Mathematical Analysis I

Code:

EA0006

Acronym:

AM I

Keywords
Classification	Keyword
OFICIAL	Interp/Personal professional attitudes and capac.
OFICIAL	Design, Development, Implementation and Operation
OFICIAL	Basic Sciences

Instance: 2010/2011 - 1S

Active?	Yes
E-learning page:	http://moodle.fe.up.pt/
Responsible unit:	Mining Engineering Department
Course/CS Responsible:	Master in Environmental Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
MIEA	63	Syllabus since 2006/07	1	-	7	56	189

Teaching language

Portuguese

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.

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

Larson, Hostetler & Edwards; Cálculo, McGrawHill
Edwards, C. Henry; Calculus. ISBN: 0-13-095006-8
Piskounov, N.; Cálculo diferencial e integral

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 with final exam

Assessment Components

Description	Type	Time (hours)	Weight (%)	End date
Attendance (estimated)	Participação presencial	72,00
Mini-tests	Exame	2,00
Homework	Teste	30,00
Midle test	Exame	2,00		2010-12-10
	Total:	-	0,00

Amount of time allocated to each course unit

Description	Type	Time (hours)	End date
Test preparation	Estudo autónomo	20
Daily study	Estudo autónomo	60
	Total:	80,00

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 three tests (T1, T2, and T3). They are worth different values in the final grade, they will take place outside class time and the themes they will cover will be beforehand revealed.

Continuous assessment grade (N1) will be based on the following formula:
N1 = k*(0.20 * T1+ 0.35 * T2+ 0.45 * T3)
k- Students’ performance in theoretical and theoretical-practical classes 0.9 ≤ k ≤ 1.1.

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

Students who reached a grade of 18 or higher have to attend an oral exam.

Examinations or Special Assignments

Not applicable

Special assessment (TE, DA, ...)

An exam with a written and/or part.

Classification improvement

An exam with a written and/or part.

Observations

This course unit is complemented by a module available on e-learning.