2025
Computational Mathematics and Optimization
Name: Computational Mathematics and Optimization
Code: MAT13278D
6 ECTS
Duration: 15 weeks/156 hours
Scientific Area:
Mathematics
Teaching languages: Portuguese
Languages of tutoring support: Portuguese
Sustainable Development Goals
Learning Goals
Establish the foundations and develop the knowledge on mathematics and numerical methods applied to engineering problems. Extend the students capacities in using computers as computation tools. Available computer packages (Matlab, Maple, etc.) and libraries for numerical methods will be used.
In the end of the course the students should be able to develop numerical computation programs and evaluate its efficiency and precision regarding memory and processing.
In the end of the course the students should be able to develop numerical computation programs and evaluate its efficiency and precision regarding memory and processing.
Contents
-Floating point arithmetics: Binary representation and operations. Absolute and relative errors. Problem condition number.
-Differentiation, integration and interpolation: Comput. derivatives of any order. Quadrature formulas, adaptive meth. Numerical errors. Lagrange, Hermite and Ck interpolation. Splines and NURBS. Interpol. curves, surfaces and volumes. Interpol. errors.
-Sol. Lin. and nonlinear eq. Syst.: Direct and iterative meth. for linear systems. Meth. for sparse, dense and large dim. syst. Newton and quasi-Newton meth. for nonlinear systems.
-Diff. equations: Funct. approximations. Finite diff. meth. Meth. for time integration (Ruge-Kutta, multistep, Newmark...). Finite element meth.
-Optimization: Unconstrained optim. Necessary optimum cond. Meth. for 1-variable funct. Meth for n-variable funct., with or without using derivatives. Constrained optim. Optimality cond. Interior point meth. Multi-objective optim. Global optim. Genetic algorith. Optimum control problems.
-Differentiation, integration and interpolation: Comput. derivatives of any order. Quadrature formulas, adaptive meth. Numerical errors. Lagrange, Hermite and Ck interpolation. Splines and NURBS. Interpol. curves, surfaces and volumes. Interpol. errors.
-Sol. Lin. and nonlinear eq. Syst.: Direct and iterative meth. for linear systems. Meth. for sparse, dense and large dim. syst. Newton and quasi-Newton meth. for nonlinear systems.
-Diff. equations: Funct. approximations. Finite diff. meth. Meth. for time integration (Ruge-Kutta, multistep, Newmark...). Finite element meth.
-Optimization: Unconstrained optim. Necessary optimum cond. Meth. for 1-variable funct. Meth for n-variable funct., with or without using derivatives. Constrained optim. Optimality cond. Interior point meth. Multi-objective optim. Global optim. Genetic algorith. Optimum control problems.
Teaching Methods
Lectures and tutoring, with each student being responsible for reading the bibliography advised by the teacher.
For some topics there may be seminars focused in specific points of the course program.
Evaluation: Homework along the semester, with final discussion.
For some topics there may be seminars focused in specific points of the course program.
Evaluation: Homework along the semester, with final discussion.
Teaching Staff (2024/2025 )
- Paulo Manuel de Barros Correia [responsible]
Certificações
