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Mathematics I
Scholar Year: 2020/2021 - 1S
| Code: |
EM11200 |
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Acronym: |
MAT |
| Scientific Fields: |
Matemática |
Courses
| Acronym |
N. of students |
Study plan |
Curricular year |
ECTS |
Contact time |
Total Time |
| EM |
97 |
|
1º |
6,0 |
75 |
162,0 |
Teaching language
Portuguese
Intended learning outcomes (Knowledges, skills and competencies to be developed by the students)
The aim of this course is to familiarize students with the mathematical method, providing them with skills to deal glibly with the mechanism of differential and integral calculus of functions of one real variable, in order to provide them the conditions to apply their knowledge in real life situations and in engineering.
Syllabus
1. Real functions of one real variable
Basic notions. Limits; properties. Continuous functions, properties, continuous extension. Intermediate-Value, Extreme-Value and inverse function theorem. Inverse trigonometric functions.
2. Differential calculus
Derivative and its interpretations; tangent and normal lines to a graph. Differentiable f., properties; differentiation rules; chain rule and inverse function theorem; derivatives of inverse trigonometric functions; differential. Rolle’s, Mean-Value and Cauchy’s Mean-Value theorem; Hospital’s rule. Higher-order derivatives; Taylor’s and Maclaurin’s formulas (Lagrange’s remainder). Monotony, local extrema, concavities.
3. Integral calculus
Antiderivatives; properties. Immediate antiderivatives. Methods: parts, substitution, decomposition. Riemann integral; properties. Indefinite integral; properties. Fundamental Theorem of Calculus, Barrow’s formula. Integration by parts and by substitution. Areas and volumes of solids of revolution. Improper integrals.
Teaching methodologies
In the theoretical-practical classes are presented the basic concepts of the different subjects of the syllabus and the proofs of the main results, followed by problems solving. In this type of classes students will acquire an overview of the themes and their interconnections.
In practical classes students will solve under the guidance of a teacher, a set of exercises, allowing them to gain a deeper understanding of the subjects discussed.
Assessment methodologies and evidences
The use of the Curricular Unit (UC) can be obtained through two evaluation processes: Continuous Assessment and Examination Evaluation.
Continuous evaluation
The continuous evaluation is based on the performance of two tests (with grades rounded to tenths). The approval conditions for continuous assessment are as follows:
1. If the average (rounded to the units) of the test scores is greater than or equal to 10 and less than 18, the student is approved with a final grade equal to said average, provided that in any of the tests the grade was higher or equal to 6.5;
2. If the average (rounded to the units) of the test scores is greater than or equal to 18, the student will have to take an oral test, the final grade being the average of these two marks. If you do not attend the oral test the final classification will be 17 values.
Retrieving one of the tests
The retrieving one of the tests is subject to possible changes in standards and the definition of the competent structures.
Examination Evaluation
The examination evaluation is based on the performance of an examination, the conditions of approval being as follows:
1. If the exam grade (rounded to the units) is greater than or equal to 10 and less than 18, the student is approved with a final grade equal to the grade of the exam (rounded to the units);
2. If the exam grade (rounded to the units) is greater than or equal to 18, the student will have to take an oral test, obtaining as a final mark the average of the classifications of said oral test and the exam. If you do not attend the oral test, the final grade will be 17 points.
Comments:
1. The tests have a duration of 2 hours and the tests 2 hours and 30 minutes, both of development and are rated on the scale of 0 to 20.
Working students, high-level athletes, association leaders and students under the Religious Freedom Act must, by the second week of the semester, contact the person responsible for the discipline, either personally or by email paula.reis@estsetubal.ips.pt , in order to present their specific characteristics, in accordance with the terms of the respective diplomas, failing which they can not be implemented due to lack of objective conditions.
Dates and times of evaluation:
Test 1: date to be defined by the Pedagogical Council
Test 2: date to be defined by the Pedagogical Council
Exam of Normal Season: date to be defined by the Pedagogical Council
Time Period Exam: date to be defined by the Pedagogical Council
Special Time Exam: date to be defined by the Pedagogical Council
Assement and Attendance registers
| Description |
Type |
Time (hours) |
End Date |
| Attendance (estimated) |
Classes |
75 |
|
|
Study |
75 |
|
| |
Total: |
150 |
Bibliography
Notes edited by the Department of Mathematics (available on the discipline page and Moodle).
Elementos de Cálculo Diferencial e Integral em R e R^n, Azenha, A., Jerónimo, M. A., McGraw Hill, 2000.
Larson, R. E., Hostetler, R. P., Edwards, B. H., Cálculo, Vol. I – 8ª edição, McGraw Hill, 2006.
Swokowski, E. W., Cálculo com Geometria Analítica, Vol. 1– 2ª edição, Makron Books, 1995.
Apostol, T, Cálculo – Vol. I – 2ª edição, Reverté, 1994.
Campos Ferreira, J., Introdução à Análise Matemática – 11ª edição, F. Calouste Gulbenkian, 2014.
Demidovitch, B., Problemas e Exercícios de Análise Matemática, Escolar Editora, 2010.
Stewart, J., Cálculo – 7ª edição, Cengage Learning, 2014.
Thomas, G. B., Finney, R. L., Cálculo, Vols. I e II – 11ª edição, Pearson-Addison Wesley, 2009.
Anton H., Bivens I., Stephen, D., Cálculo Vol. I – 10ª edição, Bookman, 2014.
Observations
Doubtful time in class:
Anabela Pereira: to de defined.
Ana Matos: to de defined.
Carla Rodrigues: to de defined.
César Fernàndez: to de defined.
Cristina Almeida: to de defined.
Dina Salvador: to de defined.
Paula Reis: to de defined;
Vanda Silva: to de defined.
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