Introduction to Numerical Methods and Computational Math

Many real-world mathematical equations cannot be solved analytically with pen and paper. Numerical methods provide the essential algorithms needed to find accurate, computer-driven solutions to these complex problems. This text-based course guides you from the absolute basics of computational mathematics to writing robust algorithms, helping you translate mathematical theory into working logical steps. You will learn to analyze computational errors, solve non-linear equations, and approximate complex functions. What you will learn: Understand the fundamental concepts of computational error, machine precision, and algorithm stability; Solve non-linear equations using root-finding algorithms like bisection and Newton-Raphson; Apply interpolation and approximation techniques to fit curves to discrete data points; Implement numerical integration and differentiation methods to calculate integrals and derivatives; Solve systems of linear equations using direct and iterative computational methods; Practice writing clean, typed Python code to execute these mathematical algorithms. The course starts with foundational definitions of numerical representation and error propagation before moving into practical solving techniques. You will read clear explanations, analyze algorithm step-by-steps, and complete written exercises to reinforce your understanding. Designed for students, engineers, and aspiring data scientists who are new to scientific computing, this course requires no advanced math degree. Start building your computational math foundation today.