Numerical Methods for Chemical Engineering with Differential Algebraic Equations

Chemical engineering processes frequently rely on complex systems of differential algebraic equations (DAEs) and partial differential equations (PDEs) to model transport phenomena, reaction kinetics, and fluid dynamics. To design and optimize these systems, you need a robust mathematical foundation and the ability to implement modern numerical solvers. This course provides a clear, step-by-step pathway from physical principles to stable numerical solutions using contemporary computing tools. You will transition from manually setting up balance equations to writing clean, structured code that solves multidimensional systems. By learning how to discretize spatial derivatives and handle algebraic constraints, you will gain the confidence to model real-world chemical reactors, separation columns, and heat transfer equipment. What you'll learn: - Understand the foundational theory of differential algebraic equations (DAEs) and how they differ from standard ordinary differential equations. - Apply spatial discretization techniques to convert partial differential equations into solvable systems of algebraic and differential equations. - Implement modern numerical solver algorithms to resolve stiff systems and algebraic constraints efficiently. - Formulate mass, energy, and momentum balances into structured mathematical models. - Practice debugging numerical instability and convergence errors using modern programming best practices. This course begins with essential mathematical definitions and classification of equations before moving into discretization techniques, boundary conditions, and solver execution. You will work through structured written explanations and step-by-step code implementations that simulate realistic chemical engineering scenarios. This course is designed for chemical engineering students, researchers, and practicing engineers who want to build a solid foundation in numerical modeling without needing advanced prior experience in numerical analysis. Start mastering chemical engineering simulation today.