Mathematics II
Objectives
Elementary knowledge in agreement with the program.
General characterization
Code
7399
Credits
6.0
Responsible teacher
Manuel Messias Rocha de Jesus
Hours
Weekly - 6
Total - 104
Teaching language
Português
Prerequisites
The student must be familiar with mathematics taught at pre-university level in Portugal (science area).
Bibliography
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ANTON, Howard; Bivens Irl; Davis Stephen - Cálculo vol I e II, 8ª edição, Bookman, 2007.
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Bento, Murteira- Probabilidades e Estatistica volI e II, McGraw-Hill.
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Spiegel, Murray- Estatistica, McGraw-Hill, 1984.
Teaching method
In theoretical sessions the contents of the course are exposed and illustrated with examples. In problem-solving sessions students will be asked to solve problems.
Any questions/doubts are clarified during classes or tutorial sessions or even in extra sessions combined directly between student and teacher.
Evaluation method
1. FREQUENCY
Any student enrolled in the Curricular Unit (including repeat students who did not obtain attendance in the 2022/2023 academic year) who does not have, in CLIP, the status of student worker and who has been absent for more than 1/3 (one third) of the practical classes taught, he does not obtain frequency and, consequently, he fails the Curricular Unit.
For a student to take any of the tests, they will have to register in CLIP at the location and dates mentioned for that purpose. On the day of the test, the student must bring with them:
a) Identification Document.
b) Test booklet (with the header not filled in).
2. CONTINUOUS EVALUATION
Continuous assessment consists of carrying out, during the semester, 2 theoretical-practical tests, in person, lasting 90th minutes each, in the form of a written test, each of which is rated from 0 to 20 points.
Let T1 and T2 be the classifications obtained in the 1st and 2nd tests, respectively. A student can only pass the subject through continuous assessment if
0.5×T1 + 0.5×T2 ≥ 9.5
In this case, the final classification will be given by this average rounded to the nearest units.
3. EXAM
All students enrolled in the Curricular Unit can take the exam, except for students who have not obtained frequency.
The theoretical-practical exam consists of taking a written test, in person, lasting 3 hours, with a rating of 0 to 20 points.
If the classification is less than or equal to 9.4, the student fails. If the classification is greater than or equal to 9.5, the student is approved with that classification, rounded to the nearest number.
4. GRADE IMPROVEMENT
Any student who wishes to improve their grade must register for this purpose in CLIP (information in the Academic Office). The classification of the improvement exam is obtained as indicated in 3. If this result is higher than the one previously obtained in the subject, it will be taken as the final grade. Otherwise, there will be no grade improvement.
Note: scientific calculators, non-alphanumeric, non-programmable, can be used for the tests. Cannot use graphing calculators.
When carrying out any test, they must also take into account the provisions of paragraph 3 of article 10 of the FCT NOVA Assessment Regulations, “When the existence of fraud or plagiarism is proven, in any of the assessment elements of a UC, students directly involved are outright rejected in the UC (…).”
Subject matter
Applications of differential calculus
-Functions of more than one variable: partial derivatives.
-Linear regression line of a set of points.
-Errors in measurements. Maximum error propagation: estimation. Addition and multiplication. Linear approximation of a function in the neighborhood of a point in the domain. Maximum error propagation: general case of a function of several variables.
Integral Calculus
-Notion of integral of a function in an interval. Average value of a function.
-Calculation of primitives and integrals. Primitive by parts.
-Differential equations of separable variables. Problems with initial conditions.
Introduction to probability and statistics
-Discrete and continuous random variables.
-Mean, variance and standard deviation of a random variable.
-The Normal distribution.
-Sample mean, variance and standard deviation.
-Mean, variance and standard deviation of the sum and mean of random variables.
-Confidence interval for the mean of a known normal population in a sample. t-student distribution.
- Significance tests for means.
-Proportion of two classes in a population. Test to compare proportions.
-Unilateral and bilateral tests.