Code: | EBE0007 | Acronym: | MAT2 |
Keywords | |
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Classification | Keyword |
OFICIAL | Basic Sciences |
Active? | Yes |
Responsible unit: | Population Studies |
Course/CS Responsible: | Master in Bioengineering |
Acronym | No. of Students | Study Plan | Curricular Years | Credits UCN | Credits ECTS | Contact hours | Total Time |
---|---|---|---|---|---|---|---|
MIB | 86 | Syllabus | 1 | - | 6 | 56 | 162 |
This course unit aims to familiarise students with mathematical concepts and tools to study functions of various variables, as well as to develop their analytical reasoning.
The student is expected to learn the basic ideas and main results of the subjects referred in the syllabus, as well as becoming familiar with the main tools of the classical Real analysis and Vector Analysis. In particular s/he must develop capacity at the level of differential and integral calculus to several variables.
The euclidean space. the Inner and cross products. Norm and distance.
Curves. Velocity and speed, length, normal and tangencial accelerations, curvature.
Some metric notions. Functions of several variables. Partial derivatives and the gradient. Geometry of level surfaces. Chain rule. Hight order parcial derivatives.
Taylor´s polynomial, remainder's formula. (1 or 2 variables).
Maximun and minimum: Hessian matrix and Lagrange multipliers.
The Riemann integral and Fubini´s Theorem. Multiple integrals; polar, cylindric and spherical coordinates. Change of variables and the Jacobian Matrix.
Paths, line integrals and gradient vector fields. Green's Theorem; applications.
Parametrized surfaces: geometry, area and surface integrals, orientation, induced orientation in the boundary of the surface. Flux over a surface.
The divergence and rotational operators. Stokes' and Gauss Theorems. Applications. Faraday's and Gauss laws.
The contents of the syllabus are introduced in theoretical and intuitive presentations, where a lot of examples and applications are given and discussed to illustrate the concepts and results. There are also practical lessons, where exercises and related problems, previously suggested, are solved. All resources are available for students at the unit’s web page.
Due to the aims of the course most of the results are presented with formal statement, sufficiently motivated and supported in geometric and analytical arguments. Most proofs are omitted but are available in the required bibliography.
Designation | Weight (%) |
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Teste | 100,00 |
Total: | 100,00 |
Designation | Time (hours) |
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Estudo autónomo | 106,00 |
Frequência das aulas | 52,00 |
Total: | 158,00 |
To be admitted to exams, students have to attend the tests
The syllabus will be divided into two mandatory tests, the first one worth 8 points and the second one worth 12 points (each of 2 hours long each).
The first test will be held in the mid of the semester, the second test will be held during the first season exam period. The final mark of the first season is the sum of the marks obtained in each test (equal or above 9,5).
Second season exam:
- In the second season exam, students may repeat both tests or just one of them (except when they are just trying to improve their mark upon previous approval).
- The mark of each part is the maximum of the marks obtained in the respective tests in both seasons (except when they are just trying to improve their mark upon previous approval in 2017/18).
- In cases of improvement of the classification the students approved in 2017/18 or they choose the system of compulsory evaluation during the semester and follow the general rules or they choose to perform only the second season examination and in this case they bhave to solve both parts of the exam.
- The final mark of the second season is the sum of the marks obtained in both parts, rounded to integers.
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Any other extraordinary evaluation may be preceded of an oral exam.