Mathematical Analysis I
Keywords |
Classification |
Keyword |
OFICIAL |
Mathematics |
Instance: 2011/2012 - 1S
Cycles of Study/Courses
Teaching language
Portuguese
Objectives
This course aims to:
1) Consolidate students’ knowledge and basic techniques of real analysis to solve practical problems;
2) Develop students’ skills to handle concepts;
3) Develop student’s independent and analytical reasoning;
4) Develop students’ skills to apply mathematical concepts to the resolution of practical problems;
5) Develop students’ skills to present their reasoning and solutions in a clear and accurate way; Students should be capable of identifying techniques of differential calculation, and should also be capable of correctly applying those techniques.
CDIO Syllabus: 1.1, 1.2, 2.2, 2.3, 2.4, 3.2
Program
Program:
1- Revision of contents studied in Secondary School
a) Calculation rules. Trigonometry.
b) Numerical successions. Finite Induction.
c) Real functions of a real variable. Limits, continuity and derivation
2- Indefinite integrals
3- Definite integrals. Application to the calculation of areas
4- Improper integrals
5- First order, linear and separable variables differential equations
6- Linear differential equation of order n and constant coefficient
7- Laplace transform
8- Numerical series
9- Polynomial approximation and Taylor’s series
Mandatory literature
George F. Simmons; Calculus with Analytic Geometry, McGrawHill. ISBN: 0-07-057642-4
Stein, Sherman K.;
Calculus and Analytic Geometry. ISBN: 0-07-061175-0
Adams, Robert A.;
Calculus. ISBN: 0-201-39607-6
Larson, Hostetler e Edwards, Barcellos; Calculo, (Vols. 1,2)
Apostol, Tom M.;
Calculus
Boyce, William E.;
Elementary differential equations and boundary value problems. ISBN: 0-471-31999-6
Maria do Rosário de Pinho e Maria Margarida Ferreira; Análise Matemática 1, Apontamentos das Aulas Teóricas , 2007
Complementary Bibliography
Wylie, C. Ray Jr.;
Advanced engineering mathematics
Teaching methods and learning activities
Theoretical Classes:
Presentation of theoretical concepts, giving special emphasis to geometric interpretations and to their practical application.
The demonstration of theoretical concepts is always made, as long as it helps the understanding. After the presentation of a theoretical concept, the students will do some exercises related to that. Throughout classes, we look for the participation of the students, not only to do exercises, but also to introduce new concepts.
Theoretical-Practical Classes:
Solving exercises that illustrate and clarify the contents studied in theoretical classes.
Practical Classes:
Orientation of the study of this course and clarification of any doubts that might come up with the resolution of the proposed exercises. Division of the class into groups of 3 or 4 students. In each practical class some of the groups will be randomly chosen. Each group will have one of its elements going to solve the problem on the board. This person is also randomly chosen. The exercise will be one of a list of 3 or 4 exercises previously indicated by the teacher.
The participation in these practical classes will be a part of the continuous evaluation of this course.
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 |
93,50 |
|
|
Written test |
Exame |
1,00 |
|
|
Written test |
Exame |
1,00 |
|
|
Written test |
Exame |
1,00 |
|
|
Final exam |
Exame |
2,50 |
|
|
Solving suggested problems |
Teste |
30,00 |
|
|
|
Total: |
- |
0,00 |
|
Amount of time allocated to each course unit
Description |
Type |
Time (hours) |
End date |
Individual study |
Estudo autónomo |
87 |
2012-02-10 |
|
Total: |
87,00 |
|
Eligibility for exams
Regardless of the distributed component evaluation, any student who was not dismissed from frequency and exceeded the absence limit of practical classes (25% of the planned classes) will NOT be allowed to do this course’s exam. Furthermore, each and every student who hasn’t exceeded the absence limit will be allowed to do the exam, regardless of his classification in the distributed component.
Calculation formula of final grade
The final classification will be obtained out of the exam grade and the grade of the evaluation in practical classes, according to the following:
MAX {0.2×P + 0.8×E, E}
P represents the grade of the distributed evaluation of practical classes and E represents the grade of the exam. They both range from 0 to 20. The result will, then, be rounded to units.
Special assessment (TE, DA, ...)
The students that, in 2004/2005, have either the military status or that of working student are dismissed from frequency and from the distributed component.
Classification improvement
Classification improvement is made with a final written exam. Its result represents 100% of the final classification.
Observations
Language of instruction: Portuguese.