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Mathematics 2017/2018

  • 6 ECTS
  • Taught in Portuguese
  • Both continuous and final Assessment

Objectives

- Understand the concepts of analysis, namely differentiation, extremes of functions and primitives;
- Calculate integral of elementary and composed functions of one or more variables and apply the concept to the computaion of areas.
- Consolidate knowledge of series and (degree in Economics) analyze the nature of numerical series for their convergence;
- Identify the types of real matrices, operate with matrices (addition, multiplication, transpose and inverse);
- Calculate determinants;
- Apply the properties of matrix operations and determinants to solving matrix equations (degree in Economics);
- Apply matrices and determinants to solve systems of equations.

Recommended Prerequisites

Knowledge acquired in Mathematics of Elementary and Secondary Education.

Teaching Metodology

The classes will be theoretical-practical, and are divided in two blocks of two hours weekly. Using illustrative problems the new concepts and mathematical methods are introduced using expositive, demonstrative and interrogative methods.
Exercises and problems (provided in advance) will be proposed to the students for solving individually or in small groups. Afterwards the solutions found and the resolution strategy are discussed with the all class.

Body of Work

1. DIFFERENTIAL AND INTEGRAL CALCULUS
1.1. Differentiation: differentiation rules (review)
1.2. Functions of several real variables: partial derivatives and extremes
1.3. Immediate Integrals.
1.4. Integration Techniques: integration of rational fractions and partial integration.
1.5. Definite integral. Applications to the computation of areas.
1.6 Double and triple integrals
2. SERIES
2.1. Introduction to succession and series
2.2. Succession
2.3. Series
2.4. Analyze the nature of numerical series for their convergence 3. LINEAR ALGEBRA
3.1. Matrix: general notions.
3.2. Matrix operations: properties and computation of addition, multiplication, transposition, inversion of matrices.
3.3. Determinants: definition, properties, computation of the determinant of a n-order matrix.
3.4.Matricial equations
3.5 Systems resolution using matrices and determinants

Recommended Bibliography

- Almeida, R. e Simões, R. (2014). Primitivas. Escolar Editora. ISBN: 978-972-592-442-6
- Larson, R., Hosteler, R. e Edwards, B. (2006). Cálculo. Volumes 1 e 2 (8ª edição). McGraw-Hill.ISBN: 972-578-144-9.
- Stewart, J. (2013). Cálculo. Volumes 1 e 2 (7ª edição). Cengage learning.
- de Sá, A.A. e B. Louro, B. (2009). "Sucessões e Séries: Teoria e Prática". Escolar Editora. ISBN: 978-972-592-238-5.

Complementary Bibliography

- Pires, C. (2011). "Cálculo para Economia e Gestão. Escolar Editora". ISBN: 9789725922989.
- Soper, J. (2004). "Mathematics for Economics and Business – An Interactive Introduction", second edition, Blackwell. ISBN 1-4051-1127-5.
- Dowling, Edwards (1994). Cálculo para Economia, Gestão e Ciências Sociais. McGraw-Hill

Weekly Planning

WEEK 0- week host
WEEK 1 - Information regarding the functioning of the course. Brief review of polynomial, exponential and logarithmic functions. Derivation: derivation rules.
WEEK 2 - Functions of several real variables: partial derivatives and extremes.
WEEK 3 – Integrals: Definitions and properties. Immediate integrals.
WEEK 4 - Integration of rational fractions.
WEEK 5 - Partial integration.Definite integral.
WEEK 6 - Definite integral. Applications to the computation of areas.
WEEK 7 - Double and triple integrals
WEEK 8 - First test and series review
Numerical series of non negative terms: convergence tests.
WEEK 9 - Series
WEEK 10 - Series and Matrices: general notions.
WEEK 11 – Matrix operations: properties and computation of addition, multiplication, transposition.
WEEK 12 - Matricial equations. Determinants: definition and properties
WEEK 13 - Computation determinants. Inverse matrix: definition and properties.
WEEK 14 – Calculating the inverse matrix. Apply matrices and determinants to solve systems of equations.

Demonstration of the syllabus coherence with the curricular unit's objectives

The selected program contents, intended to meet consistently the learning objectives that constitute the basic mathematics that will be essential for various curriculum areas the course of Economics and Management courses.

Demonstration of the teaching methodologies coherence with the curricular unit's objectives

The utilization of expositive, demonstrative and interrogative methods will allow, the student to acquire new theoretical and practical knowledge, and also enables the student to participate in the learning process, stimulating the group dynamics and individual work. By the resolution of problems, individually and in group, it enables the student to actively develop the oral, writing and critical capacity and also the capability to adapt to new situations.

relevant generic skillimproved?assessed?
Achieving practical application of theoretical knowledgeYesYes
Adapting to new situationsYesYes
Analytical and synthetic skillsYesYes
Ethical and responsible behaviourYesYes
Relating to others  
Self-assessmentYesYes
Written and verbal communications skillsYesYes
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