Numerical Methods for Chemical Engineering: Solving Initial Value Problems

Chemical engineering systems rely heavily on transient modeling, from tracking reactant concentrations in a batch reactor to predicting heat transfer over time. Understanding how to mathematically formulate and numerically solve these initial value problems (IVPs) is an essential skill for modern engineers. This text-only course guides you from fundamental mathematical definitions to writing clean, executable code to solve complex chemical systems. You will transition from theoretical differential equations to practical numerical simulation, learning how to select the right algorithms and analyze your results for physical validity. What you'll learn: - Understand the foundational theory of ordinary differential equations and initial value problems in chemical systems - Apply classic numerical methods such as Euler's and Runge-Kutta algorithms to solve transient models - Implement modern scientific Python libraries like SciPy to solve stiff and non-stiff systems of equations - Structure chemical engineering models using clean code, type hints, and structured virtual environments - Analyze error, stability, and convergence to ensure your simulations are accurate and reliable - Practice formulating mass and energy balances as solvable mathematical systems We begin with essential terminology and the core mathematical concepts of differential equations. From there, you will explore step-by-step algorithms, translate them into structured Python code, and tackle realistic chemical engineering scenarios through written exercises. This course is designed for chemical engineering students, practicing engineers, and science professionals new to numerical computing. No prior background in numerical analysis is required, though a basic understanding of algebra and introductory Python is helpful. Start modeling your chemical systems with confidence today.