Foundations of Numerical Analysis: Solving Mathematical Problems Computationally

Mathematical problems in science and engineering are often too complex to solve analytically. Numerical analysis provides the powerful algorithms needed to find accurate, approximate solutions to these real-world challenges. In this course, you will transition from theoretical mathematics to practical, computational problem-solving. You will learn how to analyze errors, approximate functions, solve systems of equations, and implement these methods conceptually using modern algorithmic structures. What you'll learn: 1. Understand the fundamentals of error propagation, round-off errors, and numerical stability. 2. Solve non-linear equations using root-finding algorithms like bisection and Newton-Raphson. 3. Interpolate data points and approximate complex functions using polynomial techniques. 4. Apply numerical differentiation and integration methods to estimate calculus operations. 5. Solve systems of linear equations and ordinary differential equations systematically. 6. Read and analyze clean algorithmic logic and modern Python-based implementations using NumPy. The course begins with essential terminology, error analysis, and foundational mathematical definitions. You will then progress through step-by-step written explanations of core algorithms, complete with clear code snippets and analytical exercises to solidify your understanding. This course is designed for beginners, students, and programmers who want a solid grounding in numerical methods. No prior advanced computing experience is required. Start exploring the mathematical algorithms that power modern scientific computing today.