Mathematical Analysis
Keywords |
Classification |
Keyword |
OFICIAL |
Mathematics |
Instance: 2009/2010 - 1S
Cycles of Study/Courses
Acronym |
No. of Students |
Study Plan |
Curricular Years |
Credits UCN |
Credits ECTS |
Contact hours |
Total Time |
MIEIC |
239 |
Syllabus since 2009/2010 |
1 |
- |
6 |
70 |
162 |
Teaching language
Portuguese
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.
Program
Revision of the contents studied in Secondary School
Polynomial function; divisibility; zeros; factorization
Rational function; simple fractions; decomposition of rational functions
Functions and derivatives (composed, inverted, continuity, graphs)
Implicit function and its derivatives
Mean value theorem (Taylor’s theorem). Applications
Anti-derivatives and integration; 1st and 2nd theorems; Average theorem; Calculation of areas
First order differential equations
Improper integrals
Numerical series
Polynomial and Taylor series
Hyperbolic functions, definition and properties; inverse hyperbolic functions
Curves; polar coordinates, length of curves, curve rotation around coordinate axis; curvature
Integration R2 and R3; double and triple integrals
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
Complementary Bibliography
Erwin Kreyszig; Adanced Engineering Mathematics, Wiley
Teaching methods and learning activities
Concepts and important results are presented in theorectical classes ,whit geometrical interpretation,with engeneering applications.Some construtive demonstrations are presented.In theorectical-practical classes,the students are guided to the resolution of selected problems.
keywords
Physical sciences > Mathematics > Mathematical analysis > Functions
Evaluation Type
Distributed evaluation without final exam
Assessment Components
Description |
Type |
Time (hours) |
Weight (%) |
End date |
Attendance (estimated) |
Participação presencial |
85,00 |
|
|
Evaluation |
Exame |
6,00 |
|
|
|
Total: |
- |
0,00 |
|
Amount of time allocated to each course unit
Description |
Type |
Time (hours) |
End date |
Personal Study (weekly) |
Estudo autónomo |
39 |
|
Preparation first examination |
Estudo autónomo |
6 |
|
Preparation second examination |
Estudo autónomo |
6 |
|
Preparation third examination |
Estudo autónomo |
12 |
|
|
Total: |
63,00 |
|
Eligibility for exams
Students have to achieve at least a 6 out of 20 in the three mini-tests, according to General Evaluation Rules of FEUP.
Students, who are repeating the course, do not need to attend classes. However, they have to attend to the tests.
Calculation formula of final grade
Final Mark will be based on the mark of the three mini-tests (1st- 6 + 2nd- 6 + 3rd- 8+4). The first and second tests will have three questions, which worth the same.
The third test will be composed by five questions, in which three of them are related with the corresponding subject (8 values= 3+3+2), and two values will be given to the question in which the students had the most difficulty to answer, while the other two questions (4 values= 2+2) will cover themes of the first and second mini-tests.
Examinations or Special Assignments
Three mini-tests will take place, and they are closed book tests. The first and second mini-test will last 90 minutes, while the third test lasts 150 minutes. If necessary, a final exam will be placed.
Students will be informed about the dates of the tests beforehand. Students should consult ‘FICHEIRO’ ‘AVISOS’ on the course page on SIFEUP.
Special assessment (TE, DA, ...)
It will take place an exam for students with a special status (working students …) that did not complete the course in the previous year.
Classification improvement
An exam, according to General Evaluation Rules of FEUP
Observations
Language of instruction is Portuguese.