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Mathematics II
Scholar Year: 2018/2019 - 2S
| Code: |
LEA06 |
|
Acronym: |
MATII |
| Scientific Fields: |
Matemática |
Courses
| Acronym |
N. of students |
Study plan |
Curricular year |
ECTS |
Contact time |
Total Time |
| EA |
3 |
|
1º |
6,0 |
75 |
162,0 |
Teaching language
Portuguese
Intended learning outcomes (Knowledges, skills and competencies to be developed by the students)
The aim of this course is to familiarize students with the mathematical method, providing them with skills to deal glibly with the mechanisms of matricial and vectorial calculus, as well as with differential calculus of functions of several variables, in order to provide them conditions to apply this knowledge in real life situations and in engineering.
Syllabus
1. Matrices
Matrix definition, special matrices. Algebraic matrix operations. Inverse matrix. Elementary operations, rank of a matrix. Linear systems. Gaussian elimination and its application to inverse matrix computation.
2. Determinants
Definition, properties and computing methods. Two applications of determinants: matrix inversion and Cramer’s Rule.
3. Eigenvalues and Eigenvectors
Definition and computation of eigenvalues and eigenvectors of a matrix. Characteristic polynomial,
algebraic and geometric multiplicities.
4. Vectorial Calculus
Definitions of inner, cross and scalar triple products. Properties and applications.
5. Differential Calculus in Rn
6. Scalar and vector fields: basic definitions. Representation of surfaces and level sets. Limits and
continuity in scalar and vector fields. Derivatives and differentiability in scalar fields. Jacobian matrix and differentiability in vector fields. Divergence and curl operators.
Teaching methodologies
Theoretical-Practical classes: theoretical exposure of the subjects followed by problems solving.
Practical classes: exercises solving.
In the theoretical-practical classes are presented the basic concepts of the different subjects of the syllabus and the proofs of the main results, followed by problems solving. In this type of classes students will acquire an overview of the themes and their interconnections.
In practical classes students will solve under the guidance of the teacher, a set of exercises, allowing them to gain a deeper understanding of the subjects discussed.
Assessment methodologies and evidences
Continuous assessment with 2 tests and/or evaluation by final examination.
Continuous Assessment
The continuous assessment consists of two tests and is subject to the following conditions:
1. To pass the student must have in each test a grade greater than or equal to 6.5 (in the scale 0-20) and an average greater than or equal to 9.5.
2. If the average of the tests (rounded to the units) is greater than or equal to 17 the student will have to take an oral test and the final grade will be the average of the classifications of the oral test and the exam (otherwise, the final grade will be
16 values).
To retrieve a test:
In order to pass a student with a score greater than or equal to 8.0 in one of the tests can retrieve one and only one of the tests. A student who has less than 8.0 in one of the tests, who was not able to perform a test or has given up in one test can only recover that test.
The recovery of a test takes place at the exact day and time of the Normal Exam and in order to do so the student must enroll in due time.
Exam-based Assessment
Students who choose not to take the continuous assessment or have not obtained approval can attend the regular exams.
The exam-based assessment is subject to the following conditions:
1. If the exam grade (rounded to the units) is greater than or equal to 10 and less than 17 the student will pass with a final grade equal to the exam grade;
2. If the exam grade is greater than or equal to 17 the student will have to take an oral test and the final grade will be the average of the classifications of oral test and the exam (otherwise, the final grade will be 16)
Observations:
• The tests last 2 hours and the exams 2 hours and 30 minutes.
• Special situations: Working Students, Athletes of High Competition, Association Leaders and Students under the Law of Religious Freedom should send an email to the Responsible Teacher (ana.matos@estsetubal. ips.pt), until the second week of the semester, to present their relevant specificity.
Dates of Evaluation Moments
Test 1: 13 de Abril, 10 a.m.
Test 2: 15 de Junho, 10 a.m.
Note: The above dates may be subject to changes that will be disclosed in due course.
1st Exam (Normal Exam): July 1, 2019, at 9:30 am.
2nd (Appeal Exam): July 15, 2019, at 9:30 am.
Special period Exam (September): Date to be defined by the Pedagogical Council.
Assement and Attendance registers
| Description |
Type |
Time (hours) |
End Date |
| Attendance (estimated) |
Classes |
0 |
|
| |
Total: |
0 |
Bibliography
Primary Bibliography
Study material edited by the Department of Mathematics (available on the UC website)
Secondary Bibliography
Giraldes, E., Fernandes, V. H. e Smith, M. P. M.;Curso de Álgebra Linear e Geometria Analítica, McGraw-Hill, Portugal,
1995
Luz, C., Matos, A. e Nunes, S.;Álgebra Linear (Volume I), ESTSetúbal, 2002
Magalhães, L. T.;Álgebra Linear como introdução à Matemática Aplicada, Texto Editora, Portugal, 1993
Laudesman, E. M. e Hestenes, M. R.;Linear Algebra for Mathematics, Science and Engineering, Prentice─Hall International, New Jersey, 1992
Apostol, T;Calculus, Vol. II, Blaisdell Publishing Company, Massachusetts, 1969
Azenha, A. e Jerónimo, M. A;Cálculo Diferencial e Integral em R e Rn, McGraw-Hill, Portugal, 1995
Observations
In order to access the study materials and all information concerning Matemática II studens must be enrolled in the ESTSetúbal E / B-Learning Platform (Moodle)
Course page on the Moodle platform:
http://moodle.ips.pt/1819/course/view.php?id=1685
Rules for taking tests and exams:
• An identification document is required during the tests.
• Enrollment for the tests and exams is mandatory, up to one week from the evaluation date, in the course page on the
Moodle platform.
• It is allowed to consult an A4 sheet, handwritten by the student himself, in the tests and exams.
• Calculation machines may not be used during the tests, nor shall tables or forms be provided.
• During the tests the handling or display of mobile phones (which should be switched off) and other electronic equipment
is not allowed.
Attendance to students in class period:
Ana Matos (E-307): Monday from 13:30 to 14:30, Tuesday from 10:00 to 10:30, Wednesday from 10:30 to 12:00
Anabela Pereira (E-354): Wednesday from 10h30 to 12:00, Thursday from 13h30 to 15:00
Patrícia Ribeiro (E-316): Wednesday from 14:00 to 15:00, Friday from 10:00 to 12:00
Paula Reis: Wednesday from 14:00 to 15:00 (E-353), Thursday from 16:30 to 17:00 (F-312), Friday from 9:00 to 10:00 (E-353) and from 11:30 to 12:00 (E-319A)
Sérgio Fernandes (E-355): Tuesday from 14:00 to 15:00, Thursday from 14:00 to 15:00
Ricardo Issa (E-307): Tuesday from 9:00 to 10:00, Thursday from 10:30 to 11:30 and from 14:30 to 15:30
Vanda Rosado (E-312): Thursday from 16:30 to 17:30
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