Introduction to Numerical Analysis and Scientific Computing

How do scientists and engineers solve complex mathematical equations that are impossible to calculate by hand? Numerical analysis provides the core computational algorithms to find precise, efficient approximations for real-world problems. This written course guides you from absolute beginner to confidently understanding and applying numerical methods. You will gain a deep conceptual grasp of how computers approximate continuous mathematics, manage rounding errors, and execute algorithms. In this course, you will: Understand the foundational concepts of floating-point arithmetic and error propagation; Apply root-finding algorithms to locate solutions for non-linear equations; Interpolate and approximate complex functions using polynomial methods; Compute numerical integrals and derivatives with high precision; Solve systems of linear equations using both direct and iterative computational methods; Model physical systems by numerically solving ordinary differential equations; Explore modern scientific computing practices using standard mathematical libraries. We begin with essential terminology and basic concepts of error analysis before moving step-by-step through core algebraic, calculus, and differential equation solvers. This course is designed for beginners, students, and engineers looking for a clear, text-based introduction to computational mathematics. Start building your scientific computing foundation today.