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.