| Code |
14355
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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 |
-
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Learning outcomes |
The main objectives of the curricular unit of Calculus II are: to develop skills and comprehension in differential and integral calculus in several real variables, providing the student with a range of essential tools on exact or applied sciences; to develop graphical perception and three-dimensional visualization; to introduce fundamental concepts and techniques on ordinary differential equations and their applications in mathematical modelling.
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Syllabus |
Ordinary differential equations.
First order differential equations: slope fields and integral curves; existence and unicity. Separation of variables and linear equations. Modelling with ODEs. Using power series and Laplace transforms for solving ODE. Euler’s method.
Topology and geometry in Rn.
Inner product, norm and distance. Exterior product. Polar, cylindrical and spherical coordinates. Lines and planes. Quadratic forms. Topological notions.
Differential calculus in Rn.
Scalar and vector functions. Graphs and level sets. Continuity. Partial derivatives and directional derivatives. Tangent plane. Differentiability. Higher order derivatives. Gradient. The chain rule. Taylor series. Local and constrained extrema. Implicit function theorem.
Multiple integrals.
Definition, Fubini’s theorem and change of variables. Double integrals: rectangular and polar coordinates. Triple integrals: rectangular, cylindrical and spherical coordinates. Applications.
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Main Bibliography |
[1] Stewart, J., Cálculo, Volume 2, Tradução da 7.ª edição norte-americana, Cengage Learning Edições Ltda, 2014
[2] Apostol, T., Cálculo, Volume 2, Reverté, 1994
[3] Boyce, W., DiPrima, R., Elementary Differential Equations and Boundary Value Problems, 10th Edition, John Wiley & Sons, Inc, 2012
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Teaching Methodologies and Assessment Criteria |
Classes are of theoretical and practical nature accompanied by the presentation of examples and the resolution of exercises.
ASSESSMENT CRITERIA
1. The evaluation can be made during the period of classes or in the final exam.
2. The assessment of knowledge throughout the teaching-learning period will be periodic and will consist of two written tests, each lasting 2 hours and with a quotation of 10 values, to be held on April 26 2021, and June 4 2021.
If there are impediments to conduct the assessment in person on the dates mentioned, we can opt for a single attendance at the end of the semester, which will take place on another date.
3. The student who obtained a classification equal to or higher than 9.5 in the evaluation carried out during the teaching activities will be exempted from the final exam.
4. Any attempt at fraud during an assessment test results in failure in Calculus II.
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Language |
Portuguese. Tutorial support is available in English.
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