Foundations of Numerical Mathematics

Analytical mathematical solutions are not always possible for complex real-world problems. This course introduces you to the essential world of numerical mathematics, enabling you to find precise, approximate solutions using structured, algorithmic techniques. You will transition from theoretical mathematics to practical numerical computation. By reading through clear, written explanations and step-by-step mathematical walkthroughs, you will learn how to formulate, analyze, and solve complex mathematical problems systematically. What you'll learn: - Understand the fundamentals of numerical error analysis, including round-off and truncation errors. - Solve non-linear equations using methods like Bisection, Secant, and Newton-Raphson. - Learn to solve systems of linear equations using direct and iterative techniques. - Apply interpolation techniques and curve fitting to approximate data points. - Perform numerical integration and differentiation using classic formulas like Simpson's and Trapezoidal rules. - Approximate solutions for ordinary differential equations using Euler and Runge-Kutta methods. The course begins with essential definitions of error propagation and floating-point representation, ensuring you have a strong theoretical foundation. From there, you will progress through structured chapters covering root-finding, linear systems, interpolation, and calculus approximation. This written course is designed for beginner students, aspiring engineers, and data analysts looking to build a rock-solid foundation in numerical methods without needing advanced prior knowledge. Start reading today to unlock the power of numerical computation and algorithmic problem-solving.