Sumários
Cálculo diferencial
18 Abril 2023, 13:00 • Rita Sousa
[26] (TP)
Derivadas direcionais em funções com mais de duas variáveis. Máximo da derivada direcional.
14.6(8), 14.6(14), 14.6(23)
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18 Abril 2023, 11:00 • Rita Sousa
Implicit differentiation. Funtions of two variables.
Exercise 10 (CUP week 8).
Directional derivatives and the gradient vector.
Exercises 1 and 2 from CUP of week 9.
Lecture 25
18 Abril 2023, 09:30 • Rita Sousa
THEORY
- The directional derivative of a real function of two real variables at a point of its domain and along a unitary vector;
- The normalization of a non-zero vector: directional derivatives along arbitrary vectors;
- First examples: partial derivatives as directional derivatives;
- Existence of directional derivative at a point and along any unitary vector when the function is differentiable at that same point;
- Formula for the directional derivative at a point and along a unitary vector when the function is differentiable at that same point;
- Identifying the directional derivative at a point and along a unitary vector as the scalar product between this vector and a second vector (when the function is differentiable at that same point): the gradient vector of a real function of two real variables at a point.
PRACTICE
The following exercises from the CUP - Week 9 were discussed:
- Ex. 1 and 3
BIBLIOGRAPHY
Section 14.6 of James Stewart, "Calculus, Early Transcendentals", International Metric Edition, 8th Edition, 2017, Cengage Learning.