| Código |
16466
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| Ano |
1
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| Semestre |
S1
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| Créditos ECTS |
6
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| Carga Horária |
TP(60H)
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| Área Científica |
Matemática
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Mode of delivery |
Attendance
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Work placements |
Not applicable
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Learning outcomes |
The curriculum unit Mathematics I aims:
>> Specific Objectives:
1. consolidate the most important concepts related to the study of real functions of one variable, namely: limits, continuity and differentiability;
2. introduce the notion of integral and some techniques of integration of real functions of one variable;
3. extend the concepts mentioned in 1. to functions of several variables.
>> General objectives:
4. develop the ability to interpret a problem, model it and solve it with the appropriate mathematical knowledge and techniques;
5. develop the capacity of abstract and logical reasoning, and linguistic rigor.
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Syllabus |
1. Real functions of a real variable
Brief topological notions
Inverse and composition of functions
Inverse trigonometric functions
Limits and continuity
1.1 Differential calculus
Definition of derivative. Geometric interpretation. Differentiability
Derivative of the composite function and derivative of the inverse function
Cauchy's rule
Optimization
1.2 Integral Calculus
Definition and properties of the Riemann Integral
Primitive and integration techniques
Fundamental Theorem of Calculus
Applications
2. Functions with several real variables (Part I)
Brief topological notions
Domains and their geometric representation
Limits and continuity
Partial and directional derivatives.
Derivative of the composite function. Chain rule
Implicit function theorem
Differentiability and tangent plane
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Teaching Methodologies and Assessment Criteria |
Theoretical-practical classes. In the first part of the class, the teacher explains mathematical concepts and solves exercises. Subsequently, in the second part of the class, the students solve exercises from the adopted bibliography, under the guidance of the teacher.
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Main Bibliography |
1. Stewart, James (2013), Cálculo, - Volume I e II, Cengage Learning.
2. Azenha, A. e Jerónimo, M. A. (1995), Elementos de Cálculo Diferencial e Integral em R e
Rn, McGraw-Hill.
3. Pires, C. (2001), Cálculo para Economistas, McGraw-Hill.
4. Carapau, Fernando (2014), Exercícios sobre Primitivas e Integrais, Edições Silabo.
5. Hoffmann, L. e Bradley, G. (2010), Calculus for Business, Economics, and the Social and Life Sciences, McGraw-Hill.
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| Language |
Portuguese. Tutorial support is available in English.
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