Computational Mathematics: Solving Equations with Numerical Methods

Many real-world problems in engineering, finance, and physics involve mathematical equations that are impossible to solve by hand. Computational mathematics provides the essential numerical techniques needed to approximate these solutions accurately using computers. In this text-only course, you will transition from theoretical mathematics to practical scientific computing, gaining the skills to set up, analyze, and solve complex equations algorithmically. What you'll learn: - Understand the fundamental principles of numerical approximation, floating-point arithmetic, and error propagation. - Apply root-finding algorithms like the Bisection and Newton-Raphson methods to non-linear algebraic equations. - Solve systems of linear equations using both direct and iterative matrix computational methods. - Implement numerical integration and differentiation techniques for calculus-based problems. - Configure basic ordinary differential equation solvers using Euler's and Runge-Kutta approaches. - Analyze algorithmic efficiency and convergence rates to choose the best method for your data. The course begins with core terminology and foundational definitions of mathematical modeling and error analysis. From there, you will progress through structured written explanations, mathematical proofs, and step-by-step algorithmic breakdowns designed for self-paced reading. This course is created for beginners in scientific computing, engineering students, and data enthusiasts, with no advanced computational background required. Start learning how to tackle complex mathematical equations with modern computational techniques today.