阿諾德常微分方程講義 (英文) 弗拉基米爾.阿諾德 9787519296674 【台灣高等教育出版社】
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物品所在地：中國大陸
原出版社：世界圖書出版公司
物品所在地：中國大陸
原出版社：世界圖書出版公司
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| *完成訂單後正常情形下約兩周可抵台。 *本賣場提供之資訊僅供參考，以到貨標的為正確資訊。 印行年月：202403*若逾兩年請先於私訊洽詢存貨情況，謝謝。 台灣(台北市)在地出版社，每筆交易均開具統一發票，祝您中獎最高1000萬元。 書名：阿諾德常微分方程講義 (英文) ISBN：9787519296674 出版社：世界圖書出版公司 著編譯者：弗拉基米爾.阿諾德 叢書名：俄羅斯數學經典 頁數：334 所在地：中國大陸 *此為代購商品 書號：1632710 可大量預訂，請先連絡。 內容簡介 本書中強調常微分方程的定性性質和幾何性質及其它們的解，全書有272個幾何插圖，卻沒有一個複雜的數學公式。全書分為5章36節。本書是阿諾德的名著，他的許多優秀作品都被翻譯為英文，本書是其中的一本，其簡明的寫作風格、嚴謹的數學基礎結合物理直覺，給人一種很輕鬆漫談式的教學特點，被譽為最優秀的常微分教材。目錄 Chapter 1 Basic Concepts§1 Phase Spaces 1 Examples of Evolutionary Processes 2 Phase Spaces 3 The Integral Curves of a Direction Field 4 A Differential Equation and its Solutions 5 The Evolutionary Equation with a One-dimensional Phase Space 6 Example: The Equation of Normal Reproduction 7 Example: The Explosion Equation 8 Example: The Logistic Curve 9 Example: Harvest Quotas 10 Example: Harvesting with a Relative Quota， 11 Equations with a Multidimensional Phase Space 12 Example: The Differential Equation of a Predator-Prey System 13 Example: A Free Particle on a Line 14 Example: Free Fall 15 Example: Small Oscillations 16 Example: The Mathematical Pendulum 17 Example: The Inverted Pendulum 18 Example: Small Oscillations of a Spherical Pendulum §2 Vector Fields on the Line 1 Existence and Uniqueness of Solutions 2 A Counterexample : 3 Proof of Uniqueness 4 Direct Products 5 Examples of Direct Products 6 Equations with Separable Variables 7 An Example: The Lotka-Volterra Model §3 Linear Equations 1 Homogeneous Linear Equations 2 First-order Homogeneous Linear Equations with Periodic Coefficients 3 Inhomogeneous Linear Equations 4 The Influence Function and b-shaped Inhomogeneities 5 Inhomogeneous Linear Equations with Periodic Coefficients §4 Phase Flows 1 The Action of a Group on a Set 2 One-parameter Transformation Groups 3 One-parameter Diffeomorphism Groups 4 The Phase Velocity Vector Field §5 The Action of Diffeomorphlsms on Vector Fields and Direction Fields 1 The Action of Smooth Mappings on Vectors 2 The Action of Diffeomorphisms on Vector Fields 3 Change of Variables in an Equation 4 The Action of a Diffeomorphism on a Direction Field 5 The Action of a Diffeomorphism on a Phase Flow §6 Symmetries 1 Symmetry Groups 2 Application of a One-parameter Symmetry Group to Integrate an Equation 3 Homogeneous Equations 4 Quasi-homogeneous Equations 5 Similarity and Dimensional Considerations 6 Methods of Integrating Differential Equations Chapter 2 Basic Theorems §7 Rectification Theorems 1 Rectification of a Direction Field 2 Existence and Uniqueness Theorems 3 Theorems on Continuous and Differentiable Dependence of the Solutions on the Initial Condition 4 Transformation over the Time Interval from to to t 5 Theorems on Continuous and Differentiable Dependence on a Parameter 6 Extension Theorems 7 Rectification of a Vector Field §8 Applications to Equations of Higher Order than First 1 The Equivalence of an Equation of Order n and a System of n First-order Equations 2 Existence and Uniqueness Theorems 3 Differentiability and Extension Theorems Chapter 3 Linear Systems Chapter 4 Proofs of the Main Theorems Chapter 5 Differential Equations on Manifolds Examination Topics Sample Examination Problems Subject Index 詳細資料或其他書籍請至台灣高等教育出版社查詢，查後請於PChome商店街私訊告知ISBN或書號，我們即儘速上架。 |
