This chapter says what a differential equation is and what it means for a function to be a solution. Vector fields are introduced and their relationship to solutions demonstrated.
Some linear algebra is introduced.
Linear differential equations are obtained from a family of solutions. Numerical methods are introduced, uniqueness of solutions is discussed, and differential inclusions are an optional section. The ideas of what a differential equation is, what its order is and whether it is ordinary or partial are introduced. After the meaning of solution is discussed, solutions are depicted on a direction field. The section ends with a statement of the fundamental existence and uniqueness theorem for first-order differential equations.