Numerical Methods for Chemical Engineering: Solving Differential-Algebraic Equations

Chemical engineering systems rely on complex mathematical models that combine dynamic rate equations with physical algebraic constraints. Understanding how to formulate and solve these differential-algebraic equations (DAEs) is essential for designing, simulating, and optimizing chemical reactors and separation processes. This course provides a clear, step-by-step path to mastering these computational techniques through written explanations and practical code examples. You will transition from basic mathematical definitions to writing robust numerical solvers for real-world engineering problems. Along the way, you will explore modern best practices, including structured code organization, vectorization for performance, and the use of modern package management to keep your engineering tools up to date. What you'll learn: - Understand the fundamental differences between ordinary differential equations and differential-algebraic equations - Classify DAE systems by their index and apply index-reduction techniques to make them solvable - Implement robust numerical integration algorithms, including implicit methods for stiff systems - Model real-world chemical processes such as multi-component distillation columns and non-isothermal reactors - Write clean, structured, and modern code to solve complex engineering equations efficiently - Troubleshoot solver convergence issues and analyze the stability of your numerical solutions The course begins with foundational concepts, defining key mathematical terms and the physical origin of algebraic constraints in chemical systems. You will then progress through numerical algorithms, hands-on modeling scenarios, and code-based implementation strategies. This course is designed for engineering students, researchers, and practicing chemical engineers who want to build a solid foundation in numerical simulation. No advanced programming background is required, though basic familiarity with algebra and calculus is helpful. Start learning today and unlock the power of computational modeling in chemical engineering.