| Code |
13403
|
| Year |
1
|
| Semester |
S2
|
| ECTS Credits |
6
|
| Workload |
TP(60H)
|
| Scientific area |
Mathematics
|
|
Entry requirements |
---
|
|
Mode of delivery |
Lectures and practical classes with face-to-face teaching.
|
|
Work placements |
Not applicable.
|
|
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.
|
|
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
|
|
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.
|
|
Teaching Methodologies and Assessment Criteria |
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. The learning evaluation consists on the realization of 2 written tests. Since a quality presence in classes means work and attention to the assigned exercises, attaining classes will help students to achieve the learning goals. There is a minimal classification of 4 values to have Exam admission.
|
|
Language |
Portuguese. Tutorial support is available in English.
|