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Elements of Mathematics I

Code:

DVAM03

Sigla:

EM I

Áreas Científicas
Classificação	Área Científica
CNAEF	Mathematics

Ocorrência: 2021/2022 - 1S

Ativa?	Yes
Página Web:	https://moodle.ips.pt/2122/course/view.php?id=481
Unidade Responsável:	Departamento de Matemática
Curso/CE Responsável:	Professional Technical Higher Education Course in Development of Videogames and Multimedia Applications

Ciclos de Estudo/Cursos

Sigla	Nº de Estudantes	Plano de Estudos	Anos Curriculares	Créditos UCN	Créditos ECTS	Horas de Contacto	Horas Totais
DVAM	28	Plano_estudos_2018_19	1	-	6	60	162

Língua de trabalho

Portuguese

Objetivos

Providing students with the basic mathematical knowledge on real functions of a single real variable required in the professional training of a top professional technician.

Resultados de aprendizagem e competências

1. Identification of properties of functions on a real variable
2. Characterization of the inverse of a trigonometric function.
3. Interpretation of the concept of limit value and computation of such limits on functions.
4. Analysis of the continuity of a function and application of Bolzano's and Weierstrass' theorems.
5. Interpretation of the concept of derivative and computation of the derivative of a function on any point, by definition.
6. Analysis of the differentiability of a function on an open interval and application of derivation rules.
7. Application of Rolle's, Lagrange's and Cauchy's Theorems.
8. Application of Taylor's formula of a function on a point.

Modo de trabalho

Presencial

Pré-requisitos (conhecimentos prévios) e co-requisitos (conhecimentos simultâneos)

Mathematical knowledge corresponding to average secondary education, namely rational number an polynomial arithmetic, solving equations and inequalities, and elementary notions of real functions of a single real variable.

Programa

1. Real functions of a real variable
1.1. Introduction to mathematical language and logical operations.
1.2. Generalities about real functions of a real variable.
1.3. Study of inverse trigonometric functions.
1.4. Notion of limit; lateral limits; properties and operations.
1.5. Continuous functions, properties and extension by continuity.
1.6. Fundamental theorems of continuity.
2. Differential calculus
2.1. Derivative of a function: concept, geometrical perspective and physical perspective; tangent and normal straight lines at a specific point.
2.2. Lateral derivatives; differentiability and its properties; derivative rules; derivatives of composite and inverse functions; inverse trigonometric functions derivatives; differential.
2.3. Fundamental theorems of differentiation.
2.4. Derivatives of higher order; Taylor and Maclaurin formulas (with Lagrange error bound). Study of monotony, extrema and concavity of a function.

Bibliografia Obrigatória

Departamento de Matemáica ESTS; Textos de Apoio editados pelo Departamento de Matemática

Bibliografia Complementar

Tom M. Apostol; Calculus - Vol 1, Wiley International
Campos Ferreira J.; Introdução à Análise Matemática, Fundação Calouste Gulbenkian. ISBN: 972-31-0179-3
Larson R., Robert P.H., Edwards B.H.; Cálculo Vol.1, McGraw-Hill
George Thomas; Cálculo Vol.1, Pearson. ISBN: 978-85-7605-115-2

Observações Bibliográficas

The review of school textbooks corresponding to "Maths-A" of secondary school is recommended

Métodos de ensino e atividades de aprendizagem

The Curricular Unit "Elementos de Matemática I" is based on 4 hours of presential teaching activities, oriented to the presentation of the fundamental concepts of the several subjects in the syllabus, proving some of these results, and solving exercises that illustrate the subjects under consideration.

These lessons are aimed to endow the students with a global view of the specific subjects and its interconnections, using a correct and objective formulation of mathematical definitions and statements, and developing the rational deductive practice, as well as presenting some practical applications of some of various notions.

The student must embark on autonomous study, based on a reading activity of the available materials and on the autonomous practice with exercises.

The information and teaching material of the Curricular Unit will be available in the corresponding Moodle platform.


Remark: Presential teaching activities are totally executed by the co-responsible teacher.

Tipo de avaliação

Distributed evaluation with final exam

Componentes de Avaliação

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

Componentes de Ocupação

Designation	Tempo (Horas)
Estudo autónomo	102,00
Total:	102,00

Obtenção de frequência

Students have two systems for evaluation: continuous evaluation or evaluation by exam.



CONTINUOUS EVALUATION

Continuous evaluation assumes a compulsory presence in at least 75% ot presential lessons and consists on the execution of 4 Mini-tests (open answer questions)

Taking as MT1, MT2, MT3, MT4 the Mini-test results (evaluated from 0 to 5 points, rounded to the decimal point), the final score FS (rounded to units) is computed as follows:



FS = MT1 + MT2 + MT3 + MT4.



Conditions to obtain positive evaluation are:

If FS is greater or equal 10 and lower than 18, the student has positive evaluation with FS as final score, provided that MT1+MT2 and MT3+MT4 are both greater or equal to 3.5 points.
In the case that the student doesn't have positive evaluation due to conditions indicated on (1.), he/she may choose to take an alternative exam to improve the lowest of the results MT1+MT2 or MT3+MT4, provided that one of these sums is equal or greater than 3.5 points.


EVALUATION BY EXAM



Students that don't reach a positive result in the continuous evaluation may take an exam, with results in the inteber scale between 0 and 20 points, and where the positive evaluation is for those students that get 10 or more points.



In any of these evaluation systems, if the final score is greater or equal 18, the student will be subject to an additional oral exam. The final score in this case will be the mean of the written and oral evaluations. If the student does not attend the oral exam, its final score will be 17 points.

Fórmula de cálculo da classificação final

FS = MT1 + MT2 + MT3 + MT4.

FS - Final score (integer values range 0-20)

MT1 - Mini-test 1 score (values range 0-5 rounded to decimal point)

MT2 - Mini-test 2 score (values range 0-5 rounded to decimal poi3t)

MT3 - Mini-test 3 score (values range 0-5 rounded to decimal point)

MT4 - Mini-test 4 score (values range 0-5 rounded to decimal point)

Avaliação especial (TE, DA, ...)

Working Students, higher competition athletes, student associations leaders and students demanding application of Religious Freedom Laws should contact the Curricular Unit Responsible teacher on this subject, no later than two weeks after the start of the teaching activities, indicating the corresponding specific circumstances, as declared by the corresponding norms. The timely application is needed so that the corresponding measures can be applied, with the needed objective conditions.

Observações

Each mini-test has a duration of 60 minutes; The alternative exam has 90 minutes, and the exam is 2 hours and 30 minutes.
In all evaluation processes the presentation of an ID with photo is compulsory.
In all written exams student may consult an specific formula sheet provided by the teachers.
The use or merely reaching for any electronic devices during the evaluation proofs is forbidden.

Co-responsible teacher: Prof. Ana Barros, Room E-305 ESTSetúbal