Numerical Methods for Chemical Engineering: Solving Non-Linear Equations

Chemical engineering processes often involve complex, non-linear relationships—from vapor-liquid equilibrium to chemical reaction kinetics—that cannot be solved with simple algebra. This text-only course guides you through the fundamental numerical methods used to solve these non-linear algebraic equations, focusing on the powerful 1D Newton-Raphson method and its practical applications. What you'll learn: - Understand the core mathematical principles behind non-linear algebraic equations in chemical processes. - Master the 1D Newton-Raphson method, including its derivation, convergence criteria, and potential pitfalls. - Implement numerical routines using modern Python, utilizing clean code structure and type hints. - Apply root-finding algorithms to real-world engineering scenarios like equation of state calculations. - Analyze convergence behavior and troubleshoot common failure modes of iterative numerical solvers. You will start with foundational definitions and key terminology before moving step-by-step from mathematical concepts to writing robust, automated numerical solvers. Designed for engineering students, researchers, and practicing professionals new to numerical computing, this course requires no advanced programming background. Start mastering the numerical tools essential for modern chemical engineering analysis today.