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Presentation
Presentation
Provides a wide range of basic mathematical knowledge, skills and tools essential for Engineering studies: describe and solve static and dynamic problems and optimize solutions on the plane; calculate lengths, areas and volumes.
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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
ULHT30-705
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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.- Real numbers. Properties of the operations with real numbers. Elements of topology. Number e.
2.- Functions. Algebra and composition of functions. Inverse function. Monotony. Trigonometric and inverse trigonometric functions. Implicit function.
3.- Limits and continuity of functions. Asymptotes. Theorems of Bolzano and Weierstrass.
4.- Derivative and differencials. Geometric interpretation. Techniques of differentiation. The chain rule. Derivative of the inverse. Implicit and parametric differentiation. Cauchy´s rule. Complete study of a function.
5.- Integral calculus in IR. The indefinite integral. Techniques of integration. Riemann´s integral. Properties. Fundamental theorem of calculus. Mean value theorem. Applications of the definite integral: lengths, areas, and volumes.
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Objectives
Objectives
Aims to deepen and develop the mastery of mathematical tools indispensable to a first degree in engineering: functional description of phenomena and analysis of their behavior; calculation of areas, length of curves, volumes of solids; techniques of minimization and maximization.
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Teaching methodologies and assessment
Teaching methodologies and assessment
Series of exercises will be proposed with the aim of consolidating knowledge and stimulating problem-solving skills. The evaluation of the discipline, expressed on a scale from 0 to 20 points, will be made at different times, including 2 midterms (40% + 50%) and individual work to be developed outside the classroom (10%). If the weighted average of these evaluations is equal to or greater than 9.5, the student will be successful in the subject, otherwise the student will be able to attend a global frequency. In the final exam, the student can improve the grade. The minimum passing grade for these assessments is also 9.5. Assessment criteria are explained at the beginning of the semester.
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References
References
Anton, H. - Calculus. 10ª ed. EUA: John Wiley & Sons, 2012
Sarrico, C. - Análise Matemática, 8ª ed. Lisboa: Gradiva, 2017
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Office Hours
Office Hours
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Mobility
Mobility
No