| Code |
12078
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| Year |
1
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| Semester |
S1
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| ECTS Credits |
6
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| Workload |
TP(60H)
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| Scientific area |
Mathematics
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Entry requirements |
None.
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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 one real variable
1.1 Topology basic concepts in R
1.2 Basic concepts of real functions of one real variable
1.3 Examples
1.4 Composition and inverse functions
1.5 Limits and continuity
1.6 Derivatives: definition and geometric interpretation. Differentiability
1.7 Derivatives of composition and inverse functions
1.8 Optimization
2. Functions from R^n to R^m
2.1 Topology basic concepts in R^n
2.2 Domains and geometrical representation
2.3 Limits and continuity
2.4 Partial and directional; Jacobian matrix
2.5 Composition function derivative. Chain rule
2.6 Implicit function theorem
2.7 Differentiability and tangent plane
2.8 Second order derivatives. Schwarz’s theorem. Hessian matrix
3. Primitives and Integral Calculus in R
3.1 Immediate primitives
3.2 Primitives by parts
3.3 Primitives by substitution
3.4 Rational function primitives
3.5 Riemann’s integral geometric interpretation
3.6 Integral Calculus Fundamental Theorem; Barrow’s rule
3.7 Applications
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Main Bibliography |
1. Stewart, James (2006), Cálculo, 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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Teaching Methodologies and Assessment Criteria |
Theoretical-practical lessons. In the first part of the lesson, the teacher exposes mathematical concepts and solves exemplary exercises. Afterwards, in the second part of the lesson, the students, by themselves, solve exercises of the bibliography, under the guidance of the teacher. The exercises are theoretical and with applications to management and economics.These exercises enable students to achieve the learning outcomes.
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Language |
Portuguese. Tutorial support is available in English.
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