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 12 - 16.2.2023
In this lecture we studied:
- Triple integrals - Change of variables:
We recalled changes of variables in general and that dV is given by multiplication by the absolute value of the determinant of the Jacobian matrix. We then considered two important particular cases: cylindrical and spherical coordinates.
Cylindrical coordinates. We defined cylindrical coordinates, this is the extension of polar coordinates with z added. We computed the determinant of the Jacobian matrix. We did a volume computation example in cylindrical coordinates.
Spherical coordinates. We defined spherical coordinates. We computed the determinant of the Jacobian matrix. We found the volume of a sphere of radius a and also the volume of a "cap" of a sphere by using triple integral in spherical coordinates.
The notions studied in this lecture can be found in section 14.6 of Adam and Essex’s Calculus book (seventh edition).