libristo formal power series and linear systems of meromorphic ordinary differential equations 1385593
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73,25 zł
Introduction to Ordinary Differential Equations Dover Publications Inc.
Książki / Literatura obcojęzyczna
Chapter 0. Preliminaries 1. Introduction 2 Complex numbers 3 Functions 4 Polynomials 5. Complex series and the exponential function 6. Determinants 7. Remarks on methods of discovery and proofChapter 1. Introduction--Linear Equations of the First Order 1. Introduction 2. Differential equations 3. Problems associated with differential equations 4. Linear equations of the first order 5. The equation y'+ay=0 6. The equation y'+ay=b(x) 7. The general linear equation of the first orderChapter 2. Linear Equations with Constant Coefficients 1. Introduction 2. The second order homogeneous equation 3. Initial value problems for second order equations 4. Linear dependence and independence 5. A formula for the Wronskian 6. The non-homogeneous equation of order two 7. The homogeneous equation of order n 8. Initial value problems for n-th order equations 9. Equations with real constants 10. The non-homogeneous equation of order n 11. A special method for solving the non-homogeneous equation 12. Algebra of constant coefficient operatorsChapter 3. Linear Equations with Variable Coefficients 1. Introduction 2. Initial value problems for the homogeneous equation 3. Solutions of the homogeneous equation 4. The Wronskian and linear independence 5. Reduction of the order of a homogeneous equation 6. The non-homogeneous equation 7. Homogeneous equations with analytic coefficients 8. The Legendre equation 9. Justification of the power series methodChapter 4. Linear Equations with Regular Singular Points 1. Introduction 2. The Euler equation 3. Second order equations with regular singular points--an example 4. Second order equations with regular singular points--the general case 5. A convergence proof 6. The exceptional cases 7. The Bessel equation 8. The Bessel equation (continued) 9. Regular singular points at infinityChapter 5. Existence and Uniqueness of Solutions to First Order Equations 1. Introduction 2. Equations with variables separated 3. Exact equations 4. The method of successive approximations 5. The Lipschitz condition 6. Convergence of the successive approximations 7. Non-local existence of solutions 8. Approximations to, and uniqueness of, solutions 9. Equations with complex-valued functionsChapter 6. Existence and Uniqueness of Solutions to Systems and n-th Order Equations 1. Introduction 2. An example--central forces and planetary motion 3. Some special equations 4. Complex n-dimensional space 5. Systems as vector equations 6. Existence and uniqueness of solutions to systems 7. Existence and uniqueness for linear systems 8. Equations of order n References; Answers to Exercises; Index
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70,54 zł
Introduction to Linear Algebra and Differential Equations Dover Publications Inc.
Książki / Literatura obcojęzyczna
Preface1. 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 Series2. 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 Theorems3. 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 Spaces4. 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 Forms5. 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 Uniqueness6. 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 Functions7. 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 Transform8. 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 Theorems9. 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
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115,96 zł
Applied Complex Variable Dover Publications Inc.
Książki / Literatura obcojęzyczna
Part I. Analytic Function TheoryChapter 1. The Complex Number Plane 1.1 Introduction 1.2 Complex Numbers 1.3 The Complex Plane 1.4 Point Sets in the Plane 1.5 Stereographic Projection. The Extended Complex Plane 1.6 Curves and RegionsChapter 2. Functions of a Complex Variable 2.1 Functions and Limits 2.2 Differentiability and Analyticity 2.3 The Cauchy-Riemann Conditions 2.4 Linear Fractional Transformations 2.5 Transcendental functions 2.6 Riemann SurfacesChapter 3. Integration in the Complex Plane 3.1 Line Integrals 3.2 The Definite Integral 3.3 Cauchy's Theorem 3.4 Implications of Cauchy's Theorem 3.5 Functions Defined by Integration 3.6 Cauchy Formulas 3.7 Maximum Modulus PrincipleChapter 4. Sequences and Series 4.1 Sequences of Complex Numbers 4.2 Sequences of Complex Functions 4.3 Infinite Series 4.4 Power Series 4.5 Analytic Continuation 4.6 Laurent Series 4.7 Double Series 4.8 Infinite Products 4.9 Improper Integrals 4.10 The Gamma FunctionChapter 5. Residue Calculus 5.1 The Residue Theorem 5.2 Evaluation of Real Integrals 5.3 The Principle of the Argument 5.4 Meromorphic Functions 5.5 Entire FunctionsPart II. Applications of Analytic Function TheoryChapter 6. Potential Theory 6.1 Laplace's Equation in Physics 6.2 The Dirichlet Problem 6.3 Green's Functions 6.4 Conformal Mapping 6.5 The Schwarz-Christoffel Transformation 6.6 Flows with Sources and Sinks 6.7 Volume and Surface Distributions 6.8 Singular Integral EquationsChapter 7. Ordinary Differential Equations 7.1 Separation of Variables 7.2 Existence and Uniqueness Theorems 7.3 Solution of a Linear Second-Order Differential Equation Near an Ordinary Point 7.4 Solution of a Linear Second-Order Differential Equation Near a Regular Singular Point 7.5 Bessel Functions 7.6 Legendre Functions 7.7 Sturm-Liouville Problems 7.8 Fredholm Integral EquationsChapter 8. Fourier Transforms 8.1 Fourier Series 8.2 The Fourier Integral Theorem 8.3 The Complex Fourier Transform 8.4 Properties of the Fourier Transform 8.5 The Solution of Ordinary Differential Equations 8.6 The Solution of Partial Differential Equations 8.7 The Solution of Integral EquationsChapter 9. Laplace Transforms 9.1 From Fourier to Laplace Transform 9.2 Properties of the Laplace Transform 9.3 Inversion of Laplace Transforms 9.4 The Solution of Ordinary Differential Equations 9.5 Stability 9.6 The Solution of Partial Differential Equations 9.7 The Solution of Integral EquationsChapter 10. Asymptotic Expansions 10.1 Introduction and Definitions 10.2 Operations on Asymptotic Expansions 10.3 Asymptotic Expansion of Integrals 10.4 Asymptotic Solutions of Ordinary Differential Equations References; Index
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t1=0.017, t2=0, t3=0, t4=0, t=0.017