### Matemática II - Gestão - Sem Ramos - Especialidades

6.0
ECTS / Credit Units
 Year: 1 / 2º Semestre Plan: 2015/16 Scientific Area: MAT Level: L1

### Semestral Hour Load

 Theorical: 32.00 Theorical-Pratical: 48.00 Pratical and Laboratorial: Fieldwork: Seminar: Internship: Tutorial:
 Assigned Internship Hours: Assigned Projects Hours: Assigned Fieldwork Hours: Assigned Study Hours: Assigned Evaluation Hours: Others:

### Degree having this Course

Degree - Branch Degree Plan Year
Gestão - Sem Ramos - Especialidades 2015/16

### Teaching Staff

Marco Paulo Ferreirinha Garapa

Responsibilities:
Ensino teórico-prático
Rafael Domingos Garanito Luís

Responsibilities:
Regência
Responsável pelas Pautas
Ensino teórico
Ensino teórico-prático

## Course Information

### Course Objectivs

0 Equip the students with theoretical and practical knowledge in Mathematics which are necessary for general and academic purposes, thus giving continuity to the work developed at curricular unit of Mathematics I.

1 Determine conditioned extremes of real functions of vector variable using the method of Lagrange Multipliers and the method of Karush-Kuhn-Tucker.

2 Learning how to evaluate integrals of functions of one real variable using techniques such as immediate (or almost immediate) integration, integration by parts, by substitution and the simplification of rational functions. Apply the concept of integral in order to solve some practical problems (e.g. calculus of areas). Learning how to solve some improper integrals.

3 Identify and solve different types of ordinary differential equations applying different methods (e.g. variable separation, variable change, variation of parameters). Know how to solve some systems of linear differential equations.

### Evaluation Criteria

Classification Type: Quantitative (0-20)
Evaluation Methodology: Use of the whiteboard for presentation, explanation of subject material and problem solving. Exposed material should be provided to students, in detail, through a textbook or other supporting documents. Evaluation: two tests (one at the middle and one at the end of the semester), each one with a weight of 50% on the final grade.

### Program Resume (get program detail)

1 - Constrained optimization

2 - Primitives of real functions of one real variable

3 - Ordinary Differential Equations

### Main Bibliography

Apostol Tom M. (1983). Cálculo. Editora Reverté Ltda.
Ferreira, J. Campos (1999). Introdução à Análise Matemática. Fundação Calouste Gulbenkian.
Piskounov, N. (1990). Cálculo Diferencial e Integral. Editora Lopes da Silva.
McCann, Roger C. (1982). Introduction to ordinary differential equations. Harcourt Brace Jovanovich, New York.
Stewart J. (2008). Calculus. Thomson Brooks/Cole.

### Student Support

Wednesday, 2 pm - 5 pm,  (prof. Rafael Luís)

Wednesday, 11:30 am - 12:30 am,  (prof. Marco Garapa)