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ISCTE-IUL  >  Education  >  LG , LGM

Mathematics (1 º Sem 2016/2017)

Code: L5027
Acronym: L5027
Level: 1st Cycle
Basic: No
Teaching Language(s): Portuguese, English
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 18.0 h/sem 0.0 h/sem 36.0 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 The overall goal of this course is to introduce students to the fundamental concepts of Linear Algebra and Diferential Calculus in Rn. We will develop skills in the aforementioned concepts and apply them in solving problems in economics and management.
Program 1. Matrices
Definitions and operations with matrices
Linear combination. Linear dependence and independence
Matrix inverse

2. Systems of linear equations
Gaussian elimination. Classification.

3. Determinants
Definition and properties
Matrix inverse

4. Vector Spaces
Vector subspaces
Span, base and dimension
Coordinate vectors and change of basis

5. Linear transformations
The matrix of a linear transformation
Kernel and range
Change of basis.
Eigenvalues and eigenvectors. Diagonalization
Quadratic forms

6. Inner product
Inner product and norm
Orthogonality
Orthonormal basis

7. Differential Calculus in Rn
Topology
Functions of several variables
Domains
Limits and continuity
Partial derivatives
Directional derivatives
Differentiation
Gradient and Jacobian matrix
Chain rule
Higher order derivatives. Schwarz Theorem. Hessian matrix.
Homogeneous functions. Euler Theorem.
Evaluation Method Continuous assessment consists:
1. Midterm test (30%)
2. Group assignment (20%)
3. Final test (50%)
Minimum grade of 8 out of 20 is required for each one of both tests and group assignment.
Assessment by examination consists of doing an exam in the 1st examination period.
Students who have failed may take the exam in the 2nd examination period.
Students are required to take an oral exam, if the grade is higher than 16.
Teaching Method LM1. Expositional: presentation of the theoretical concepts
LM2. Participative: solving exercises and problems
LM3. Active: group assignment
LM4. Autonomous work: individual study should be complemented with the bibliography and by solving exercises and problems given by the lecturer, according to the class planning.
Observations
Basic Bibliographic Nakos, G. and Joyner, D., Linear Algebra With Applications, Brooks/Cole Publishing Company, 1998.

Marsden, J. and Weinstein, A., Calculus III. Springer-Verlag, New York, 1985.

Ferreira, M.A. e Amaral, I., Álgebra Linear, Vol. 1 - Matrizes, Edições Sílabo, 2009.

Ferreira, M.A. e Amaral, I., Álgebra Linear, Vol. 2, Edições Sílabo, 2011.

Ferreira, M.A. e Amaral, I., Cálculo diferencial em Rn, Edições Sílabo, 2011.

Complementar Bibliographic Strang, G., Introduction to Linear Algebra, Wellesley-Cambridge Press, 2009.

Blyth, Thomas Scott, and Edmund F. Robertson. Basic linear algebra. Springer, 2002.

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