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# Mathematical Analysis

 Code: EIC0004 Acronym: AMAT

Keywords
Classification Keyword
OFICIAL Mathematics

## Instance: 2013/2014 - 1S (of 09-09-2013 to 20-12-2013)

 Active? Yes Responsible unit: Mathematics Section Course/CS Responsible: Master in Informatics and Computing Engineering

### Cycles of Study/Courses

Acronym No. of Students Study Plan Curricular Years Credits UCN Credits ECTS Contact hours Total Time
MIEIC 204 Syllabus since 2009/2010 1 - 6 70 162

### Teaching Staff - Responsibilities

Teacher Responsibility
Rui Paulo Soares Ribeiro

### Teaching - Hours

 Lectures: 3,00 Recitations: 2,00
Type Teacher Classes Hour
Lectures Totals 1 3,00
Rui Paulo Soares Ribeiro 3,00
Recitations Totals 8 16,00
Rui Paulo Soares Ribeiro 12,00
Jaime Duarte Rodrigues 4,00

### Teaching language

Suitable for English-speaking students

### Objectives

This course aims to acquaint students with the differential and integral calculus, in order to make them able to apply basic tools of mathematical analysis in problem solving related with subjects of this degree. This course also aims to expand students’ knowledge, so that they can solve new kinds of problems. At the end of this course, the learning outcomes are: 1. To solve derivatives of functions, draw graphics and study functions in general 2. To solve integrals and use them in various engineering applications 3. To use different integration techniques and differential equations 4. To use series and polynomials, to dominate the approximation concepts.

### Learning outcomes and competences

As a result of this course,one the students shouldbe aquainted with teh folloing matters:

1. To solve derivatives of functions, draw graphics and study functions in general

2. To solve integrals and use them in various engineering applications

3. To use different integration techniques and differential equations

4. To use series and polynomials, to dominate the approximation concepts.

Presencial

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

Knowledge of pre-calculus at the level of the high school program of Math A

### Program

1-      Differenciation

2-      Applications of differenciation

a.       Maxima, minima, function growth, concavities

b.      Graphs

c.       Applications to engineering problems

3-      Integration

a.      Indefinite integral

b.      Definite integral

c.       Fundamental Theorem

4-      Integration Techniques

5-      Application of integration

6-      Differential Equations

a.       First Order Differential Equations

b.      Second Order Differential Equations

7-      Series

a.       Convergence criteria

b.      Trigonometric series, power series ...

8-      Function approximation

a.       Taylor series

b.      Fourier series

### Mandatory literature

Apostol, Tom M.; Calculus. ISBN: 84-291-5001-3
APONTAMENTOS ELABORADOS PELO REGENTE E DISPONIBILIZADOS NO SIFEUP NA PÁGINA DA DISCIPLINA
SALLAS-HILLE-ETGEN ; CALCULUS ONE AND SEVERAL VARIABLES;WILEY
Saturnino Salas, Einar Hille, Garrett Etgen; Calculus. ISBN: 978-0471-69804-3 (or previous edition)

### Complementary Bibliography

Erwin Kreyszig; Adanced Engineering Mathematics, Wiley

### Teaching methods and learning activities

At the theoretical lectures (T) one presents and discusses the proposed program at a theoretical level with the support of applied examples. The theoretical and practical classes (TP) are intended for analysis and applied problem solving by the students. One aims to use the acquired skills in the theoretical lectures to address, and correctly solve, the typical examples and problems. This methodology allow us to evaluate the student´s skills, the level of acquired knowledge and the mathematical reasoning to solve the problems with  increasing level of complexity.

### keywords

Physical sciences > Mathematics > Mathematical analysis > Functions

### Evaluation Type

Distributed evaluation without 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 92,00
Frequência das aulas 70,00
Total: 162,00

### Eligibility for exams

In order to attend the mini-test ,the students need to to be in conformity with the general standards of evaluation of FEUP

All registered students are allowed to attend partial exams.
Students, who are repeating the course, do not need to attend classes. However, they have to attend to the mini-tests.

### Calculation formula of final grade

The final grade will be calculated taking into account the average ratings of the three mini-tests. Each mini-tests has equal weight in the final grade. In the case of an “appeal exam” on the subject of a specific mini-test, the grade obtained in the later replaces the marks obtained in the corresponding mini-test in the calculation of the final grade. In the case of a “appeal exam” on the entire matter, the student waives the classification previously obtained in the mini-tests and the final grade will be the one obtained at the “appeal exam”.

### Examinations or Special Assignments

Three assessment mini-tests (closed-book) will take place during the semester. The date, time, duration and classrooms of the assessment tests, as well as for the appeal test, will be communicated well in advance in the file “Avisos” of the discipline´s site at SIFEUP

### Special assessment (TE, DA, ...)

It will be done through special examination, provided that it is required at convenient dates. Students with special conditions (TE, DA, ..), although exempt of  classes, MUST realize the mini-tests and submit themselves to the rules of the general evaluation of the course

### Classification improvement

To the appeal exam are admitted the students who have obtained frequency, the ones that attended the mini-tests and DID NOT obtained more than 9.5 points on a scale of 0 to 20 in the weighted average of mini-tests. On appeal the student may repeat the evaluation on the subject of ONE of mini-tests of their choice, or choose for the appeal on the entire matter.

### Observations

Language of instruction is Portuguese.