Numerical Methods for Chemical Engineering: Solving Nonlinear Equations

Chemical processes are inherently complex, often governed by systems of nonlinear equations that cannot be solved with simple algebra. To design reactors, calculate phase equilibria, or model transport phenomena, you need robust numerical techniques. This text-based course guides you through the fundamental mathematical concepts and algorithms required to solve these complex engineering problems. You will start by understanding foundational terminology, error analysis, and convergence criteria before moving into practical numerical applications. By the end of this course, you will be able to confidently set up and solve multi-variable nonlinear models simulating real-world chemical processes. What you will learn: Understand the core mathematical principles of single-variable and multi-variable nonlinear systems; Apply the Newton-Raphson method and its variations to chemical engineering problems; Formulate systems of equations for multi-component flash calculations and reactor design; Implement iterative solver algorithms with robust convergence criteria; Analyze numerical stability and diagnose common solver errors. We begin with essential mathematical definitions and basic iterative concepts, then progress to multi-variable systems and practical chemical engineering case studies. This course is designed for engineering students, researchers, and practicing professionals looking for a clear, step-by-step guide to numerical solvers without requiring advanced programming prerequisites. Start mastering numerical methods for chemical engineering today.