Solving 2D Nonlinear Equations in Chemical Engineering

Solving coupled nonlinear equations is at the heart of chemical engineering, from sizing complex chemical reactors to calculating vapor-liquid equilibrium. This text-only course guides you through the fundamental theory and practical implementation of the two-dimensional Newton-Raphson method, translating physical chemical systems into robust numerical models. What you'll learn: - Understand the mathematical foundations of the 2D Newton-Raphson method and Jacobian matrices. - Formulate multi-variable nonlinear equations for chemical reactors and mass transfer systems. - Implement the numerical solver step-by-step using clean, vectorized MATLAB or Octave code. - Handle convergence issues, initial guess selection, and physical boundary constraints like non-negative concentrations. - Analyze solver performance and debug common numerical errors in algebraic systems. You will start with key terminology and basic mathematical concepts before moving on to constructing Jacobian matrices and writing structured, iterative solver scripts for real-world chemical processes. This text-based guide ensures you understand every line of code and the physical principles behind it. This course is designed for engineering students and practicing chemical engineers who want to build their own custom numerical solvers from scratch. A basic understanding of algebra and introductory programming concepts is recommended. Begin mastering numerical methods for chemical engineering today.