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ISCTE-IUL  >  Education  >  LG

Optimization (2 º Sem 2016/2017)

Code: L5023
Acronym: L5023
Level: 1st Cycle
Basic: No
Teaching Language(s): English, Portuguese
Friendly languages:
Be English-friendly or any other language-friendly means that UC is taught in a language but can either of the following conditions:
1. There are support materials in English / other language;
2. There are exercises, tests and exams in English / other language;
3. There is a possibility to present written or oral work in English / other language.
1 6.0 0.0 h/sem 54.0 h/sem 0.0 h/sem 0.0 h/sem 0.0 h/sem 0.0 h/sem 1.0 h/sem 55.0 h/sem 95.0 h/sem 0.0 h/sem 150.0 h/sem
Since year 2016/2017
Pre-requisites N.A.
Objectives This course intends to develop Calculus tecnhiques, in particular some adequate for solving practical managerial and economic problems of optimization.
Program 1.Optimization in  Rn
1.1 Non linear Optimization
1.1. Summary of extremes in R.
1.2 Unconstrained optimization in Rn.
1.3 Unconstrained optimization in Rn.
1.2. Linear Programming
1.2.1 Introduction.
1.2.2 Graphical and simplex methods.
1.2.3 Special cases: problems with redundant, infeasible and unbounded solutions.
1.2.4 Sensitivity analysis.

2. Series
2.1 Definitions and examples.
2.2 Convergence of series.
2.3 Series of functions and power series.

3. Integral calculus in R
3.1 Calculus of anti-derivatives.
3.2 Riemman Integral.
3.3 Integral and areas.

4. Introduction to ordinary differential equations (ODE).
4.1 Definitions and generalities.
4.2Analysis and solutions of some first order ODE.

Evaluation Method Students may choose between continuous assessment or assessment by examination.
Continuous assessment consists:
1. Midterm test (40%)
2. Group assignment (20%)
3. Final test (40%)
Minimum grade of 8 (out of 20) for any evaluation item.
Assessment by examination consists of doing an exam in the 1st examination period.
Students who have failed may take the exam at the 2nd examination period.
If their grade is higher than 16, students are required to submit to an oral examination.
Teaching Method LM1. Expositional: presentation of the theoretical concepts.
LM2. Participative: solving exercises.
LM3. Active: Group assignment.
LM4. Autonomous work: read the recommended bibliography and  solving  problems given by the lecturer, according to the class planning.
Basic Bibliographic Ferreira, M.A.M. e I. Amaral (1996). Primitivas e Integrais, Lisboa: Edições Sílabo, (5ª edição).

Ferreira, M.A.M. e I. Amaral (1996). Integrais Múltiplos e Equações Diferenciais, Lisboa: Edições Sílabo.

Ferreira, M.A.M e Amaral, I. (2002). Cálculo Diferencial em IRn. Colecção Matemática Vol. 2, Lisboa: Edições Sílabo, 5ª edição.

Ferreira, M.A.M (1999). Sucessões e Séries. Colecção Matemática Vol. 10, Lisboa: Edições Sílabo.

Ferreira, M.A.M. e Amaral, I. (1995). Programação Matemática. Colecção Matemática Vol. 7, Lisboa: Edições Sílabo, 2ª edição.

Chiang, A. C. Fundamental Methods of Mathematical Economics. ed. McGraw-Hill, Inc, 1984.

Marsden, J. and Weinstein, A., Calculus III. Springer-Verlag , New York, 1985.
Complementar Bibliographic Apostol, Tom M. Calculus, volume I. John Wiley & Sons, 2007.