Numerical Methods for Chemical Engineering: Solving DAEs and ODEs

Chemical engineering systems often involve complex physical processes where ordinary differential equations (ODEs) and algebraic boundary conditions must be solved simultaneously. Understanding how to classify, set up, and numerically solve these differential-algebraic equations (DAEs) is critical for modern process simulation and design. By completing this text-only course, you will learn how to translate physical boundary conditions into structured mathematical models and solve them systematically. What you'll learn: 1. Understand the core differences between ODEs and algebraic equations in chemical systems. 2. Classify boundary conditions and define active interior domains using mathematical masking. 3. Formulate differential-algebraic equation (DAE) systems representing chemical processes. 4. Apply modern numerical solvers to handle stiff equations and algebraic constraints. 5. Translate physical process constraints into structured numerical vectors. 6. Analyze chemical engineering models using modern scientific computing principles. This course begins with the foundational mathematics of chemical engineering systems and the basic terminology of DAEs, followed by step-by-step written derivations and code-based implementations. This course is designed for chemistry, biochemistry, and chemical engineering students, as well as practicing engineers looking for a clear, text-based introduction to numerical methods. No advanced prior numerical analysis experience is required. Start mastering the numerical methods that power modern chemical engineering simulations today.