Mathematical Analysis II
| Áreas Científicas |
| Classificação |
Área Científica |
| OFICIAL |
Matemática |
Ocorrência: 2020/2021 - 2S
Ciclos de Estudo/Cursos
| Sigla |
Nº de Estudantes |
Plano de Estudos |
Anos Curriculares |
Créditos UCN |
Créditos ECTS |
Horas de Contacto |
Horas Totais |
| BINF |
60 |
Study Plan |
1 |
- |
6 |
75 |
162 |
Docência - Responsabilidades
Língua de trabalho
Portuguese
Obs.: Portugês
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. 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.
Resultados de aprendizagem e competências
Not applicable
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 adouble 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, volume 2, Wiley, 1969. ISBN: 978-0-471-00007-5
Tom M . Apostol; Calculus, Wiley, 1967. ISBN: 9780471000051
Bibliografia Complementar
Acilia Azenha e Maria Amélia Jerónimo; Elementos de Cálculo Diferencial em R e Rn, McGrawHill, 1995. ISBN: 972-8298-03-X
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 two written tests each one contributing 50% to the final assessment.
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:
2 tests, with a weight of 50% each;
Exam:
100% of the exam grade.
If it is not possible to carry out the test and/or
examination in person, because of the pandemic, an
oral test may be required of all students who obtaina rating greater than or equal to 9.5 values. The
final classification will be the classification
obtained in the oral exam.