Numerical Analysis: Foundations and Exam Preparation

Numerical analysis is the backbone of scientific computing, engineering, and advanced mathematical examinations. Understanding how to approximate solutions to complex mathematical problems is essential when exact analytical solutions are impossible to find. This text-only course guides you from the fundamental definitions of error and approximation to advanced numerical techniques, ensuring you build both conceptual clarity and exam-ready problem-solving skills. What you'll learn: Understand the core principles of error analysis, including round-off and truncation errors in modern computing; Solve non-linear equations using classic iterative methods such as bisection, secant, and Newton-Raphson; Apply interpolation techniques, including Lagrange and Newton's divided difference formulas, to approximate functions; Master numerical differentiation and integration methods like the Trapezoidal and Simpson's rules; Formulate numerical solutions for ordinary differential equations using Euler's and Runge-Kutta methods; Analyze the convergence and stability of different numerical algorithms to evaluate their efficiency. The course starts with basic terminology and error propagation, moving step-by-step through algebraic equations, interpolation, and calculus approximations. You will learn through detailed written derivations, step-by-step solved examples, and conceptual practice questions. Designed for beginners in numerical methods, undergraduate mathematics students, and independent learners preparing for competitive mathematical exams. No prior exposure to numerical analysis is required. Start reading today to build a strong, logical foundation in numerical methods.