Classic numerical methods

This chapter discusses some classic numerical methods. These topics can essentially be found in most introductory computational or numerical methods books. The purpose of this discussion is to build the foundation for subsequent chapters while introducing some solutions to physical problems, as well as some simple Python code, use of libraries, and plotting. The topics covered in this chapter include the calculation of series; the solution of nonlinear algebraic equations or root finding; optimization or finding the minimum of a function; interpolation of data; function approximation; matrices and eigensystems; integration of algebraic functions or data; and finite differences. Lastly, the process of converting symbolic mathematical expressions into numerical functions that can be evaluated with specific values is discussed. The solution of differential equations is covered in detail in the subsequent chapter.