Numerical Methods for Chemical Engineering with 1D Finite Difference

Solving transport and reaction equations is at the heart of chemical engineering, but analytical solutions are rarely possible for complex systems. This text-only course guides you through the fundamental mathematical concepts and numerical methods required to set up, discretize, and solve engineering equations on a computer. You will start with foundational definitions of discretization, grid generation, and numerical error before diving into practical implementation. By working through clear explanations and structured exercises, you will transform mathematical descriptions of physical systems into structured, solvable algebraic equations. You will gain a solid understanding of how to discretize spatial domains and build computational grids that form the backbone of modern chemical engineering simulations. What you'll learn: - Understand the core principles of finite difference discretization for spatial domains - Configure uniform grid point locations across a defined reactor length - Set up boundary conditions and initial values for one-dimensional chemical engineering models - Translate physical transport equations into solvable systems of algebraic equations - Apply modern Python patterns including type hints and clean array operations to write readable numerical code - Analyze discretization errors and understand the impact of grid resolution on simulation accuracy The course begins with foundational concepts of numerical approximation and grid spacing, gradually moving into setting up the mathematical matrices for transport-reaction equations. You will practice translating these mathematical frameworks into clean, step-by-step algorithms. This course is designed for beginners in computational engineering, chemistry students, and chemical engineers looking to build a strong foundation in numerical methods from scratch. No advanced programming or numerical analysis experience is required; basic math and familiarity with coding concepts are all you need to begin. Start building your engineering simulation skills today by mastering the fundamentals of finite difference discretization.