Computation
Code
10677
Academic unit
Faculdade de Ciências e Tecnologia
Department
Departamento de Informática
Credits
3.0
Teacher in charge
Jorge Carlos Ferreira Rodrigues da Cruz, Pedro Manuel Corrêa Calvente Barahona
Weekly hours
3
Total hours
49
Teaching language
Português
Objectives
Knowledge
- Learn the fundamental concepts in numerical computation
- Know the methods commonly used in different areas of numerical computation
- Understand the errors commited in numerical computations
- Discuss the applicability and convergence of the numerical methods
Competences
- Identify suitable numerical methods for solving problems in science and engineering
- Use the capabilities of MATLAB for the implementation of numerical methods
- Analyze the results obtained by numerical computation
- Use MATLAB for simulation and visualization in science and engineering
Soft Skils
- Model formulation
- Analysis of results
- Ability to research literature
- Usage of a numerical computing project
Prerequisites
Students should have some basic programming knowledge. However, the program of the course includes a brief introduction to MATLAB and its computational aspects in a user''''s perspective.
Subject matter
Introduction to Numerical Computation
- Mathematical Modeling, Numerical Methods and Problem Solving
- Numbers and Representation (IEEE)
- Errors and Propagation
Roots of Nonlinear Equations
- Bracketing Methods: Bisection and False Position
- Open Methods: Secant, Newton-Raphson and Brent
Systems of Linear Equations
- Linear Algebraic Equations and Matricial Representation
- Direct Methods: Gauss Elimination
- Iterative Methods: Jacobi and Gauss-Seidel
Systems of Nonlinear Equations
- Newton-Raphson Method
Optimization
- One-Dimensional Unconstrained Optimization: Golden-Section, Newton-Raphson and Brent
- Multidimensional Unconstrained Optimization: Direct Methods and Gradient Methods
- Constrained Optimization: Linear Programming
Curve Fitting
- Linear Regression
- Lest Squares Method
- Nonlinear Regression
Numerical Integration
- Newton-Cotes Formulas: Trapezoidal Rule and Simpson''''s Rules
- Integration of Functions: Romberg Integration, Gauss Quadrature
- Adaptive Quadrature
Ordinary Differential Equations
- Initial-Value Problems
- Single Step Methods: Euler and Runge-Kutta
- Adaptive Methods and Stiff Systems
Bibliography
Steven C. Chapra. Applied Numerical Methods with MATLAB for Engineers and Scientists, 3rd edition, McGraw-Hill Inc., 2011.
Steven C. Chapra, Raymond P Canale. Numerical Methods for Engineers, 6rd edition, McGraw-Hill Inc., 2010.
Cleve Moler. Numerical Computing with MATLAB, SIAM 2004.
Teaching method
The theoretical lectures present several numerical methods, highlighting their strengths and limitations in solving various problems in science and engineering. The kaboratory classes discuss practical examples of applications in science and engineering using MATLAB as a programming environment.
The unit should have a strong practical component. During the laboratory classes, motivating case studies in several areas of science and engineering will be discussed together with the presentation of implementations (MATLAB) of numerical methods appropriate to their resolution. The assessment of the practical component is based on a numerical computing project that will integrate some of the numerical methods implemented during the practical classes.
Evaluation method
Evaluation Components
The assessment consists of two components: a laboratory component and the theoretical-practical component.
Laboratory Component and Frequency
The laboratory component is based on a numerical computing project developed during the practical sessions in group (3 students) under the guidance of the teacher.
During the practical sessions will be made two evaluation forms F1 and F2 to be solved on the computer using the project implemented.
The assessment of the laboratory component (CompL) is the simple average of the grades of the two evaluation forms (F1 and F2):
CompL = (F1 + F2) / 2.
For frequency, it is necessary that F1 >= 10 or F2 >= 10.
Who obtained frequency in 2013/2014, if not enrolled in any practical turn, keeps the assessment of the practical component. Otherwise, if enrolled in any practical turn, the previous assessment will be canceled and the note of the practical component will be achieved in 2014/2015.
Theoretical-practical component
The theoretical-practical component consists of two tests (during the class period) or an examination. The tests and the exam are individual, written and without consultation.
The assesment of the theoretical-practical component (CompTP) is the simple average of the test scores (T1 and T2) or exam grade (Ex):
CompTP = (T1 + T2) / 2 or CompTP = Ex.
To obtain approval, it is necessary that CompTP >= 7.5 .
Final Grade
The final grade (NF) for the students with frequency is:
- NF = CompTP, if CompTP < 7.5;
- NF = (CompL + CompTP) / 2, if CompTP >= 7.5 .
All grades (F1, F2, T1, T2, Ex, CompL and CompTP) are rounded to one decimal place, except the final grade (NF) which is rounded to the nearest unit.