Mathematical Analysis I

Code:

EMG0002

Acronym:

AM I

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2014/2015 - 1S

Active?	Yes
Responsible unit:	Mining Engineering Department
Course/CS Responsible:	Bachelor in Mining and Geo-Environmental Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
LCEEMG	29	Plano de estudos oficial a partir de 2008/09	1	-	6	56	162
MIEA	47	Syllabus since 2006/07	1	-	6	56	162

Teaching language

Suitable for English-speaking students

Objectives

This course unit is based on the understanding and application of a compact and synthetic operational language which is necessary to the (mathematical) development of fundamental concepts and themes during this Integrated Masters. It also acts as a link between the secondary and university education.
The themes taught in this course unit are considered a tool/language of reasoning organization, and consequently a basic support to the quantitative formulation of problems, which is a typical engineering exercise.

The aims of this course unit are:
Knowledge:
- Review of concepts such as number, function, succession, limit and derivative
- Introduction of the concept of integral;
- Operation of multivariable functions;

Comprehension:
- A coherent connection of mathematical concepts: derivative, differential and integral;
- Identification of situations of its application;
- Mathematical formulation of simple and concrete problems and operation of its symbolic representation;

Application:
- To apply the acquired knowledge in simple problems of physics and engineering in general;
- To use algebraic manipulators in the implementation and resolution of those problems.

Learning outcomes and competences

Students will be able to:
- Usef concepts such as number, function, succession, limit, derivative and integral;
- Introduction of the concept of integral;
- Operate on multivariable functions;
- Coherently connect themathematical concepts of derivative, differential and integral;
- Identify applications;
- Mathematically formulate simple and concrete problems and operation of its symbolic representation;
- Apply the acquired knowledge in simple problems of physics and engineering in general;
- Use algebraic manipulators in the implementation and resolution of those problems.

Working method

Presencial

Program

Basic concepts:
- Number, variable, function;
- Study of functions;
- Coordinate systems;
- Successions and series;
- Functions limits and continuity.

Differential calculus:
- Derivative;
- Higher- order derivatives;
- Derivation rules;
- Physical and geometrical concepts of derivative;
- Differential;
- Physical and geometrical meaning;
- Theorems of derivable functions;
- Taylor series and its use

Integral calculus:
- Concept of integral;
- Primitive;
- Indefinite integral;
- Geometrical meaning;
- Integration techniques;
- Definite integral;
- Fundamental theorem;
- Improper integrals with infinite limits or discontinuous functions;
- Applications (areas, volumes by the method of slices, arch length, centre of mass).

Functions of various variables:
- Geometrical meaning;
- First and higher order partial derivatives.

Mandatory literature

Carlos Madureira; Derivação e Integração

Complementary Bibliography

Edwards, C. Henry; Calculus. ISBN: 0-13-095006-8
Piskounov, N.; Cálculo diferencial e integral
Larson, Ron 1941-; Cálculo. ISBN: 85-86804-56-8 (vol. 1)

Teaching methods and learning activities

All the topics of the program will be taught trying to enable students to interiorise the corresponding concepts and methods, besides the formal aspects. The concepts will be orally presented and the board will be used and occasionally images of calculation machines and the computer applications referred on “Software” will be projected.
Classes should be complemented by a significant autonomous work outside class time by the students.

Software

Maxima

keywords

Physical sciences > Mathematics > Mathematical analysis

Evaluation Type

Distributed evaluation without final exam

Assessment Components

Designation	Weight (%)
Participação presencial	10,00
Teste	90,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Estudo autónomo	110,00
Frequência das aulas	52,00
Total:	162,00

Eligibility for exams

Students cannot miss more classes than allowed by the rules (there will be a attendance sheet in every class).

Calculation formula of final grade

Continuous assessment comprises four tests (T1, T2, T3,T4).

Final grade will be :
ND =  0.2 * T1+ 0.25 * T2+ 0.2 * T3 + 0.25 * T4 + 0.1 * K

k - Students’ performance in theoretical and theoretical-practical classes.

Students, who do not reach a passing grade in the continuous assessment component, have to attend a resit exam, which will be their final grade.

Students who reach a grade of 18/20 or higher have to attend an oral exam.

Special assessment (TE, DA, ...)

An exam with a written and/or oral part.

Classification improvement

An exam with a written and/or oral part.