微分方程是一門表述自然法則的語言。理解微分方程解的性質，是許多當代科學和工程的基礎。常微分方程（ODE's）是關於單變數的函數，一般可以認為是時域變數。學習內容包括：利用解釋、圖形和數值方法求解一階常微分方程，線性常微分方程，尤指二階常係數方程，不定係數和參變數，正弦和指數信號：振動、阻尼和共振，複數和冪，傅立葉級數，週期解，Delta函數、卷積和拉普拉斯變換方法，矩陣和一階線性系統：特徵值和特徵向量，非線性獨立系統：臨界點分析和相平面圖。
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.
