Numerical Methods for Chemical Engineering: Linear and Nonlinear Systems

Chemical engineering relies heavily on mathematical models to design reactors, simulate transport phenomena, and optimize industrial processes. To build these models successfully, you must first master the numerical techniques that solve complex systems of equations. This text-based course bridges the gap between theoretical mathematics and practical engineering applications, starting with foundational concepts before moving to hands-on computational workflows. You will learn how to formulate, analyze, and solve the mathematical equations that describe chemical processes. Through clear explanations and structured written exercises, you will gain the confidence to apply numerical algorithms to real-world engineering problems. What you'll learn: - Understand the core mathematical principles of linear systems and matrix operations in engineering contexts - Solve systems of nonlinear equations using iterative methods like Newton-Raphson - Apply modern numerical libraries and structured arrays to automate complex calculations - Analyze chemical process models, such as mass balances and equilibrium stages, using systematic numerical approaches - Evaluate error propagation and convergence behavior to ensure computational accuracy The course begins with fundamental definitions and essential linear algebra concepts. You will then progress step-by-step through solving single nonlinear equations, scaling up to multi-variable systems, and implementing modern computational best practices for chemical engineering simulations. This course is designed for undergraduate chemical engineering students, practicing engineers looking to refresh their mathematical skills, and beginners interested in process modeling. No advanced mathematical background is required to start. Begin your journey toward mastering chemical engineering computations today.