The book begins with numerical linear algebra, which is essential for solving large systems of equations, and continues with nonlinear equations, a cornerstone for modeling equilibrium and reaction kinetics. Ordinary differential equations are then addressed, covering both initial value and boundary value problems, with an emphasis on their role in describing dynamic behavior and transport phenomena. The section concludes with partial differential equations, which are fundamental for capturing spatial and temporal variations in heat, mass, and momentum transfer.

The second part of the book presents a curated set of solved problems, each supported by Python code and figures. Covering topics such as parameter estimation, confidence intervals, and bioreactor optimization, the problems emphasize both steady-state and dynamic systems. Each example covers the deriving governing equations, related code, and interpreting results, providing a consistent learning path, while additional discussions encourage students to explore related concepts beyond the presented problem.