| Code |
14630
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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 |
Mathematics A (secondary course).
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Learning outcomes |
To acquire knowledge, theoretical and practical, on the differential calculus and integral calculus in R. Apply the basic tools of mathematical analysis to treatment and resolution of problems.
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Syllabus |
1. Real Numbers: order relations; absolute value. 2. real functions of real variable: definition and examples; composition of functions; inverse of a function; graphic representation; exponential and logarithmic function; trigonometric and inverse functions; hyperbolic functions; continuous functions and fundamental properties. 3. Differential calculation in R: definition of derivative; derivation rules; derived function; higher-order derivatives; Rolle, Lagrange, Cauchy and Taylor theorems; calculation of limits; monotony and local extremes; inflection points and concavities; optimization problems; asymptotes; Taylor and Maclaurin polynomials. 4. Integral calculation in R; primitivation; Riemann integral: definitions and examples; properties of integrable functions; fundamental theorem of calculus; integration by substitution and integration by parts; geometric applications. 5. Numerical Series and Power Series: convergence criteria; Power series; Taylor series.
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Main Bibliography |
Main Bibliography:
Alberto Simões, Apontamentos de Cálculo I, UBI.
F. R. Dias Agudo, Análise Real, Vol. I, Escolar Editora, 1989.
J. Campos Ferreira, Introdução à Análise Matemática, 6ª Edição, Fundação Calouste Gulbenkian, 1995.
Tom M. Apostol, Cálculo I, Editorial Reverté, 1994.
Supplementary Bibliography:
James Stewart, Cálculo - 5ª edição, volume 1 e volume 2, CENGAGE Learning, 2008.
Lang, S., A first course in Calculus, 5th edition,Undergraduate texts in Mathematics, Springer.
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Teaching Methodologies and Assessment Criteria |
The evaluation will be periodic.
There is a minimum score of 6 values for the student to be admitted to the exam.
They will carry out 3 practical tests (T1, T2, T3).
The quotation for the various tests will be:
First test (T1): 8 values.
Second test (T2): 8 values.
Third test (T3): 4 values.
The teaching-learning (CEA) classification will be:
CEA = T1 + T2 + T3
The final classification (CF) will be:
CF = Not allowed if CEA <6
CF = E if 6 <= CEA <10
CF = CEA if CEA >= 10
being E the exam classification.
If fraudulent practice is detected in taking the tests, the student will be Not Admitted to the Exam.
Grade Defense: If the final grade in the curricular unit is higher than 17 values, the student can choose between getting a final grade of 17 values or taking a complementary test (oral and/or written) to defend the grade on a date prior to exam.
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Language |
Portuguese. Tutorial support is available in English.
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