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Fundamentals of Calculus

Code:

PA20

Sigla:

FC

Áreas Científicas
Classificação	Área Científica
OFICIAL	Matemática

Ocorrência: 2023/2024 - 1S

Ativa?	Yes
Página Web:	https://moodle.ips.pt/2324/course/view.php?id=2269
Unidade Responsável:	Departamento de Matemática
Curso/CE Responsável:	Professional Technical Higher Education Courses in Aeronautics Production

Ciclos de Estudo/Cursos

Sigla	Nº de Estudantes	Plano de Estudos	Anos Curriculares	Créditos UCN	Créditos ECTS	Horas de Contacto	Horas Totais
TSPPA	37	Plano de Estudos 2015_16	1	-	6	60	162

Língua de trabalho

Portuguese

Objetivos

The general objective of this course unit is to provide students with the basic mathematical knowledge required in the professional training of a top professional technician.

Resultados de aprendizagem e competências

By the end of term time, students should be able to:

1. Understand logical operations, their properties, quantifiers and interpret them in mathematical propositions.


2. Understand different ordered sets of numbers, the arithmetic operations and their properties.


3. Solve equations, inequalities and systems of linear equations.


4. Identify a real function and understand the elementary mathematical functions.


5. Analyse the properties of a real function and perform operations with elementary mathematical functions.


6. Calculate the derivative of a real function.


7. Apply derivatives to solve geometric, physical or real world problems.


8. Interpret and describe the characteristics of calculus objects.

Modo de trabalho

Presencial

Programa

1. Logic and set theory
1.1 Algebra of propositions. Operators, priorities and properties.
1.2 Conditions and sets; universal quantifier and existential quantifier.
1.3 Operations and relations in set theory.
1.4 Applications between sets. Injective, surjective and bijective applications.

2. Real numbers and operations
2.1 Natural numbers, integers, rational and irrational numbers.
2.2 Arithmetic operations and order relationships in real numbers.
2.3 Roots and their properties.
2.4 Powers of rational exponent and their properties.

3. Equations and inequalities
3.1 Division of polynomials and Ruffini rule; roots and multiplicity; factorization of polynomials.
3.2 Linear and quadratic equations and inequalities.
3.3 Systems of equations.

4. Real functions
4.1 Real function: graph and analytical expression.
4.2 Composition of functions and inverse function.
4.3 Monotony, extremes, concavity, parity and periodicity.
4.4 Trigonometric circle and trigonometric functions.
4.5 Piecewise functions and absolute value function.
4.6 Exponential and logarithmic functions. Power and logarithms with arbitrary base.

5. Derivative of a real function
5.1 Average variation rate of a function in an interval. Instantaneous variation rate at a point. Geometric and physical interpretation.
5.2 Derivative of a function. Derivation rules and calculation of derivatives.
5.3 Tangent and normal straight lines of a real function.

Bibliografia Obrigatória

Franco de Oliveira, A.; Lógica e Aritmética, Gradiva, 1991
Sullivan, M.; Precalculus - 11th edition, Pearson, 2020. ISBN: 978-0135189405

Bibliografia Complementar

Kelly, J.; The Essence of Logic, Prentice Hall, 1997. ISBN: 0-13-396375-6
Larson, R., Hostetler, R. P., Edwards, B. H.; Cálculo – Vol. I – 8ª edição, McGraw Hill, 2006
Rosen, Kenneth H.; Matemática Discreta e Suas Aplicações, McGraw Hill, 2010. ISBN: 978-85-7726-036-2

Métodos de ensino e atividades de aprendizagem

CU Fundamentos de Cálculo has a teaching load of 4 hours per week.

In the classes, the fundamental concepts of the different topics of the course program will be presented and the main results will be demonstrated. Students will carry out, under the guidance of the teacher, a set of exercises, with a view to a deeper understanding of the topics covered and a greater consolidation of knowledge. In class, students should acquire a global view of the themes and their interconnections, accompanied by a correct and objective formulation of mathematical definitions, the precise statement of propositions and the practice of deductive reasoning.

It will be up to the student, a posteriori, to carry out an autonomous study on the topics covered and deepen their knowledge, using the study material recommended in the CU bibliography and the support of the professor during the respective office hours.

The CU will have all the information centralized on the Moodle platform.

Tipo de avaliação

Distributed evaluation without final exam

Componentes de Avaliação

Designation	Peso (%)
Teste	100,00
Total:	100,00

Componentes de Ocupação

Designation	Tempo (Horas)
Estudo autónomo	102,00
Frequência das aulas	60,00
Total:	162,00

Obtenção de frequência

The approval in this UC (curricular unit) can be obtained through two assessment processes: Continuous Evaluation or Exam Evaluation.

CONTINUOUS EVALUATION
The Continuous Evaluation presupposes the accomplishment of 3 summative tests and, for freshmen students, a compulsory attendance of at least 75% of the classes.
Let T1 and T2 be the grades (from zero to 8 values, rounded to tenths) obtained in the first two summative tests and MT the grade (from zero to 4 values, rounded to tenths) obtained in the last summative test. The final classification CF (rounded to units) will be the plain sum of the three grades.

The approval conditions are as follows:

1. If CF is greater than or equal to 10 and less than 18, the student passes on with a final grade equal to CF, provided that both T1 and T2 are greater than or equal to 2.5 values.
   
   


2. If a student fails the approval conditions referred in point 1, the student can recover the lowest grade obtained in T1 and T2 by performing a recovery test on the date of the normal period exam, provided that T1 or T2 is greater than or equal to 2.5 values. 

EVALUATION BY EXAM
Students who have not obtained approval for Continuous Assessment may take an exam, being approved as long as they obtain a grade of 10 or higher.

NOTE: In any of the evaluation processes, whenever the final classification is greater than or equal to 18 values, the student must carried out an oral test, obtaining as a final grade the average of the classifications of the written test and of the said oral test . If the student does not attend the oral test, the final classification will be 17 values.

Fórmula de cálculo da classificação final

CF = T1 + T2 + MT
or
Exam evaluation

Avaliação especial (TE, DA, ...)

Working students, high-level athletes, association leaders and students under the Religious Freedom Law must address, until the second academic week of the semester, to the head of the Curricular Unit to present their pertinent specificities, in accordance with the terms of the respective diplomas under penalty of failure to enforce them for lack of objective conditions.

Melhoria de classificação

In this course unit passed students of this academic year may only apply to their improvement classification in the supplementary period exam.

Observações

• Each one of the first two summative tests shall be of 90 minutes, the last summative test shall be of 45 minutes, the recovery test of 90 minutes and each exam of 150 minutes.


• To perform the recovery test and/or exams, an identification document with photo has to be presented.


• During assessment tests and examinatiom, only the enquiry form given by the teacher is allowed; handling or displaying any electronic equipment is prohibited.