Chapter 22 - Ordinary Differential Equations (ODEs) Initial-Value Problems

Abstract

Differential equations are relationships between a function and its derivatives. They are used to model systems in numerous engineering and science fields. For example, a simple differential equation relates the acceleration of a car with its position. Unlike differentiation where analytic solutions can usually be computed, in general, finding exact solutions to differential equations is difficult. Therefore, numerical solutions are critical to making these equations useful for designing and understanding engineering and science systems. Because differential equations are so common in engineering, physics, and mathematics, the study of them is a vast and rich field that cannot be covered in this introductory text. This chapter covers ordinary differential equations with specified initial values, which is a subclass of differential equations problems called initial value problems. To reflect the importance of this class of problem, Python has a whole suite of functions to solve such equations. By the end of this chapter, you should understand what ordinary differential equation initial value problems are, how to pose these problems to Python, and how these Python solvers work.