Mathematics I

Code:

EM191

Acronym:

EM191

Keywords
Classification	Keyword
OFICIAL	Basic Sciences

Instance: 2016/2017 - 1S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	First Degree in Engineering Sciences

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:CE	63	PE2007- Perfil Engenharia Geográfica	1	-	7,5	-
		PE2007- Perfil Engenharia Alimentar	1	-	7,5	-
		PE2007- Perfil Engenharia Agronómica	1	-	7,5	-

Teaching language

Portuguese

Objectives

An efficient use of the notions and techniques of linear algebra and analysis to address issues in the areas of the undergraduate curricula in whose Schedule this course is included.

Learning outcomes and competences

The syllabus meets the need for students to become familiar with the objects and methods of Analysis and Linear Algebra, giving emphasis to examples. Being taught during the first semester of the first year of the graduation, its content has been adjusted to its introductory character and was subject to judicious choices of primary and elementary mathematics. In the list of taught topics there are some that will be used and generalized in later years of the graduation, and others whose study will be essentially completed in this course.

The presentation in the lectures is organized in accordance with the syllabus and the intended outcomes. Students are encouraged to practice the syllabus through exercises, to work in advance the proposed problems and to participate in their discussion at the practical lessons, and also to read mathematical works of unexcelled quality, helping further to improve their knowledge and command of mathematical language and techniques.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Basic knowledge of the set of real numbers and functions.

Program

Linear algebra: Systems of linear equations; matrices; Gauss method. Algebra of matrices. Inverse matrix. Characteristic of a matrix. Determinat. Cramer's rule. Diagonalization of matrices. Examples of problems whose solution benefits from models using systems of linear equations.

Calculus: Functions; trigonometric functions and its inverses; exponentials and logarithms; limits and continuity of functions; derivatives. Inverse trigonometric functions and their

derivatives. Rolle, Lagrange and Cauchy theorems. Primitivation: different methods.

Integration: Riemman integral. Fundamental Theorem of Calculus. Integration: different methods. Evaluation of areas. Improper integrals. 

Polinomial approximation and numerical series: Taylor polinomials. Numerical series: basic properties and criteria for convergence of series- ratio, integral and Leibnitz criterion.

Mandatory literature

Anton Howard; Álgebra linear com aplicações. ISBN: 978-85-7307-847-3
Adams Robert A.; Calculus. ISBN: 0-201-82823-5

Teaching methods and learning activities

Lectures and classes: The content of the syllabus is presented in the lectures, where examples are given to illustrate the concepts. There are also practical lessons, where previously proposed exercises and related problems are solved. Reading suggestions, additional bibliography and other resources are available for students at the unit’s web page and FCUP library.

keywords

Physical sciences > Mathematics > Applied mathematics

Evaluation Type

Distributed evaluation with final exam

Assessment Components

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

Eligibility for exams

Not applicable

Calculation formula of final grade

1. There will be 3 quizzes throughout the semester. The first and the second will be scored on a 0-6 range and the third on a 0-7 range.

2 . A student obtaining a total sum of 9.5 from the quizzes will be exempt from taking the normal period exam. In such a case, the final grade in the class will be the rounded total sum of the scores of the 3 quizzes.For a student who completes the normal period exam, the final grade will be entirely and uniquely dependent on the exam grade. In particular, such a student may fail the class, regardless of performance in the quizzes.

Clearly, this does not apply to the non-normal period exam, which can be considered an attempt to improve a previously obtained grade.

3 - The exam will have three parts corresponding to the quizzes and with the same scores.

Examinations or Special Assignments

Not applicable.

Internship work/project

Not applicable.

Special assessment (TE, DA, ...)

Students may take a written ou an oral exam after justified requirement.

Classification improvement

Students may improve their grades through a second exam.

Observations

Attention called to Article 13th of the Regulamento Geral para Avaliação dos Discentes de Primeiros Ciclos, de Ciclos de Estudos Integrados de Mestrado e de Segundos Ciclos da U.Porto (19th May 2010).