What is Numerical Analysis?

Numerical Analysis · Axiom Academy

INTRO What is Numerical Analysis? The art and science of computing approximate answers to mathematical problems Try to find the exact area under this curve. Move the slider to explore the function. Compare exact mathematical answers with their computer representations. Click on each card to learn about different types of errors in numerical computing. Simplifications in our mathematical model of reality Inaccuracies in measured input values Errors introduced during calculation ❓ The Three Fundamental Questions Click each card to reveal the key questions that drive numerical analysis. Numerical Analysis is the study of algorithms that use numerical approximation to solve mathematical problems, with careful attention to errors and efficiency. Finding roots of equations (Newton's method, bisection) Interpolation and approximation of functions Numerical integration and differentiation Solving systems of linear equations Solving differential equations numerically Weather forecasting, rocket trajectories, financial modeling, medical imaging, AI training — all rely on numerical methods. Without them, modern science and engineering would be impossible.

This is the written version of the interactive lesson above. See the full Numerical Analysis course.