This workshop introduces the fundamental concepts of numerical analysis, tailored to establish the essential theoretical groundwork required for quantum algorithmic design. The lectures will discuss various classes of differential equations and examine the canonical numerical methods traditionally used for their integration. By surveying these classical methods, the workshop aims to build a common mathematical vocabulary among researchers from diverse disciplinary backgrounds. A central focus will be the fundamental analytical properties of numerical schemes, specifically delving into treatments of convergence, stability, and consistency. By reviewing the computational bottlenecks of classical integration, this workshop motivates the transition toward quantum algorithms.

Target Audience: This workshop is designed for a multidisciplinary cohort coming from diverse scientific backgrounds. No prior familiarity with numerical methods or classical numerical analysis is assumed. The primary objective is to provide an accessible entry point for non-experts, ensuring all participants possess the prerequisite theoretical intuition necessary to engage with the quantum algorithms presented in the second workshop.