Mathematical Analysis I

Code:

EC0001

Acronym:

AMAT1

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2009/2010 - 1S

Active?	Yes
Responsible unit:	Mathematics Division
Course/CS Responsible:	Master in Civil Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
MIEC	355	Syllabus since 2006/2007	1	-	7	75	187

Teaching language

Portuguese

Objectives

OBJECTIVES:
Consolidate, closing some gap, the math skills acquired by students in secondary school. Develop scientific-mathematician reasoning. Understand, handle and apply the concepts of integration of real variable functions and series. Provide a base set of math skills required for the proper functioning of other course curriculum units. Develop the ability of being receptive to the application of mathematical concepts.

PREVIOUS KNOWLEDGE:
Students should have basic knowledge on real functions of a real variable, derivation, polynomials and logic.

PERCENTUAL DISTRIBUTION:
Scientific component: 100%

EXPECTED SKILLS:
At the end of the term, students should, in each of the following strands, be able to:
Knowledge: Describe the main achievements in the area of basic training of mathematical analysis, notably in the field of differential and integral calculus, numerical series and polynomial approximation of real variable functions by Taylor Polynomials. Identify the techniques to use in solving proposed problems.
Understanding: Build suitable attitude and thought for solving engineering problems.
Application: Develop a solid foundation for subsequent course units, enabling the proper use of the techniques and the rigorous formulation of problems.

Program

0. Mathematics and knowledge
1. Revision
Elements of logic, functions and relations
Set of numbers
Infinitesimal; comparison scales
Continuity of functions
2. Derivability and limited developments
3. Integration
4. Successions and numerical and functional series

Mandatory literature

Apostol, Tom M.; Calculus. ISBN: 84-291-5002-1
Sebastião e silva; Compendio de Matematica, Gep

Complementary Bibliography

Caraça, Bento de Jesus 1901-1948; Conceitos fundamentais da matemática
Departamento de Matemática; Exercios de análise matemática I e II, IST Press

Teaching methods and learning activities

All the classes are theoretical-practical, where concepts and results are presented using geometric interpretation (whenever possible) and examples. Classes may either follow an Anglo-Saxon methodology (manipulate and then define) or a continental methodology (define and then get to real situations).
Examples are presented.
Students should understand the concepts and be capable of calculating. During the semester, students will be aware of the available computer tools and their capacities and limitations. Besides, students will learn how to use them and they will also be supervised on problem solving.

Evaluation Type

Distributed evaluation without final exam

Assessment Components

Description	Type	Time (hours)	Weight (%)	End date
Attendance (estimated)	Participação presencial	90,00
	Total:	-	0,00

Eligibility for exams

Classes, which are exclusively theoretical-practical, are mandatory.
Admission to exams will be according to Article 4 of General Evaluation Rules of FEUP (Students have to attend to 75% of the classes).

Calculation formula of final grade

Final Mark will be based on two mini-tests. Each of them is divided into two parts: the first part is based on class exercises and a second part.

It will take place a new test, in order to students repeat one of the two mini-tests. Students, who want to attend to this test, have to enrol at the Secretaria do MIEC (Secretariat of the course) up to 24 hours after the results are known.

Students will also have the chance to be assessed in four classes, by doing exercises (two before the first test (CE1_2) and other two between the first and the second test (CE3_4)). These exercises will worth four values.

CE1_2 – exercises done before the first test (two values)
T1- First test (ten values)
T1= Max {CE1_2, first part of the first test} + second part of the first test (two + eight values).

CE3_4- exercises done between the first and second test (two values)
T2- Second test (ten values)
T2- Max {CE4, first part of the second test} + second part of the second test (two + eight values).

Students, who want to repeat one of the tests, will be assessed in the same way. It will be considered the maximum between the grade of the mini-test and the test that has been repeated.

FM- Final Mark- 20 values
FM- T1+T2

Examinations or Special Assignments

"Mini-test", only for the students with a final mark of 9 out of 20. This test will be an additional chance for students that are close to reach a passing mark.

Special assessment (TE, DA, ...)

SPECIAL RULES FOR MOBILITY STUDENTS: Proficiency in Portuguese; Evaluation by exam and/or coursework(s) defined in accordance with student profile.

Classification improvement

According to General Evaluation Rules of FEUP

Observations

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Working time estimated out of classes: 4 hours