Numerical Analysis Practice Questions

In this course, you will be practicing numerous questions in the intricacies of numerical methods, providing a rigorous exploration of fundamental concepts essential for practical problem-solving. We commence with a detailed examination of floating-point arithmetic and errors and a meticulous review of calculus concepts. Moving into the realm of nonlinear equations, we explore the Bisection method, Fixed point method, Secant and Newton’s methods, and the convergence of iterative algorithms. Transitioning to systems of linear equations, we embark on a comprehensive review of linear algebra, delve into Gaussian elimination, pivoting, and matrix factorization, and explore iterative methods for sparse systems. The course proceeds with function approximation, covering Polynomial (smooth) interpolation, Spline (piecewise) interpolation, and Least squares fitting. Additionally, we address the complexities of numerical differentiation and integration or quadrature. Lastly, we navigate the realm of Ordinary Differential Equations (ODEs), providing background insights on ODE initial value problems and exploring numerical methods such as Euler’s method, Taylor and Runge-Kutta methods, and Systems of first-order ODEs. Throughout this course, you will actively practice questions in these topics, equipping you with the skills to tackle real-world numerical challenges and build a robust foundation in Numerical Analysis.