Numerical Methods in Chemical Engineering: LU Decomposition and Matrix Algebra

Chemical engineering systems—from multi-stage distillation columns to complex reactor networks—rely heavily on solving large systems of linear equations. Understanding the underlying mathematics and computational algorithms is essential for designing, simulating, and optimizing these processes. This text-based course guides you from the fundamental principles of matrix algebra to the practical implementation of robust numerical solvers. You will transition from manual calculation concepts to writing clean, efficient numerical scripts, giving you the tools to tackle real-world engineering simulations with confidence. What you'll learn: Understand the core terminology and mathematical foundations of linear systems in chemical engineering; Master Gaussian elimination algorithms both with and without partial pivoting; Implement LU decomposition to solve repetitive process design calculations efficiently; Practice translating mathematical models into structured Python code using modern NumPy conventions; Analyze numerical stability, rounding errors, and pivoting strategies in engineering computations; Apply matrix solvers to practical engineering scenarios, including mass balances and piping networks. Our structured written modules begin with foundational definitions, ensuring you grasp the mathematics before moving into algorithmic steps. You will work through detailed, written step-by-step derivations and complete practical coding exercises designed to reinforce your learning. This course is ideal for undergraduate chemical engineering students, process engineers, and researchers looking to build a solid computational foundation. No advanced programming background is required. Start reading today to master the computational tools of modern chemical engineering.