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Presentation
Presentation
The Calculus II curricular unit introduces the essential concepts and tools of differential and integral calculus of functions from Rn in Rm, generalizing many of the topics on real functions of a real variable covered in the Calculus I curricular unit. We aim to extend the mathematical training started in the first semester through the development of the ability to abstract and logical reasoning in formulating and solving multidimensional problems, formalizing them with rigor and precision, but without neglecting the virtues of intuitive thinking. The main objective is to provide an introduction to multidimensional Mathematical Analysis, showing the rigorous side of Calculus and establishing the theoretical foundations for further studies in Science and Engineering.
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Class from course
Class from course
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Degree | Semesters | ECTS
Degree | Semesters | ECTS
Bachelor | Semestral | 5
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Year | Nature | Language
Year | Nature | Language
1 | Mandatory | Português
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Code
Code
ULHT41-714
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Prerequisites and corequisites
Prerequisites and corequisites
Not applicable
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Professional Internship
Professional Internship
Não
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Syllabus
Syllabus
1. Space Rn 2. Curves and paths 3. Real functions of several real variables 4. Vector functions of several real variables 5. Line integrals of scalar fields 6. Line integrals of vector fields 7. Double integrals of scalar fields
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Objectives
Objectives
- Know the algebraic, topological and geometric structures of Rn - Parameterize a curve in Rn from its cartesian equation - Know some cartesian equations of conics and quadrics - Understand the concepts and definitions related to functions from Rn to Rm: limits, continuity, partial derivatives, directional derivatives and differentiability - Apply the chain rule in a context of functions with several variables - Determine and classify the local extrema of a real function of several variables - Compute line integrals of scalar fields and vector fields - Know how to use line integrals in applications to Physics - Compute double integrals using Fubini's theorem - Find an appropriate change of variables and apply the change of variables formula for double integrals - Apply Green's theorem in the resolution of problems involving line integrals and double integrals - Compute volumes limited by the graph of a continuous function
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Teaching methodologies
Teaching methodologies
Creation and availability of short videos on topics related to the subject taught, as well as historical curiosities, playful problems and applications to the real world.
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References
References
- SARRICO, C. (2009). Cálculo Diferencial e Integral para Funções de Várias Variáveis. Esfera do Caos.
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Assessment
Assessment
Teste 1 (50%) + Teste 2 (50%) ou Prova Global (100%) ou Exame de Recurso (100%)
A avaliação contínua consiste na realização de dois testes e/ou de uma prova global. A nota de avaliação contínua é calculada como o máximo entre a média aritmética dos dois testes e a nota da prova global.
A classificação de cada teste será considerada atá às décimas e o arredondamento às unidades só será feito na média aritmética das duas classificações.
Para obter aprovação à unidade curricular, é necessário que a nota de avaliação contínua ou do exame de recurso seja maior ou igual a 9,5 valores. Em cada teste ou no exame de recurso o aluno pode ser chamado para uma prova oral, em qualquer circunstância e sem restrições, para confirmar a nota perante o docente.
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Mobility
Mobility
Yes
