Numerical Analysis covers fundamental and advanced concepts in computational methods for solving mathematical problems that are difficult or impossible to solve analytically. Topics include error analysis, numerical solutions of nonlinear equations, interpolation and approximation, numerical differentiation and integration, numerical solutions of linear systems, eigenvalue problems, and numerical solutions of ordinary and partial differential equations. Students engage in a combination of lectures, laboratory sessions, and hands-on projects to apply these concepts effectively. Emphasis is placed on developing and analyzing efficient algorithms using programming languages or computational software such as MATLAB or Python. Practical activities include implementing root-finding algorithms like Newton-Raphson and bisection methods, constructing interpolation polynomials, applying numerical integration techniques like trapezoidal and Simpson's rules, and solving differential equations using methods like Euler's and Runge-Kutta. Students will also learn to assess the accuracy, stability, and convergence of numerical methods and apply best practices in minimizing computational errors and optimizing algorithm performance.
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