本书是苏联/俄罗斯数学家阿诺德为本科生写的讲义，内容简明扼要，读者只需掌握线性代数、基础分析和常微分方程知识。主要包括以下内容：单一阶方程的一般理论；波传播理论中的Huygens原理；弦振动；傅里叶方法；振荡理论和振动原理；调和函数特性；拉普拉斯基本解及位势；双层位势；球函数、麦克斯韦定理和可去奇点定理；用拉普拉斯方程解边界值问题；线性方程和线性系统理论。

Preface to the Second Russian Edition
1.The General Theory for One First-Order Equation Literature.
2.The General Theory for One First-Order Equation (Continued)
Literature
3.Huygens'Principle in the Theory of Wave Propagation
4.1The Vibrating String (d'Alembert's Method)
4.1.The General Solution
4.2.Boundary-Value Problems and the Cauchy Problem
4.3.The Cauchy Problem for an Infinite String.d'Alembert's Formula
4.4.The Semi-Infinite String
4.5.The Finite String.Resonance
4.6.The Fourier Method
5.The Fourier Method (for the Vibrating String)
5.1.Solution of the Problem in the Space of Trigonometric Polynomials
5.2.A Digression
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