Class Numerical Methods

In many engineering applications the need arises to solve mathematical problems that either do not have an analytical solution, or the analytical solution is too computationally expensive to determine. In those situations, an approximate solution can often be obtained using numerical analysis algorithms. In this curricular unit we study a set of algorithms that solve some of the most common classes of problems, ranging from determining the zeros of non-linear equations to solving ordinary differential equations. This knowledge plays a central role in an engineering course, given the complexity of many real life mathematical models.

Not applicable

Floating point Arithmetics. Representation of integer and real numbers. Errors in floating point arithmetics. Error propagation. Non-linear equations. Bissection method, false position and secant. Newton and fixed point methods. Systems of linear equations. Iterative methods. Systems of non-linear equations. Newton's method. Polynomial interpolation. Polynomial forms. Interpolation formulas. Numerical differentiation. First and second order derivatives. Numerical integration. Simple and composite rules. Ordinary differential equations. Euler's and Runge-Kutta's methods. Convergence. Errors

The teaching methodology adopted was carefully designed to effectively address each of the specified objectives, providing students with an in-depth and comprehensive understanding of the numerical methods to be studied. During classes, practical case studies are conducted, providing students with the opportunity to apply the theoretical concepts learned to real-world situations, so that students develop their problem-solving and critical thinking skills. The flipped classroom methodology will also be used.

Atkinson, K. - Numerical Analysis. John Wiley and Sons, New York; Chapra, S. and Canale, R. - Numerical methods for Engineers. McGraw-Hill Book Comp-New York Pina, Heitor - Métodos Numéricos. McGraw-Hill-Lisboa