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This text is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation.

• ## 2: First Order Equations

In this chapter, we study first-order differential equations for which there are general methods of solution.
• ## 3: Numerical Methods

In this chapter we study numerical methods for solving a first-order differential equation
• ## 4: Applications of First Order Equations

In this chapter, we consider applications of first order differential equations.
• ## 5: Linear Second Order Equations

In this Chapter, we study a particularly important class of second order equations. Because of their many applications in science and engineering, second order differential equation have historically been the most thoroughly studied class of differential equations. Research on the theory of second order differential equations continues to the present day.
• ## 6: Applications of Linear Second Order Equations

In this Chapter, we study applications of linear second order equations.
• ## 7: Series Solutions of Linear Second Order Equations

In this Chapter, we study a class of second order differential equations that occur in many applications, but cannot be solved in closed form in terms of elementary functions.