Numerical Methods for Physics and Engineering

When analytical math cannot solve complex physical equations, numerical methods step in to simulate reality. This text-based course guides you through the foundational algorithms used to model physical systems, fluid dynamics, and particle behavior. You will transition from understanding raw mathematical formulas to writing clean, efficient code that approximates physical phenomena. By studying core computational principles, you will gain the confidence to simulate real-world systems and analyze the stability of your models. What you'll learn: - Understand the foundational terminology of numerical approximation and discretization. - Apply finite difference methods to solve ordinary and partial differential equations. - Implement iterative matrix inversion techniques for large systems of linear equations. - Analyze numerical stability, convergence behavior, and error propagation. - Explore particle-based modeling techniques, including Monte-Carlo simulations. - Utilize modern scientific computing practices using Python and vectorized libraries. The course begins with foundational concepts of discretization and error analysis before progressing to differential equations, matrix solvers, and particle simulations. You will read clear explanations, analyze code snippets, and work through conceptual exercises to solidify your understanding. This course is designed for students, engineers, and self-taught programmers new to scientific computing. No advanced background in computational physics is required, as we build up from basic calculus and linear algebra concepts. Start coding your own physical simulations today.