Numerical Methods and Algorithms for Beginners

Solving complex mathematical models requires robust computational algorithms when exact analytical solutions are impossible. This course introduces foundational numerical methods and shows you how to translate mathematical concepts into practical code. You will gain a clear understanding of computer arithmetic, error propagation, and algorithm selection for scientific computing tasks. What you'll learn: • Understand basic numerical error sources, floating-point representation, and precision limits. • Implement root-finding algorithms such as bisection and Newton-Raphson methods. • Apply direct and iterative techniques to solve systems of linear equations. • Perform numerical integration and differentiation using approximation formulas. • Solve ordinary differential equations using Euler and Runge-Kutta schemes. • Utilize modern Python tools like NumPy for vectorized operations. The course begins with essential terminology, basic definitions, and floating-point error theory before moving into structured algorithmic step-by-step explanations and code snippets. This course is ideal for beginners, engineering students, and developers seeking a practical intro to computational mathematics with no advanced background required. Start reading to build your computational problem-solving skills today.