Code: | M1001 | Acronym: | M1001 | Level: | 100 |
Keywords | |
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Classification | Keyword |
OFICIAL | Mathematics |
Active? | Yes |
Web Page: | https://moodle.up.pt/course/view.php?id=527 |
Responsible unit: | Department of Mathematics |
Course/CS Responsible: | Bachelor in Computer Science |
Acronym | No. of Students | Study Plan | Curricular Years | Credits UCN | Credits ECTS | Contact hours | Total Time |
---|---|---|---|---|---|---|---|
L:B | 0 | Official Study Plan | 3 | - | 6 | 56 | 162 |
L:CC | 95 | Plano de estudos a partir de 2014 | 1 | - | 6 | 56 | 162 |
L:F | 0 | Official Study Plan | 2 | - | 6 | 56 | 162 |
3 | |||||||
L:G | 0 | study plan from 2017/18 | 2 | - | 6 | 56 | 162 |
3 | |||||||
L:Q | 0 | study plan from 2016/17 | 3 | - | 6 | 56 | 162 |
MI:ERS | 129 | Plano Oficial desde ano letivo 2014 | 1 | - | 6 | 56 | 162 |
To become acquainted with the basic concepts and techniques of calculus, at the level of real-valued functions of a single real variable, as well as sequences and series.
Capacity of solving calculus problems. Autonomy on the solution of exercises.
0. Generalities on functions:
Polynomial functions. Trigonometric functions. Exponential functions.
1. Limits and continuity:
Sequences of real numbers. Basic results on sequences. Real-valued functions of a real variable. Limits. Continuity. Intermediate Value Theorem and Weierstrass Extreme Value Theorem.
2. Derivatives and antiderivatives:
Derivatives. Geometric and physical interpretation of derivatives. Differentiation rules. Derivative of the inverse. Inverse trigonometric functions and their derivatives. Theorems of Rolle, Lagrange and Cauchy, L ́Hôpital’s Rule. Applications to the study of the behaviour of a function and computation of minima and maxima. Antiderivatives and antiderivatives of elementary functions. Computing antiderivatives by substitution and by parts. Antiderivatives of rational functions.
3. Integration:
Riemann’s integral. Fundamental Theorem of Calculus. Integration by substitution and integration by parts. Computation of areas. Improper integrals.
4. Polynomial approximation and series:
Taylor polynomials. Numerical series. Basic properties. Convergence tests: Leibniz, ratio and integral.
designation | Weight (%) |
---|---|
Exame | 100,00 |
Total: | 100,00 |
designation | Time (hours) |
---|---|
Estudo autónomo | 106,00 |
Frequência das aulas | 52,00 |
Total: | 158,00 |