| Code |
13403
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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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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 IR.I nt he end on this curricular unit the student must be able to:
a) Solving some 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) Compute implicit derivatives.
g) Integrate functions of several variables.
h) Apply the integral calculus to compute areas and volumes.
In each weekly 2 hours class, there will be part of the lesson dedicated to a theoretical approach to the program subjects. In the other part students are encouraged to solve the assigned exercises.
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Syllabus |
1. Introduction to differential equations. Separable and linear first order equations and constant coefficients second order linear equations.
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 constrains: Lagrange multipliers; Chain rule and implicit derivatives.
4.Integral Calculus in R^n: Riemann integral: definition and examples; Properties of integrable functions; Change of coordinates; Applications.
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Main Bibliography |
- Apostol,T.M., "Calculus",Volume II, John Wiley & Sons, 1968.
- Lang, S., "Calculus of Several Variables", Undergraduate Texts in Mathematics, Third Edition, Springer-Verlag,
1987.
-Stewart, J., Cálculo, Volumes 1 and 2, North American 7th edition translation, Cengage Learning, 2013.
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Teaching Methodologies and Assessment Criteria |
The learning evaluation consists on the realization of 2 written tests.
Learning evaluation grade: T1+T2
There is a minimal classification of 4 values to have Exam admission.
The only exception to this rule is for students who have already passed the course and who register to improve their grade in a subsequent academic year, in which case admission will be guaranteed.
Students who do not meet the 50% attendance requirement and do not obtain the minimum grade for Exam admission will be classified on the grade sheet with the designation NANF (Not Admitted, Did Not Attend). Exceptions to this rule are Working Students (classified as Frequência or NANAM) and students who have already passed the course and register for improvement in a subsequent year (classified as Frequência).
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Language |
Portuguese. Tutorial support is available in English.
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