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Fundamentals of Calculus

Code:

PA020

Sigla:

Áreas Científicas
Classificação	Área Científica
OFICIAL	Matemática

Ocorrência: 2023/2024 - 1S

Ativa?	Yes
Página Web:	https://moodle.ips.pt/2324/course/view.php?id=2271
Unidade Responsável:	Departamento de Matemática
Curso/CE Responsável:	Professional Technical Higher Education Courses in Aeronautics Production - Centro Aeronáutico de Ponte de Sor

Ciclos de Estudo/Cursos

Sigla	Nº de Estudantes	Plano de Estudos	Anos Curriculares	Créditos UCN	Créditos ECTS	Horas de Contacto	Horas Totais
GAIR	8	Plano de Estudos 2016_17	1	-	6	60	162

Docência - Responsabilidades

Docente	Responsabilidade
Hugo Alexandre Sacristão Carrasco

Docência - Horas

Theorethical and Practical :

4,00

Type	Docente	Turmas	Horas
Theorethical and Practical	Totais	1	4,00
Theorethical and Practical	Hugo Alexandre Sacristão Carrasco		4,00

Língua de trabalho

Portuguese

Objetivos

The general objective of the UC is to provide students with the basic mathematical knowledge necessary in the professional training of a higher professional technician.

Resultados de aprendizagem e competências

At the end of the UC, the student should be able to:

Know logical operations, their properties, quantifiers and interpret them into mathematical propositions;

Recognize the different ordered sets of numbers, arithmetic operations and their properties;

Solve equations, inequalities and systems of linear equations;

Identify a real function of a real variable and recognize elementary mathematical functions;

Analyze the properties of a real function of a real variable and perform operations with elementary mathematical functions;

Calculate the derivative function of a real function of a real variable;

Apply the calculation of derivatives to solve problems of a geometric or physical nature, or real life;

Interpret and describe the characteristics of calculation 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, integer, 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 1st and 2nd degree equations and inequalities;
3.3 Systems of equations.
4. Real functions of real variable
4.1 Real function of real variable: 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 Functions defined by branches and module function;
4.6 Exponential and logarithmic functions. Power and logarithms with arbitrary base.
5. Derivatives of real functions of real variables
5.1 Average rate of variation of a function over an interval. Instantaneous rate of change at a point. Geometric and physical interpretation;
5.2 Derived function. Derivation rules and calculation of derivatives;
5.3 Tangent and normal lines to the graph of a function.

Bibliografia Obrigatória

J. Campos Ferreira; Elementos de Lógica Matemática e Teoria de Conjuntos
J. Campos Ferreira; Introdução à Análise Matemática
T. Apostol ; Calculus Vol.1
F. R. Dias Agudo; Análise Real

Métodos de ensino e atividades de aprendizagem

The UC has a teaching load of 4 hours per week. In classes, the fundamental concepts of the different topics of the discipline 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 more in-depth understanding of the topics covered and a greater consolidation of knowledge. In classes, students must acquire a global view of 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, afterwards, to carry out an independent study on the topics covered and deepen their knowledge, using the study material recommended in the UC bibliography and the support of the UC professor during their respective office hours.
The UC will have all the information and specific materials, 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

Students have two assessment systems: continuous assessment and assessment by exam.

CONTINUOUS EVALUATION
Continuous Assessment presupposes, for 1st year students enrolled for the 1st time, mandatory in-person attendance of at least 75% of academic classes and consists of carrying out 2 tests, T1 and T2 classified from zero to 8 points, and a minitest, MT classified from zero to 4 values, rounded to the nearest tenth.
The final CF classification (rounded to the nearest unit) is obtained by adding the classifications from the 2 tests and the mini-test.
The approval conditions are as follows:

If CF is greater than or equal to 10 and less than 18, the student is approved with a final grade equal to CF, as long as T1 and T2 are both greater than or equal to 2.5 values.

If the student does not obtain approval due to not meeting the conditions of point 1, the student may take, on the date of the regular examination, a make-up test to redeem the lowest classification obtained between T1 and T2, provided that one of these tests is equal to or greater than 2.5 values.

EVALUATION BY EXAM
Students who have not passed the Continuous Assessment will be able to take an exam, passing as long as they obtain a classification greater than or equal to 10 points.

In any of the assessment systems, whenever the final classification is greater than or equal to 18 points, the student must take an oral test, obtaining as a final grade the average of the classifications of the written test and the aforementioned oral test. If the student does not attend the oral test, the final grade will be 17 points.

Fórmula de cálculo da classificação final

CF = T1 + T2 + MT
or
Final Exam Classification

Avaliação especial (TE, DA, ...)

Students with worker-student status, high-competition athletes, association leaders and students under the Religious Freedom Law must go, by the second academic week of the semester, to the person responsible for the curricular unit to present their relevant specificities, in the terms set out in the respective diplomas, otherwise they cannot be executed due to a lack of objective conditions.

Melhoria de classificação

Students approved in the current academic year will only be able to improve their classification in this UC in the second exam, as long as they are duly registered in the Academic Division.

Observações

Each test will last 90 minutes, the mini-test will last 45 minutes, the recovery test will last 90 minutes and the exams will last 2 hours and 30 minutes.

To take the assessment tests, it is mandatory to present an identification document with a photograph.

During the tests, only the form provided by teachers is permitted.

During the tests, the use, handling or display of any electronic equipment is not permitted.

The tests are individual, so any type of communication or consultation with third parties during the tests is expressly prohibited, with the exception of the teacher who will be invigilating the tests.

Whenever there is a situation of fraud proven in assessment tests carried out in person or remotely in this UC, it will be canceled and the student will be subject to the application of the IPS Student Disciplinary Regulations.

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