MS-A0211 - Differential and Integral Calculus 2, Lecture, 10.1.2023-20.2.2023
Kurssiasetusten perusteella kurssi on päättynyt 20.02.2023 Etsi kursseja: MS-A0211
Lecture 4 - 19.1.2023
Suorituksen vaatimukset
In this lecture we studied:
- Partial derivatives of functions of several variables. We defined directional derivatives and partial derivatives by using the limit definition in analogy with the one-variable case. We computed some first and second partial derivatives. We stated the theorem that f_xy = f_yx is true whenever the 2nd partial derivatives are continuous.
- Tangent plane. We reviewed the general equation of a plane through a point (a, b, c) and with normal vector <n_1,n_2,n_3>. That is, n_1(x-a) + n_2(y-b) + n_3(z-c) = 0. Then, we found the equation for the tangent plane to the surface of a function of two variables z = f(x,y) at (a,b). We computed the tangent plane in a simple example, and we gave conditions for the tangent plane to be horizontal.
- Versions of the Chain rule. We reviewed the chain rule in one variable, and we stated different versions in two variables. You can find in the folder a handwritten note with the different versions.
The notions studied in this lecture can be found in sections 12.3, 12.4 and 12.5 of Adam and Essex’s Calculus book (seventh edition).