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Presentation
Presentation
The curricular unit of Calculus I introduces the essential concepts and tools for differential and integral calculus of real-valued functions of a real variable. It is intended to extend the mathematical training acquired in secondary education by developing the capacity for abstraction and logical reasoning in formulating and solving problems, formalizing them with rigor and precision, but without neglecting the virtues of intuitive thinking. The main objective is to provide an introduction to Mathematical Analysis, showing the rigorous side of Calculus and establishing the theoretical foundations for further studies in areas of 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
ULHT41-705
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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. Sets and functions
2. Algebraic and topological notions of real numbers
3. Natural numbers and method of mathematical induction
4. Sequences
5. Real-valued functions of a real variable: limits, continuity, differentiability and integrability
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Objectives
Objectives
- Consistently apply the language of sets and functions in formulating and solving problems in Mathematics
- Solve equations and inequations in the set of real numbers
- Apply the method of mathematical induction in the demonstration of P(n) properties
- Understand the definitions of bounded sequence, monotone sequence and limit of a sequence
- Calculate limits of sequences
- Understand the definitions of limit, continuity and differentiability of real-valued functions of a real variable
- Calculate limits of real-valued functions of a real variable
- Know the techniques of primitivation by parts, by substitution and of rational functions
- Know how to apply Barrow's formula and the fundamental theorem of Calculus
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Teaching methodologies and assessment
Teaching methodologies and assessment
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
- SÁ, A. A., & LOURO, B. (2020). Cálculo Diferencial e Integral em R (2ª edição). Matcubo.
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Office Hours
Office Hours
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Mobility
Mobility
No
