Mathematics I

Code:

1EC104

Acronym:

MATI

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2022/2023 - 1S

Active?	Yes
Web Page:	https://moodle.up.pt/course/view.php?id=659
Responsible unit:	Agrupamento Científico de Matemática e Sistemas de Informação
Course/CS Responsible:	Bachelor in Economics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
LECO	324	Bologna Syllabus since 2012	1	-	6	63	162

Teaching language

Portuguese

Objectives

Students will learn how to study real multivariable functions and how to use this in decision making. The students will namely be able to find the actions (i) that maximize the results, given a restriction on the factors used and (ii) that minimize the factors given an objective, through optimization with and without constraints. The depth of the study will be that which is appropriate in a degree in Economics.

Applications to Management and Economics will be provided when appropriate.

Students will also be able to do mathematics on a computer.

Learning outcomes and competences

The students will be endowed with the technical tools indispensible for a successful career in Management.
Students will learn how to study real multivariable functions and use that knowledge in the context of optimization problems.
Students will also gain the skills to do mathematics on a computer.

Working method

B-learning

Program

Study of real functions of several real variables:

• Graphs and domain;
• Partial derivatives; differentiable functions; gradient; tangent plane, the chain rule;
• Differentiability; approximation of functions, Taylor formula;
• Homogeneous functions;
• The Implicit Function Theorem and study of functions defined implicitly;
• Maxima and minima of functions;
• Lagrange multipliers for constrained optimization.

Mandatory literature

Marsden, Jerrold E.; Vector calculus. ISBN: 978-1-4292-2404-8

Complementary Bibliography

Cerqueira, António de Melo da Costa; Funções reais definidas em IRn. ISBN: 972-578-130-9

Teaching methods and learning activities

A mixture of lecture and example class will be used as appropriate. Besides the classes there is an online course in the e-learning platform of the university. This includes foruns (for obtaining help with the teaching staff), auto-evaluation for assessing the progression of the student´s individual learning process, and all the materials needed in class.

Once a week there is a Lab session in class where students work to solve a challenge and present their results. 

Software

Maxima

keywords

Physical sciences > Mathematics > Mathematical analysis

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Designation	Weight (%)
Exame	100,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Estudo autónomo	103,50
Frequência das aulas	58,50
Total:	162,00

Eligibility for exams

One final exam or one global test plus two mini-tests.

The assessment consists of performing (i) 2 moments of continuous assessment of short duration (up to 30 minutes), to be carried out during the semester and in the classroom, and (ii) a global test lasting 1h 30m. The final classification will be the better of the two grades: (a) global test grade, and (b) the weighted average between the global test grade (80%) and the 2 moments of continuous assessment of short duration (20%). The global test will evaluate answers to questions of mathematics development and application. The moments of continuous assessment address conceptual issues, and the normal follow-up to classes will be sufficient to enable the student to perform them.

The final exam will take 1h 30m and coincide with the date of the global test.

The appeal ("recurso") exam will work under the same terms as the global test or the final exam, whichever is more advantageous for the student. For exams of special seasons, the possibility of using the continuous assessment classification is not considered.

 

Calculation formula of final grade

Continuous assessment: the better of the two grades (a) classification of the global test and (b) weighted average between the classification in the global test (80%) and the 2 moments of continuous assessment of short duration (20%).

Final exam assessment: exam grade.

Special assessment (TE, DA, ...)

In accordance with the RAC.

Classification improvement

In accordance with the RAC.