Phase Plots and Numerical Methods for Chemical Engineering

Chemical engineering processes, from catalytic reactors to biological systems, are governed by complex dynamical equations. To design and control these systems, you must be able to predict their behavior over time and analyze their stability. This course offers a clear, text-based path to mastering initial value problems and phase space analysis. You will learn how to translate physical chemical processes into mathematical models, solve them numerically, and construct phase plots that visually reveal system stability and equilibrium points. What you will learn: Understand the foundational concepts of ordinary differential equations and initial value problems in chemical engineering; Set up and solve coupled differential equations using numerical solvers like MATLAB's ode45; Generate and interpret phase plots to track state trajectories and identify steady-state behaviors; Analyze the stability of equilibrium points, including nodes, saddles, and focal points in reactor dynamics; Apply modern numerical techniques to handle stiff systems common in chemical reaction kinetics. The course begins with core definitions and the mathematical foundations of dynamical systems. You will then progress through structured, written explanations and code examples that show you how to build and analyze phase portraits for classic chemical engineering systems, such as the continuously stirred-tank reactor. This course is designed for engineering students and professionals who want a practical introduction to numerical modeling. No advanced programming background or complex mathematical prerequisites are required. Begin your journey into process dynamics and system analysis today.