Elements of Mathtematics I

Scholar Year: 2020/2021 - 1S

Courses

Head Teacher Responsability Júlia Maria da Rocha Vilaverde Justino Head Júlia Maria da Rocha Vilaverde Justino Head

Weekly workload Hours/week T TP P PL L TC THE EL OT OT/PL TPL S Type of classes 4 Lectures Type Teacher Classes Hours Theorethical and Practical classes Totals 1 4,00 Júlia Justino   4,00

Teaching language

Portuguese

Intended learning outcomes (Knowledges, skills and competencies to be developed by the students)

Provide students with the basic mathematical knowledge required in the professional training of a top professional technician.

Syllabus

1. Real Functions of Real Variable
1.1. Introduction to mathematical language and logical operations.
1.2. Generalities about real functions of real variable.
1.3. Study of inverse trigonometric functions.
1.4. Notion of limit; lateral boundaries; properties and operations.
1.5. Continuous functions, properties and continuity extension.
1.6. Fundamental theorems of continuous functions.
2. Differential Calculus in R
2.1. Notion of derivative of a function: definition and interpretations in geometric and physical terms; equations of the lines tangent and normal to the graph of a function at a point.
2.2. Lateral derivatives; differentiability and their properties; derivation rules; derived from the compound function and the inverse function; derived from inverse trigonometric functions; notion of differential.
2.3. Fundamental theorems of differentiable functions.
2.4. Derivatives of higher order; Taylor and Maclaurin formulas (Lagrange remnants). Application to the study of monotony, extremes and concavities.

Teaching methodologies

Lessons are theoretical-practical where the fundamental concepts on the different subjects of the program are presented and some exercises that illustrate the topics are solved, after which the students will carry out, under the guidance of the teacher, problem solving exercises that will allow them to consolidate knowledge on the covered topics.

Assessment methodologies and evidences

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 tests, a set of tasks regularly proposed for autonomous work, and a compulsory attendance between the tests of at least 75% of the classes.
Assigning by T1, T2 and T3 the scores (from zero to 20 values, rounded to tenths) obtained in each of the 3 tests and by TA the classification of the autonomous work (from zero to 20 values, rounded to tenth), the final classification CF (rounded to units) will be calculated as follows:

CF = 0.85x [(T1 + T2 + T3) / 3] + 0.15xTA.

The approval conditions are as follows:
1. If CF is greater than or equal to 10 and less than 17, the student is approved with a final mark equal to CF, provided that the classification in any of the tests was greater than or equal to 6.0 values.
2. If CF is less than 10, students will be able to recover a maximum of the two lowest marks by performing recovery tests on the date of the normal period exam, provided that CF is greater than or equal to 6.5 values or in some have obtained a rating of at least 9.5 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 17 values, the student must present an oral test, obtaining as a final mark 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 16 values.

Attendance system

• The Continuous Evaluation presupposes a compulsory attendance between tests of at least 75% of classes.
• 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.

Assement and Attendance registers

Primary Bibliography

Secondary Bibliography

Observations

Useful information
• Students must be enrolled in ESTSetúbal's E / B-Learning platform (Moodle 2.0), in order to have access to support materials and all information about the UC Elements of Mathematics I.
• In addition to the face-to-face component, support for students is also done in forums of questions through the Moodle platform.
• The tests last for 1 hour and the exam lasts 2 hours and 30 minutes.
• On the day of the test, before entering the room, the student will have to give the teacher a test book (totally blank). The acquisition of the test book is done previously in the reproduction.