Numerical Methods and Matrix Decompositions for Chemical Engineers

Chemical engineering problems—from reactor design to transport phenomena—often boil down to solving complex systems of linear equations. To model these systems accurately, engineers must master the mathematical foundations of numerical linear algebra. This course equips you with the essential matrix computation techniques needed to analyze, model, and solve engineering problems computationally. You will transition from manual algebraic setups to understanding how modern computational algorithms handle large-scale engineering systems. What you'll learn: Understand the core terminology of linear systems, matrix properties, and eigenvalues; Apply LU, QR, and Cholesky decompositions to solve linear systems efficiently; Analyze complex engineering datasets using Singular Value Decomposition (SVD); Manage large-scale process simulation models using modern sparse matrix techniques; Practice translating physical engineering problems into solvable matrix equations; Explore how modern computational libraries implement these numerical methods for optimal performance. This course begins with foundational definitions of matrices, vectors, and basic operations before moving into advanced decomposition techniques and sparse systems. You will read clear explanations and study structured examples that connect mathematical theory directly to chemical engineering applications. This course is designed for beginner chemical engineering students, process engineers, and researchers looking to build a strong foundation in numerical methods without needing prior advanced computational experience. Start mastering the numerical tools that power modern chemical engineering simulations today.