Foundations of Numerical Analysis and Scientific Computing

To solve real-world engineering and scientific problems, standard analytical formulas are often not enough. This course introduces you to the core mathematical principles and numerical algorithms used to find accurate, computer-driven solutions to complex equations. You will transition from theoretical calculus and algebra to practical, algorithmic problem-solving using modern computational techniques. What you'll learn: - Understand foundational errors, stability, and convergence in numerical approximations - Solve systems of linear and non-linear equations using iterative and direct methods - Apply interpolation and curve-fitting techniques to model complex data sets - Implement numerical integration and differentiation algorithms for continuous functions - Solve ordinary and partial differential equations using finite difference methods - Practice writing efficient, clean computational code with modern array-handling libraries This text-based course begins with essential terminology, mathematical definitions, and error analysis before guiding you through step-by-step algorithmic implementations. You will study code snippets, analyze convergence proofs, and work through comprehensive written exercises designed to build your confidence. This course is designed for beginners, engineering students, and data professionals looking to build a strong foundation in computational mathematics. No advanced programming background is required, though a basic understanding of algebra and calculus is helpful. Start learning today to unlock the power of scientific computing.