常微分方程(英文版)
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作者编者:孙书荣//韩振来//张超
出版社山东大学
ISBN9787560762555
出版时间2018-11
装帧其他
开本其他
定价42元
货号30485466
上书时间2024-10-12
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目录
Chapter 1 Introduction
1.1 Differential Equations and Mathematical Models
1.2 Basic Concept
1.3 Direction Fields
Chapter 2 First-Order Differential Equations
2.1 Introduction: Motion of a Falling Body
2.2 Separable Equations
2.3 Linear Equations
2.4 Exact Equations
2.5 Special Integrating Factors
2.6 Substitutions and Transformations
Chapter 3 Existence and Uniqueness Theory
3.1 Picard's Existence and Uniqueness Theorem
3.2 Existence of Solutions of Linear Equation
3.3 Estimates of Error and Approximate Calculation
3.4 Continuation of Solutions
3.5 Continuous Dependence of Solutions
Chapter 4 Theory of Higher-Order Linear Differential Equations
4.1 Basic Theory of Linear Differential Equations
4.2 Homogeneous Linear Equations with Constant Coefficients
4.3 Undetermined Coefficients and the Annihilator Method
4.4 Method of Variation of Parameters
4.5 Cauchy-Euler Equation
4.6 Solution by Power Series
4.7 Laplace Transforms
Chapter 5 Systems of Differential Equations
5.1 Introduction
5.2 Existence and Uniqueness Theorem for Linear Systems
5.3 Properties of Solutions of First-Order Linear Systems
5.4 Homogeneous Linear Systems with Constant Coefficients
5.5 Complex Eigenvalues
5.6 The Matrix Exponential Function
5.7 Nonhomogeneous Linear Systems
Chapter 6 Stability
6.1 Introduction
6.2 Linear Systems in the Plane
6.3 Almost Linear Systems
6.4 Lyapunov's Direct Method
Chapter 7 Fractional Differential Equations
7.1 Riemann-Liouville Integrals
7.2 Riemann-Liouville Derivatives
7.3 Relations between Riemann-Liouville Integrals and Derivatives
7.4 Caputo's Derivative
7.5 Existence and Uniqueness Results for Riemann-Liouville Fractional Differential Equations
7.6 Existence and Uniqueness Results for Caputo Fractional Differential Equations
Chapter 8 Dynamic Equations on Time Scales
8.1 Basic Definitions
8.2 Differentiation
8.3 Integration
References
内容摘要
本书主要介绍了常微分方程的相关知识，内容包括一阶线性微分方程、存在性和唯一性定理、高阶微分方程定理、微分方程组、稳定性等。为了便于学生
更好地掌握，书中列举了大量的典型例题，且大部分章节后面配有对应的习题，学生可以更好地检验自己对相关知识的掌握程度。
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