Numerical Methods and Linear Algebra for Chemical Engineering

Chemical engineering systems—from reactor design to transport phenomena—rely heavily on mathematical models that require robust numerical solutions. Understanding the underlying linear algebra is essential for setting up and solving these complex engineering equations. This text-based course delivers a clear, step-by-step pathway to mastering vectors, basis sets, and numerical methods specifically tailored for chemical engineering applications. Through structured written explanations and practical engineering scenarios, you will transition from fundamental mathematical definitions to solving real-world simulation problems. You will learn how to represent physical systems mathematically and use structured approximation techniques to simplify complex calculations. What you'll learn: - Understand foundational vector spaces, basis sets, and linear independence in engineering contexts - Master the Gram-Schmidt orthogonalization process to construct orthogonal basis sets - Apply matrix transformations to model chemical processes and transport phenomena - Learn modern dimensionality reduction concepts and state-space representations for process control - Solve systems of linear equations representing mass and energy balances - Practice formulating numerical approximations for complex, multi-variable engineering systems This course begins with core terminology and vector definitions before guiding you through orthogonalization techniques and numerical implementations. It is designed for engineering students, researchers, and practicing chemical engineers who want to build a strong mathematical foundation for modern process modeling. No advanced linear algebra background is required to begin. Start building the mathematical foundation to power your engineering simulations today.