1. Definition of terms and review of linear algebra -- 1.1 Basic definitions -- 1.1.1 What is a differential equation? -- 1.1.2 Solution to a differential equation -- 1.1.3 Family of solutions -- 1.1.4 Direction fields -- 1.2 Some linear algebra -- 1.2.1 Matrices -- 1.2.2 Systems of linear equations -- 1.2.3 Matrix addition and subtraction and scalar product -- 1.2.4 Transpose of a matrix -- 1.2.5 Dot product and matrix multiplication -- 1.2.6 Determinants -- 1.2.7 The inverse of a square matrix -- 1.2.8 Matrix form of a system of linear equations -- 1.2.9 Linear dependence -- 1.2.10 Eigenvalues and Eigenvectors -- 1.2.11 Diagonalization --

2. Linear first order differential equations -- 2.1 Linear first order DE -- 2.1.1 Bernoulli differential equation -- 2.2 Separable differential equations -- 2.3 Exact differential equations -- 2.4 Homogeneous differential equations -- 2.5 Existence and uniqueness --

3. Homogeneous second order differential equations -- 3.1 Linear homogeneous DE -- 3.2 Linear independence and the Wronskian -- 3.2.1 Linear independence -- 3.2.2 The Wronskian -- 3.3 Solving ay" + by' + cy = g(x) -- 3.3.1 The method of undetermined coefficients -- 3.3.2 Variation of parameters --

Bibliography -- Index.