Numerical Methods in Chemical Engineering: Solving Linear Systems

Chemical engineering processes rely on complex mathematical models, but solving these systems by hand is often impossible. Understanding how to represent physical systems as linear transformations is the key to unlocking computational solutions. This text-based course guides you from the absolute basics of linear algebra to applying numerical methods for solving systems of equations in chemical engineering contexts. You will learn to translate physical conservation laws into solvable mathematical models. What you'll learn: - Understand the fundamentals of linear algebra, including vectors, matrices, and interpreting the equation Ax = b as a linear transformation. - Formulate chemical process models, such as mass and energy balances, into systems of linear equations. - Apply numerical methods like Gaussian elimination, LU decomposition, and iterative solvers to find engineering solutions. - Explore vectorization and modern computational formulations to set up your equations for efficient digital solving. - Analyze the stability, convergence, and error bounds of numerical solutions to ensure physical accuracy. The course starts with essential mathematical definitions and the physical meaning of linear transformations. You will then progress through step-by-step written explanations of numerical algorithms, culminating in practical engineering applications such as reactor design and distillation column modeling. This course is designed for chemistry, biochemistry, and chemical engineering students or professionals who want a clear, beginner-friendly introduction to numerical methods. No prior advanced programming or high-level engineering experience is required. Start mastering the mathematical foundations of chemical process modeling today.