Mathematical Analysis II

Code:

EEC0007

Acronym:

AMAT2

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2014/2015 - 2S

Active?	Yes
Responsible unit:	Department of Electrical and Computer Engineering
Course/CS Responsible:	Master in Electrical and Computers Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
MIEEC	311	Syllabus	1	-	8	77	216

Teaching language

Portuguese

Objectives

Aims: To develop techniques of differential and integral calculus.

This course unit aims to develop students’ skills on the manipulation of concepts of this course unit and to develop their independent and creative reasoning.

Learning outcomes and competences

Learning Outcomes:
1) To correctly apply mathematical techniques included in the program.
2) To select the appropriate mathematical tools to solve problems.
3) To clearly display techniques involved in problem solving.
4) To analyse and criticise results obtained in problem solving. CDIO Syllabus: 1.1, 2.4

 

Working method

Presencial

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

Solid background in Real analysis. Attendance of AMAT1.

Program

1. Vector functionswith  real variable: domain, graph. Continuity and derivatives. Curve and tangent vector.

2. Real functions and vector variable Domain, graph, level set of real function of vector variable Topological notions Limits and continuity; Calculation rules Rn curves Partial derivatives; Directional derivatives; Derivative of a function Relationship between derivability and continuity Gradient vector; Geometrical interpretation Normal line and tangent plan at point on the surface in R3 Higher order derivatives Implicit derivation Chain rule Taylor’s formula.

3. Functions defined in Rn: maximum and minimum Critical points; Classification of critical points Conditioned maximum and minimum; Lagrange multipliers.

4. Vector functions of vector variable Limits and continuity; Differentiability Derivative of a function at a point; Jacob matrix Inverse function theorem

5. Multiple integrals. Double and triple integrals Change of variable in multiple integrals; Polar, cylindrical and spherical coordinates.

6. Line integrals.

Mandatory literature

Maria do Rosário de Pinho, Maria Margarida Ferreira; Apontamentos das aulas teóricas de AM2, pdf na página, 2007

Complementary Bibliography

Paula Rocha; Cálculo II, Universidade de Aveiro
Roland E. Larson, Robert P. Hostetler, Bruce H. Edwards; Cálculo com geometria analítica. ISBN: 85-216-1108-0
William E. Boyce, Richard C. DiPrima; Elementary differential equations and boundary value problems. ISBN: 0-471-31999-6

Comments from the literature

Os estudantes poderão escolher qualquer das muitas obras que cobrem os contéudos. As aulas em si seguirão de perto os apontamentos de MRP e MMF assim como o livro Cálculo II de Paula Rocha.

Teaching methods and learning activities

Educational activities:
1) In theoretical and in theoretical-practical classes students should actively take part of the discussion by answering to questions and questioning the processes in the formulation and problem solving.
2) Individual resolution of exercises during theoretical-practical classes. Students should be capable of identifying the mathematical concepts involved and study the support material related to them and apply them on the resolution of exercises.
3) Resolution of self-evaluation tests.

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Designation	Weight (%)
Exame	50,00
Teste	50,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Estudo autónomo	140,00
Frequência das aulas	70,00
Total:	210,00

Eligibility for exams

To be admitted to exams, students cannot miss more classes than allowed by the rules (25% of theoretical-practical classes).

Students who attended this course in previous years can attend classes this year in a special class where attendance is optional. 

Calculation formula of final grade

Assessment components: 1) First test (T1) – March 2) Second test (T2)- April  3) Exam (E) - to be decided by the services 4) Recurso (resit) exam (R) Final Grade will be based on the tests plus exam (T1 + T2+E): T1 has a weight of 5/20, T2 has a weight of 5/20 and the final exame has a weight of 10/20.    Alternatively  the students can choose to do merely the R exam.  Students, who get approval (a weighted grade of the two tests plus final exam) are dismiised from the R exam. However they may  improve their grades in the R  exam.

Examinations or Special Assignments

To be decided in each class.

Internship work/project

N/A

Special assessment (TE, DA, ...)

Students with a special status (working students or military personnel) do not need to attend classes.

They can choose any method of evaluation.

Classification improvement

Students can improve their grades by attending the recurso R (resit) exam. It weights 20/20 of the final grade.

Observations

All tests or exams are  closed book  and students are not allowed to use calculators. It will be given a form.