Mathematical Analysis II
| Áreas Científicas |
| Classificação |
Área Científica |
| OFICIAL |
Matemática e Informática |
Ocorrência: 2019/2020 - 2S
Ciclos de Estudo/Cursos
| Sigla |
Nº de Estudantes |
Plano de Estudos |
Anos Curriculares |
Créditos UCN |
Créditos ECTS |
Horas de Contacto |
Horas Totais |
| BIOT |
82 |
Study Plan |
1 |
- |
6 |
75 |
162 |
Docência - Responsabilidades
Língua de trabalho
Portuguese
Objetivos
The goal is to carry on developing the mathematical reasoning initiated in Mathematical Analysis I and apply it, in this case, to functions of several variables, to be able to meet the demands of other curriculum units.
Resultados de aprendizagem e competências
On completing the curriculum unit, the students should have acquired the necessary skills in differential calculus and integration of functions of several variables, including the fundamental theorems of calculus. They should also be able to solve some differential equations that appear in several applications of engineering.
Modo de trabalho
Presencial
Programa
Functions of several variables: Domains; graphs. Topological notions. Limits in R2: geometric interpretation, concept, theorems. Continuity in Rn. Directional derivatives and its geometric interpretation. Partial derivatives and its geometric interpretation. Partial derivatives of higher order. Differentiability. Theorems on differentiability. Chain rule. Stationary points in em Rn. Method of Lagrange multipliers.
Multiple integrals: Double integrals. Applications to mechanics (mass, inertia moments). Interpretation of a double integral as a volume. Change of variable (polar coordinates). Triple integrals. Change of variables (cylindrical and spherical coordinates).
Differential equations: Definitions. First order differential equations. Change of variable in differential equations. N-th order differential equations. Linear differential equations with constant coefficients: complete and homogeneous. Applications.
Bibliografia Obrigatória
Tom M. Apostol; Calculus, Vol.I , Wiley, 1967
Tom M. Apostol; Calculus, Vol.II, Wiley, 1969
A. Azenha. e M.A. Jerónimo; Cálculo Diferencial e Integral em Rn., McGrawHill
C. Ferreira; Introdução à Análise Matemática., Fundação Calouste Gulbenkian
Métodos de ensino e atividades de aprendizagem
Theoretical classes with lecturing periods with application examples followed by small tasks to be done by the students in order to consolidate the contents previously taught. Practical classes dedicated to problem solving, individually or in small groups.
The assessment will be done through a final written exam or, alternatively by student option, by three written tests.
Tipo de avaliação
Distributed evaluation with final exam
Componentes de Avaliação
| Designation |
Peso (%) |
| Teste |
100,00 |
| Total: |
100,00 |
Componentes de Ocupação
| Designation |
Tempo (Horas) |
| Estudo autónomo |
102,00 |
| Frequência das aulas |
60,00 |
| Total: |
162,00 |
Obtenção de frequência
Not applicable
Fórmula de cálculo da classificação final
Continuous evaluation:
• 3 tests: 1st test with a weight of 40%, 2nd and 3rd tests with a weight of 30%;
All with a minimum score of 6 values.
• If a final grade uses 16 or higher, an oral exam will be
required for the final grade of the student.
Exam:
• Classroom regime: 100% of the exam grade.
• Distance regime: 100% of the exam grade, if a final classification
is equal to or higher than 16 values,
an oral exam will be required, and the final classification of the student
will be carried out.
At any time during the assessment
(continuous assessment tests and final exam),
an oral test may be required from the student
(by videoconference or in person, if possible),
with specific questions on the subject evaluated, which will lead to the student's
final classification. student at the time of assessment, on a scale of 0
(zero) to 20 (twenty) values.