The book begins with a discussion of definitions, terminology, and basic analytic procedures and then introduces solution curve families and Picard's theorem. Later chapters cover everything from algorithms used to solve first-order equations and higher-order linear equations to Kepler's laws of motion and linear differential equations with power series solutions.

Many differential equations are solved with a variety of example solutions. Rather than expecting students to master specialized software, the book offers optional tutorials and templates for solving differential equations using the Voyage 200 and TI-92 Plus calculators.

In addition to providing a wide-ranging overview of the fundamentals of ordinary differential equations, the book explores several more esoteric subjects:

• the calculus of variations
• the Riccati equation
• elliptic integrals and elliptic functions
• linear differential equations not in standard form
• Hamilton's principle
• cubic and hyperbolic spline interpolation

With its thorough coverage of both standard and intermediate level topics in ordinary differential equations, the book can be used to individualize instruction depending on students' interests and goals.