# Basic Mathematical Tools and Techniques

## Abstract

This chapter contains basic concepts and theories for differential equations, focusing on different approaches and methodologies for stability analysis. They provide the mathematical tools needed for model analysis described in earlier chapters. The ideal way to learn the materials in this chapter is through their applications in Chapter 2. For students who are interested in more in-depth reading on the theories of ordinary differential equations and finding more examples, exercises, as well as proofs, classical textbooks of Coddington and Levinson (Theory of ordinary differential equations. McGraw-Hill Education, New York, 1985) [11], Hale (Ordinary differential equations. Dover Publications, New York, 2009) [24], Hartman (Ordinary differential equations, 2002) [25], and Piccinini, Stampacchia and Vidossich (Ordinary differential equations in \(\mathbb {R}^n\). Springer, New York, 1984) [51] are excellent sources.