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Calculus I

Code 14630
Year 1
Semester S1
ECTS Credits 6
Workload TP(60H)
Scientific area Mathematics
Entry requirements Mathematics A (secondary course).
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.
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.
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.
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.
Language Portuguese. Tutorial support is available in English.
Last updated on: 2022-02-11

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