Riemann Sums
Riemann sums are a mathematical method used in calculus to approximate the definite integral of a function, representing the area under a curve. They work by dividing the area into rectangles (or other shapes) and summing their areas, with the approximation improving as the number of subdivisions increases. This concept is fundamental for understanding integration and its applications in fields like physics, engineering, and economics.
Developers should learn Riemann sums when working on numerical analysis, scientific computing, or data science projects that involve approximating integrals, such as in simulations, optimization algorithms, or machine learning models. It's particularly useful for implementing numerical integration methods in code, like in Python with libraries such as NumPy or SciPy, to solve real-world problems where analytical solutions are impractical.