Numerical Methods for Chemical Engineering: Differential-Algebraic Equations

Chemical engineering systems often involve complex physical processes where dynamic changes happen alongside instant physical constraints. To model these systems accurately, engineers rely on Differential-Algebraic Equations (DAEs), which can be challenging to solve without the right mathematical tools. This text-based course guides you through the fundamental principles of setting up, analyzing, and solving these systems numerically. You will transition from basic calculus and algebraic concepts to confidently structuring and simulating chemical engineering models. By studying detailed mathematical breakdowns and practical code implementations, you will learn how to handle index problems, ensure consistent initial conditions, and avoid common simulation errors. What you'll learn: - Understand the fundamental differences between ordinary differential equations and differential-algebraic equations - Determine the index of a DAE system and apply index reduction techniques - Establish consistent initial conditions for stable numerical simulation - Apply modern numerical solvers to simulate chemical reactors and separation columns - Structure process models using clean, readable Python code to run simulations reliably - Troubleshoot convergence errors and solver instability in chemical process models This course begins with essential definitions and core mathematical concepts, ensuring you build a solid theoretical foundation. You will then progress through structured written examples that demonstrate how to translate chemical transport and thermodynamic equations into solvable numerical models. This course is designed for undergraduate students, junior engineers, and self-directed learners in chemical engineering or computational science who want to learn how to solve algebraic and dynamic equations. No prior background in advanced numerical analysis is required. Start reading today to build and solve robust dynamic models for chemical engineering applications.