1. Understand the finite limitation of numerical algorithms;
2. Work with error estimates and understand the propagation of errors in algorithms;
3. Interpolate and extrapolate data by interpolation and least squares;
4. Apply to data science and experimental measurements;
5. Approximate, derive and integrate functions by numerical methods;
6. Apply to non-elementary functions;
7. Solve non-linear equations and systems by numerical methods;
8. Approximate the solution of ordinary differential equations, including systems;
9. Approximate the solution of problems with partial differential equations;
10. Develop elementary computational projects;
11. Apply to various engineering and graphical visualization problems.
1. Basic Concepts
1.1. Numerical representation and introduction to MATLAB (or Python).
1.2. Errors and conditioning.
2. Equations and Systems
2.1. Data interpolation and extrapolation. Least Squares Method - Discrete L2 projection.
2.2. One-dimensional equations - Secant and Newton methods.
2.3. Systems of Linear and Nonlinear Equations – Fixed Point Methods, Newton.
3. Integration and numerical differentiation
3.1. Integration and Ordinary Differential Equations – Euler, Runge-Kutta and adaptive methods.
3.2. Numerical differentiation and integration - general and elementary case (several variables).
3.3. Equations with Partial Derivatives – Finite Differences, Splines and Finite Elements.
The course's classes are theoretical-practical, exploring practical application cases whenever possible. It is intended that the learning environment evolve in a dynamic and interactive way, based on an organized reasoning structure.
In addition to the various documents, such as notes made by the professor and the subject's governor, as well as other colleagues who teach the same subject at other leading universities in Portugal, made available by the professor in the moodle, below is the list of traditional manuals reference of the discipline.
K. Atkinson, (1989) An Introduction to Numerical Analysis , Wiley & Sons, 2nd. Ed.
R. L. Burden, J. D. Faires & A. C. Reynolds, (1987) Numerical Analysis , Weber & Schmidt, 2nd. Ed.
D. Kincaid & W. Cheney, (2002) Numerical Analysis: Mathematics of Scientific Computing , Brooks/Cole, 3rd Ed.,
H. Pina, (1995) Métodos Numéricos , McGraw-Hill.
S. J. Chapman (2003) Programação em MatLab para Engenheiros, Pioneira Thomson Learning, São Paulo
A. Quarteroni, F. Saleri, P. Gervasio (2014), Scientific Computing with MATLAB and Octave. Springer, 4th edition
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