| Code |
15851
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| Year |
1
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| Semester |
S2
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| ECTS Credits |
6
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| Workload |
TP(60H)
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| Scientific area |
Mathematics
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Entry requirements |
Not applicable
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Mode of delivery |
Lectures and practical classes with face-to-face teaching.
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Work placements |
Not applicable.
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Learning outcomes |
This course constitutes an introduction to differential and integral calculus in R^n. At the end of this curricular unit, the student must be able to:
a) Solve some first and second-order ordinary differential equations
b) Compute limits of functions of several variables.
c) Investigate the continuity of functions of several variables.
d) Compute the derivatives of functions of several variables.
e) Apply the derivatives to compute maximums and minimums.
f) Integrate functions of several variables.
g) Apply integral calculus to compute areas and volumes.
h) Solve line integrals.
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Syllabus |
1. Ordinary differential equations: separable equations; first-order linear differential equations; second-order linear differential equations with constant coefficients
2. Functions from R^n into R ^m: Brief notions of topology in R^n; Functions from R^n into R^m; Limits; Continuity
3. Differential Calculus in R^n: Partial derivatives and directional derivatives; Differentiability of functions from R^n into R^m; Derivatives of higher order; Schwarz’s theorem; Local and absolute extreme values; Extremes with constraints: Lagrange multipliers
4. Integral Calculus in R^n: Riemann integral: definition and examples; Properties of integrable functions; Change of coordinates; Applications
5. Line integrals: parameterization of curves; line integrals of scalar functions (length); line integrals of vector fields; Green's Theorem
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Main Bibliography |
- Apostol, T.M., "Cálculo", Volume 1 e 2, Reverté, 1993.
- Azenha, A., Jerónimo, M.A., Elementos de Cálculo Diferencial e Integral em R e Rn, McGraw-Hill, 1995
- Stewart, J., Cálculo, Volumes I e II, Tradução da 6a edição Norte-Americana, Cengage Learning, 2010.
- Course Slides (Moodle)
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Teaching Methodologies and Assessment Criteria |
In each weekly 2-hour lesson, the teacher in charge uses about 1 hour of class time to explain the concepts necessary for understanding the subjects taught and also indicates other sources of consultation for independent study. In the remaining time, students are encouraged to complete a list of exercises proposed by the lecturer. The teaching-learning assessment consists of 3 written tests. Attendance is included in the continuous assessment since good attendance necessarily means continuous and dedicated work on the proposed exercises. The minimum mark for admission to the exam is 5 in the teaching-learning classification.
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Language |
Portuguese. Tutorial support is available in English.
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