Code: | M111 | Acronym: | M111 |
Keywords | |
---|---|
Classification | Keyword |
OFICIAL | Mathematics |
Active? | Yes |
Responsible unit: | Department of Mathematics |
Course/CS Responsible: | Bachelor in Physics |
Acronym | No. of Students | Study Plan | Curricular Years | Credits UCN | Credits ECTS | Contact hours | Total Time |
---|---|---|---|---|---|---|---|
L:AST | 15 | Plano de Estudos a partir de 2008 | 1 | - | 7,5 | - | |
L:F | 48 | Plano de estudos a partir de 2008 | 1 | - | 7,5 | - | |
L:M | 108 | Plano de estudos a partir de 2009 | 1 | - | 7,5 | - | |
MI:EF | 59 | Plano de Estudos a partir de 2007 | 1 | - | 7,5 | - |
To learn the basic concepts of the Differential and Integral Calculus about functions of one real variable.
The student should know the basic concepts of Real Analysis of functions in one variable. More precisely, the concepts of convergent sequence, derivative, primitive, integral, and Taylor series will be studied. It is also intended that this unit will make the students work more rigorously with concepts that, thus far, were introduced only in an intuitive way (area, for instance).
Sequences. Limits. Continuity of real functions of a real variable. Bolzano and Weierstrass theorems. Inverse trigonometrical functions. Derivatives. Local extrema. The Taylor polynomial. Anti-derivatives. The Riemann integral and its basics properties. The fundamental theorem of Calculus. Improper integrals (possibily only the case that is necessary for integral criterion for the convergence of series). Numerical series and power series: convergence criteria. Sequences and series of real functions of a real variable: pointwise and uniform convergence; convergence criteria; series of continuous functions.
The contents of the syllabus are presented in the lectures, where examples are given to illustrate the concepts. There are also practical lessons, where exercises and related problems are solved. All resources are available for students at the unit’s web page.
designation | Weight (%) |
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Exame | 50,00 |
Teste | 50,00 |
Total: | 100,00 |
The regular evaluation will be based on two tests (08/11 and 20/12) and a final examination, the classification distributed over five points in each test 10 and in the final exam.
To qualify for the second test, the student must obtain at least one point in the first test and to qualify for the final examination, the student must obtain at least one point in the second test, should still get 4 values in the sum of the two tests. In the final examination the student must obtain at least 4 values.
There will be an extra exam available to any student who has not passed in the regular evaluation.
Students with more than four absences to practical classes will be excluded for fouls.