《微分方程数值解》(Basic Theory of Ordinary Differential Equations)英文版[DJVU]
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电驴资源
电驴资源简介
| 资源介绍 |
| 语言: 英文 |
| 地区: 大陆 |
| 图书fenlei: 科技 |
| 中文名: 微分方程数值解 |
| 发行时间: 2007年 |
| 原名: Basic Theory of Ordinary Differential Equations |
| 资源格式: DJVU |
| 版本: 英文版 |
简介:  djvu 阅读器： http://windjview.sourceforge.net/ 用Foxit Reader最新版打开pdf 内容介绍： 《常微分方程基础理论(影印版)》为开展常微分方程研究工作的读者提供必要的准备知识，可作为本科高年级和研究生常微分方程课程教材。《常微分方程基础理论(影印版)》内容分为四部分：第一部分（第一、二、三章）的内容包括解的存在性、唯一性、对数据的光滑依赖性，以及解的非唯一性；第二部分（第四、六、七章）讨论线性常微分方程，书中用矩阵的S-N分解代替Jordan分解，前者的计算较后者更容易；第三部分（第八、九、十章）讨论非线性常微分方程的稳定性、渐近稳定性等几何理论；第四部分（第五、十一、十二、十三章）讨论常微分方程的幂级数解，包括线性常微分方程的奇点fenlei及非线性常微分方程当参数或自变量趋向某奇点时的渐近解等。 内容截图： 
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目录: Preface Chapter Ⅰ.Fundamental Theorems of Ordinary Differential Equations Ⅰ-1.Existence and uniqueness with the Lipschitz condition Ⅰ-2.Existence without the Lipschitz condition Ⅰ-3.Some global properties of solutions Ⅰ-4.Analytic differential equations Exercises Ⅰ ChapterⅡ.Dependence on Data Ⅱ-1.Continuity with respect to initial data and parameters Ⅱ-2.Differentiability Exercises Ⅱ Chapter Ⅲ.Nonuniqueness Ⅲ-1.Examples Ⅲ-2.The Kneser theorem Ⅲ-3.Solution curves on the boundary of R(A) Ⅲ-4.Maximal and minimal solutions Ⅲ-5.A comparison theorem Ⅲ-6.Sufficient conditions for uniqueness Exercises Ⅲ Chapter Ⅳ.General Theory of Linear Systems Ⅳ-1.Some basic results concerning matrices Ⅳ-2.Homogeneous systems of linear differential equations Ⅳ-3.Homogeneous systems with constant coefficients Ⅳ-4.Systems with periodic coefficients Ⅳ-5.Linear Hamiltonian systems with periodic coefficients Ⅳ-6.Nonhomogeneous equations Ⅳ-7.Higher-order scalar equations Exercises Ⅳ Chapter Ⅴ.Singularities of the First Kind Ⅴ-1.Formal solutions of an algebraic differential equation Ⅴ-2.Convergence of formal solutions of a system of the first kind Ⅴ-3.The S-N decomposition of a matrix of infinite order Ⅴ-4.The S-N decomposition of a differential operator Ⅴ-5.A normal form of a differential operator Ⅴ-6.Calculation of the normal form of a differential operator Ⅴ-7.Classification of singularities of homogeneous linear systems Exercises Ⅴ Chapter Ⅵ.Boundary-Value Problems of Linear Differential Equations of the Second-Order Ⅵ-1.Zeros of solutions Ⅵ-2.Sturm-Liouville problems Ⅵ-3.Eigenvalue problems Ⅵ-4.Eigenfunction expansions Ⅵ-5.Jost solutions Ⅵ-6.Scattering data Ⅵ-7.Refiectionless potentials Ⅵ-8.Construction of a potential for given data Ⅵ-9.Differential equations satisfied by reflectionless potentials Ⅵ-10.Periodic potentials Exercises Ⅵ Chapter Ⅶ.Asymptotic Behavior of Solutions of Linear Systems Ⅶ-1.Liapounoff's type numbers Ⅶ-2.Liapounoff's type numbers of a homogeneous linear system Ⅶ-3.Calculation of Liapounoff's type numbers of solutions Ⅶ-4.A diagonalization theorem Ⅶ-5.Systems with asymptotically constant coefficients Ⅶ-6.An application of the Floquet theorem Exercises Ⅶ Chapter Ⅷ.Stability Ⅷ-1.Basic definitions Ⅷ-2.A sufficient condition for asymptotic stability Ⅷ-3.Stable manifolds Ⅷ-4.Analytic structure of stable manifolds Ⅷ-5.Two-dimensional linear systems with constant coefficients Ⅷ-6.Analytic systems in R2 Ⅷ-7.Perturbations of an improper node and a saddle point Ⅷ-8.Perturbations of a proper node Ⅷ-9.Perturbation of a spiral point Ⅷ-10.Perturbation of a center Exercises Ⅷ Chapter Ⅸ.Autonomous Systems Ⅸ-1.Limit-invariant sets Ⅸ-2.Liapounoff's direct method Ⅸ-3.Orbital stability Ⅸ-4.The Poincare-Bendixson theorem Ⅸ-5.Indices of Jordan curves Exercises Ⅸ Chapter Ⅹ.The Second-Order Differential Equation (d2x)/(dt2)+h(x)*(dx)/(dt)+g(x)=0 Ⅹ-1.Two-point boundary-value problems Ⅹ-2.Applications of the Liapounoff functions Ⅹ-3.Existence and uniqueness of periodic orbits Ⅹ-4.Multipliers of the periodic orbit of the van der Pol equation Ⅹ-5.The van der Pol equation for a small ε > 0 Ⅹ-6.The van der Pol equation for a large parameter Ⅹ-7.A theorem due to M.Nagumo Ⅹ-8.A singular perturbation problem Exercises Ⅹ Chapter Ⅺ.Asymptotic Expansions Ⅺ-1.Asymptotic expansions in the sense of Poincare Ⅺ-2.Gevrey asymptotics Ⅺ-3.Flat functions in the Gevrey asymptotics Ⅺ-4.Basic properties of Gevrey asymptotic expansions Ⅺ-5.Proof of Lemma Ⅺ-2-6 Exercises Ⅺ Chapter Ⅻ.Asymptotic Expansions in a Parameter Ⅻ-1.An existence theorem Ⅻ-2.Basic estimates Ⅻ-3.Proof of Theorem Ⅻ-1-2 Ⅻ-4.A block-diagonalization theorem Ⅻ-5.Gevrey asymptotic solutions in a parameter Ⅻ-6.Analytic simplification in a parameter Exercises Ⅻ Chapter ⅩⅢ.Singularities of the Second Kind ⅩⅢ-1.An existence theorem ⅩⅢ-2.Basic estimates ⅩⅢ-3.Proof of Theorem ⅩⅢ-1-2 ⅩⅢ-4.A block-diagonalization theorem ⅩⅢ-5.Cyclic vectors (A lemma of P.Deligne) ⅩⅢ-6.The Hukuhara-Turrittin theorem ⅩⅢ-7.An n-th-order linear differential equation at a singular point of the second kind ⅩⅢ-8.Gevrey property of asymptotic solutions at an irregular singular point Exercises ⅩⅢ References Index |