微分方程是一门表述自然法则的语言。理解微分方程解的性质，是许多当代科学和工程的基础。常微分方程（ODE's）是关于单变量的函数，一般可以认为是时域变量。学习内容包括：利用解释、图形和数值方法求解一阶常微分方程，线性常微分方程，尤指二阶常系数方程，不定系数和参变数，正弦和指数信号：振动、阻尼和共振，复数和幂，傅立叶级数，周期解，Delta函数、卷积和拉普拉斯变换方法，矩阵和一阶线性系统：特征值和特征向量，非线性独立系统：临界点分析和相平面图。
Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues and eigenvectors; and Non-linear autonomous systems: critical point analysis and phase plane diagrams.
