Volterra discrete equations* Contains an approach based on the estimates for norms of operator functions

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### Linear algebra Politechnika Gdańska

**MATEMATYKA**

Podręcznik dla studentów Politechniki Gdańskiej, którzy zamierzają pogłębić wiedzie z zakresu algebry liniowej w języku angielskim. Spis treści: 1. BEATRICES 1.1 Introduction 1.2 Some types of matrices 1.3. Equal matrices 1.4. Matrix addition 1.5. Scalar multiplication 1.6. Transpose of a matrix 1.7. Symmetric and skew-symmetric matrices 1.8. Matrix multiplication 1.9. The trace of a square matrix 1.10. Exercises 1.11. Answers 2. DETERMINANTS 2.1. Introduction 2.2. Properties of determinants 2.3. Exercises 2.4. Answers 3. INVERTIBLE MATRICES 3.1. Introduction 3.2. A method of obtaining the inverse of a square matrix 3.3. Exercises 3.4. Answers 4. SYSTEMS OF LINEAR EQUATIONS 4.1. Introduction 4.2. Cramer's theorem 4.3. Method of matrix inversion 4.4. Method of Gaussian elimination 4.5. The rank of a matrix 4.6. Fundamental theorem for systems of linear equations 4.7. Application of Gaussian elimination to find the inverse of a matrix 4.8. Exercises 4.9. Answers 5. EIGENVALUES AND EIGENVECTORS 5.1. Introduction 5.2. Eigenvalues and eigenvectors 5.3. Symmetric and skew-symmetric matrices 5.4. Useful properties 5.5. Application to ordinary differential equations 5.6. Case of repeated roots 5.7. Nonhomogeneous equation. Variation of parameters 5.8. Undetermined coefficients 5.9. Exercises 5.10. Answers REFERENCES

Sklep: ksiegarnia.edu.pl

### Algebraic and Algorithmic Aspects of Differential and Integral Operators Springer, Berlin

**Książki / Literatura obcojęzyczna**

This book constitutes the proceedings of the 5th International Meeting on Algebraic and Algorithmic Aspects of Differential and Integral Operators, AADIOS 2012, held at the Applications of Computer Algebra Conference in Sofia, Bulgaria, on June 25-28, 2012. The total of 9 papers presented in this volume consists of 2 invited papers and 7 regular papers which were carefully reviewed and selected from 13 submissions. The topics of interest are: symbolic computation for operator algebras, factorization of differential/integral operators, linear boundary problems and green's operators, initial value problems for differential equations, symbolic integration and differential galois theory, symbolic operator calculi, algorithmic D-module theory, rota-baxter algebra, differential algebra, as well as discrete analogs and software aspects of the above.

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