Mathematical Analysis II

Code:

BIOT008

Sigla:

AM II

Áreas Científicas
Classificação	Área Científica
OFICIAL	Matemática e Informática

Ocorrência: 2022/2023 - 2S

Ativa?	Yes
Unidade Responsável:	Departamento de Matemática e Informática
Curso/CE Responsável:	Undergraduate in Biotechnology

Ciclos de Estudo/Cursos

Sigla	Nº de Estudantes	Plano de Estudos	Anos Curriculares	Créditos UCN	Créditos ECTS	Horas de Contacto	Horas Totais
BIOT	140	Study Plan	1	-	6	75	162

Docência - Responsabilidades

Docente	Responsabilidade
Clara Sofia Gomes Carlos

Docência - Horas

Theorethical and Practical :

4,00

Type	Docente	Turmas	Horas
Theorethical and Practical	Totais	3	12,00
	Clara Sofia Gomes Carlos		8,00
	Carlos Joel Gonçalves Cruz		4,00

Língua de trabalho

Portuguese
Obs.: Português

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 1, Wiley, 1967. ISBN: 9780471000051
Tom M. Apostol; Calculus, volume 2, Wiley, 1969. ISBN: 978-0-471-00007-5

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 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	87,00
Frequência das aulas	75,00
Total:	162,00

Obtenção de frequência

Not applicable

Fórmula de cálculo da classificação final

Continuous evaluation:
3 tests(T) each and mandatory attendance at 80% of classes.

Final Classification (CF):
CF=0,40T1+0,30T2+0,30T3

Exam:
100% of the exam grade.

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