ISCTE-IUL > Education > LGIL

Complements of Mathematics (2 º Sem 2019/2020)

Code:	02239
Acronym:	02239
Level:	1st Cycle
Basic:	No
Teaching Language(s):	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.

Semester	ECTS Credits	Theoretical Lesson (T)	Theoretical and Pratical Lesson (TP)	Practical and laboratorial lesson (PL)	Seminary (S)	Field Work (TC)	Training Period (E)	Tutorial Orientation (OT)	Contact Hours	Autonomous Work	Others (O)	Total Load Hours [?]Contact Hours + Autonomous Work
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	2019/2020
Pre-requisites	Mathematics
Objectives	Once acquired the fundamental knowledge of the functions of a variable, in this UC it is intended to address contents related to functions of more than one variable. Thus, it is intended to introduce and develop competences of the elementary notions of Linear Algebra and Differential Calculus in Rn. The UC seeks to promote an adequate learning of the mathematical tools of these concepts and the development of skills to apply them to practical problems, in particular management, finance and industrial and logistical management.
Program	1. Linear Algebra 1.1 Matrices: definition and algebra of matrices. Properties. Liner independence. Rank. Inversion of Matrices 1.2 Systems of linear equations: Gauss elimination and classification 1.3 Determinants: Definition and properties. Inversion of matrices 1.4 Eigenvalues and Eigenvectors 1.5. Quadratic forms 1.6 Graph Theory 2 Differential calculus in Rn 2.1 Functions of two or more variables - Topological notions. Domains. Limits and continuity 2.2 1st order partial derivatives; linear approximations; chain rule, gradient vector, directional derivative. Differentiation 2.3 Partial derivatives of a higher order.Schwarz's theorem; Hessian matrix 3 Maximum and Minimum values - functions of more than one variable 3.1 Absolute Maximum and Minimum values 3.2 Lagrange multipliers 3.3 Conditions for the existence of maxima and minima in stationary points 4 Integrals in Rn 4.1 Double integrals 4.2 Some dual-integrals applications
Evaluation Method	1 Periodic Evaluation: - Minimum attendance of 24 lessons. - Mid-term test (40%): written test carried out during the academic period; minimum score of 8.0 values. - Group evaluation activities (20%); minimum score of 8.0 values. - Written Test (40%): written test in the 1st evaluation period; minimum score of 8.0 values. 2 Exam: a written test (with a weight of 100%), in the first season or in the 2nd season of the evaluation period.
Teaching Method	The learning methodologies (LM) used for this course are: LM1. Expositional: presentation of theoretical concepts LM2. Participative: analysis and resolution of exercises and problems LM3. Active: with the realization of group evaluations LM4. Self-study, autonomous work by the student, according to course schedule. The assessment is two folded: the periodic evaluation and the exams.
Observations	Remarks on the assessment: 1 A student is excluded from the periodic assessment, automatically going to the exam in any of the following conditions: - getting an average grade lower than 8.0 values on the group evaluations'. - getting a grade lower than 8.0 values in the mid- term test. 2 Group evaluation has a 15 minutes duration, taken in class on two different occasions. Group have 2 students, communicated to the teacher until two weeks before the first evaluation. 3. The grade of group evaluations is the average of the two evaluations. Repeating students may choose any of the evaluation methods, subject to the same rules. In any case, the minimum grade is 9.5. Students with a final grade higher than 16 v., will have to take a defense test.
Basic Bibliographic	Howard Anton, Chris Rorres, Álgebra Linear com Aplicações, 10ª Edição, 2012, Bookman James Stewart, Cálculo Volume 2 -- Tradução da 8ª. Edição Norte Americana, 2017, Cengage Learning James Stewart, Calculus -- Early Transcendentals, 8 Edition, 2017, Cengage Learning
Complementar Bibliographic	Knut Sydsaeter, Peter Hammond, Arne Strom & Andrés Carvajal, Essential Mathematics for Economic Analysis, 5th edition, 2016, Pearson Chiang, A. C. Fundamental Methods of Mathematical Economics. ed. McGraw-Hill, Inc, 1984