Numerical Methods for Chemical Engineering: Matrix Decompositions

Modeling chemical processes often leads to massive systems of linear equations that are computationally expensive to solve. Understanding how to efficiently decompose matrices is essential for simulating reactors, transport phenomena, and thermodynamic systems. This course guides you through the core mathematical principles of matrix decompositions, focusing on LU and Cholesky methods. You will gain the skills to analyze symmetric positive-definite matrices and apply structured numerical techniques to engineering problems. What you'll learn: Understand the fundamental role of linear algebra and matrix systems in chemical engineering models; Master LU decomposition and its application to solving systems of linear equations; Explore the properties of symmetric positive-definite matrices in physical systems; Apply Cholesky decomposition to optimize computational efficiency in process simulations; Analyze the theoretical and practical advantages of Cholesky factorization over standard LU methods; Implement these numerical algorithms using modern scientific computing concepts and structured workflows. We begin with foundational mathematical definitions before moving step-by-step through decomposition algorithms. You will then explore how these numerical methods are applied directly to steady-state chemical engineering problems. This course is designed for engineering students, researchers, and beginning professionals who want to strengthen their numerical computing foundations without needing advanced prior knowledge of matrix algorithms. Start reading today to optimize your engineering calculations and master matrix decompositions.