Numerical Methods in Chemical Engineering: Solving Linear Equations

Chemical engineering processes often involve complex networks of reactors, separators, and heat exchangers that are difficult to analyze by hand. To design and optimize these systems, you must be able to translate physical processes into mathematical models and solve them efficiently. This course guides you through the core numerical methods used to solve linear algebraic equations in chemical engineering. You will learn how to represent physical systems as matrix equations (Ax=b) and resolve them using systematic mathematical techniques and modern computational workflows. What you'll learn: - Understand the fundamental principles of linear algebra as applied to chemical processes. - Apply Gaussian elimination to reduce systems of equations to upper triangular form. - Formulate mass and energy balances for multi-unit chemical systems into solvable matrix equations. - Use modern computational tools and Python libraries to solve high-dimensional linear systems. - Analyze matrix conditioning and identify potential numerical errors in process simulations. You will start by mastering foundational mathematical definitions and the core mechanics of matrix operations. From there, you will progress to step-by-step algorithmic solutions and practical chemical engineering case studies, all explained through clear, written text and structured exercises. This course is designed for engineering students and professionals seeking a solid, accessible introduction to numerical methods. No prior experience with advanced matrix theory or scientific programming is required. Start mastering the mathematical foundations of chemical engineering today.