Base Knowledge
Mathematics: differential and integral calculus.
Teaching Methodologies
Expository method will be used to explain theoretical subjects and to analyse and solved problems. Theoretical subjects and application examples will be presented.
Each chapter will begins with motivation examples and will ends with the analysis of application examples. Exercises will be discussed, solved and analysed. Emphasis will be placed on the critical analysis of the selection criteria for mathematical techniques and consequent results.
Free mathematics software will be presented and analysed.
In Moodle, will be available all the necessary documents for this course unit: textbook, exercise book, forms, math tables.
Learning Results
– Develop ability to define and analyze mathematical problems, choose the most effective solving methods, interpret and analyze results.
– Provide basic knowledge of Linear Algebra.
– Identify, understand and solve problems involving linear systems and matrix calculus.
– Perform basic concepts or theory of errors.
– Apply concepts related to the numerical resolution of linear systems, nonlinear equations, polynomial interpolation and definite integrals.
– Understand the limitations of analytical techniques and develop the capacity to use numerical methods.
– Use mathematical software to analyze and solve problems.
Program
1. Matrices.
– Definitions.
– Operations and properties.
2. Systems of linear equations.
– Definitions.
– Operations with matrices and properties: matrices condensation and characteristic.
– Classification and resolution of systems of linear equations:
i) Direct methods: Gauss elimination;
ii) Iterative methods: Jacobi and Gauss-Seidel.
– Applications.
3. Theory of errors (brief remarks).
– Introduction.
– Definitions.
4. Roots of nonlinear equations.
– Introduction.
– Location of roots: graphical method and Bolzano’s theorem.
– Bisection and Newton’s methods: iterative rules, error and stopping criteria.
– Computational aspects.
– Applications.
5. Polynomial interpolation.
– Introduction.
– Uniqueness of the interpolating polynomial.
– Interpolating polynomial using Lagrange and Newton’s forms.
– Interpolation error.
– Computational aspects.
– Applications.
6. Numerical integration.
– Introduction.
– Trapezoidal and Simpson’s rules.
– Numerical integration error.
– Computational aspects.
– Applications.
Curricular Unit Teachers
Grading Methods
- - Exame - 100.0%
Internship(s)
NAO
Bibliography
Recommended:
– Caridade, C.M.R., (2024). Matemática Aplicada, DFM, ISEC.
– caridade, C.M.R. (2024). Diapositivos das aulas de Matemática Aplicada, DFM, ISEC.
– Caridade, C.M.R. (2024). e-MAIO (Módulos de Aprendizagem Interativa online) em https://dfmoodle.isec.pt/
-Caridade, C.M.R. (2024). Matemática Aplicada, MOODLE ISEC em https://dfmoodle.isec.pt/
Additional:
– Agudo, F.R.D. (1996). Introdução à Álgebra Linear e Geometria Analítica, Escolar Editora, Lisboa.
– Ferreira, M.A. (2016). Álgebra Linear – Exercícios – Livro 1: Matrizes e determinantes, Edições Silabo. ISBN: 9789726188506.
– Monteiro, A. (2010). Matrizes, Coleção Dashofer, Learning & Higher Education. ISBN: 978-989-642-083-3
– Strang, G. (2016). Introduction to Linear Algebra (5ª ed.), Wellesley-Cambridge Press. ISBN: 97809802332776.
– Chapra, S.C. (2008). Métodos numéricos para engenharia (5ª ed.). São Paulo: McGraw-Hill. ISBN: 9788580555684
– Rodrigues, J.A. (2003). Métodos numéricos – Introdução, aplicação e programação. Lisboa: Edições Sílabo.
-Santos, F.M. (2002). Fundamentos de Análise Numérica. Lisboa: Edições Sílabo. ISBN: 978-989-561-003-7