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Presentation
Presentation
This subject comprises the fundamental methods in Calculus associated to real functions in one variable. It is a fundamental area in general engineering courses and other scientific areas. It basically comprehends the classical methods in differential and integral calculus.
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Class from course
Class from course
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Degree | Semesters | ECTS
Degree | Semesters | ECTS
Bachelor | Semestral | 6
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Year | Nature | Language
Year | Nature | Language
1 | Mandatory | Português
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Code
Code
ULHT12-1
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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. Mathematical Logic:
- Designation and proposition. Logical value of a proposition. Conjunction and disjunction of propositions. Set, intersection, and union of sets.
2. Real Numbers:
- Rational and irrational numbers. Order and absolute value.
3. Real Functions of a Real Variable:
- Generalities about functions. Polynomial and rational functions. Trigonometric functions. Exponential and logarithmic functions.
4. Limit:
- Definition and properties of function limits. Continuity of functions.
5. Derivative:
- Geometric interpretation. Rules of differentiation. Higher-order derivatives.
6. Global Study of a Function:
- Monotony and relative extrema. Concavity and inflection points. Asymptotes. Graphs.
7. Integration:
- Immediate primitive. Integration by substitution and by parts. Definite integral, fundamental theorem of calculus. Applications of integration (areas of planar figures).
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Objectives
Objectives
This subject provides students with the knowledge to use, creatively and independently, in diverse contexts:
LG1: mathematical symbolic language and mathematical reasoning;
LG2: fundamental concepts and results of differential calculus, enabling the study of real functions of a real variable;
LG3: methods to determine the primitive of a function;
LG4: fundamental notions of integral calculus, enabling the calculation of simple integrals and the determination of areas of planar domains.
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Teaching methodologies and assessment
Teaching methodologies and assessment
- At the same time new ideas are presented to the students, applications of such ideas or their geometric interpretation will be discussed.
- Students are encouraged to actively participate in the class and engage in the discussion of the presented concepts. Illustrative examples and counterexamples are provided.
- In the theoretical-practical classes, students are invited to analyze and solve problems involving the concepts presented in the theoretical classes.
- The continuous assessment consists of:
- 3 intermediate tests (A = average of the 3 intermediate tests) and
- a final test covering the entire subject (B = grade of the final test).
- The final grade (NF) in the course is calculated as follows:
- NF = 0.3*A + 0.7*B if A > B and B > 6
- NF = B if A < B or B < 6
- In the 2nd and the 3rd stages of evaluation, approval is obtained with a minimum grade of 9.5 points in the written test.
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References
References
- Lages Lima, E.; Análise Real, Vol.I (6ª ed.), Col. Matemática Universitária, IMPA, Rio de Janeiro, 2002.
- Sárrico, C.; Análise Matemática – Leitura e exercícios, Col. Trajetos Ciência 4, Gradiva, Lisboa, 1999.
- Apostol, Tom M.; Cálculo Vol.I (2ª ed.), Reverté, 1994 ISBN 9788429150155
- Guerreiro, J.S.; Curso de Análise Matemática, Escolar Editora ISBN 9789725922224
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Office Hours
Office Hours
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Mobility
Mobility
No