Mathematics I

Code:

M193

Acronym:

M193

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2015/2016 - 1S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Bachelor in Geology

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:CTA	88	Plano de estudos de 2008 até 2015/16	1	-	7,5	70	202,5
L:G	67	P.E - estudantes com 1ª matricula anterior a 09/10	1	-	7,5	70	202,5
		P.E - estudantes com 1ª matricula em 09/10	1	-	7,5	70	202,5
L:Q	56	Plano de estudos Oficial	1	-	7,5	70	202,5

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

Calculus: Functions; trigonometric functions and its inverses; exponentials and logarithms; derivatives. Rolle, Lagrange and Cauchy theorems. Applications. Integration and primitives. Fundamental Theorem of Calculus. Improper integrals. Evaluation of areas, volumes of solids of revolution and the lenght of a graph.

Analysis: Differential equations of first order: separable; linear. Second order differential equations: linear, homogeneous, with constant coefficients. Examples of problems whose solution benefits from models with differential equations.

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

Recommended reading:

Adams - Calculus, a complete course

Anton, Rorres - Elementary Linear Algebra

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 will be scored on a 0-6 range and the other two 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).