Lecture 12


The learning goals:

  1. How to integrate in spherical coordinates? (the most important topic of the lecture)
  2. Some application for integration.
  3. Recap of the course
  4.  Exam model


1. How to integrate in spherical coordinates?

(This topic we did not have time to fully cover on Tuesday. The Lecture slide material for this is in Lecture 11)

Look the following Youtube-video  by Houston Math Prep. Note that In the video the Greek letter rho (instead of r) is used in spherical coordinates for the radius.

Read from Active Calculus Multivariable (one of the open access books, link can be found from Materials section) the section

Triple Integrals in Spherical Coordinates from Chapter 11.8. It is very good to do the activities suggested in the book.


2. Some application of the integration

Read the slides of the lecture 12. They have all the needed examples. These applications are not the core material of  the course, but show different areas mainly from physics where double and triple integrals are used.

3. Recap of the course

On the slides there are collected together all the essential topics of the course, and given some study tips. Go trough them.

4. Exam model

See the instructions for the exam in the MyCourses -page, in General section. There is one old exam and then there is Model exam, that shows you how the exam will look like at Monday without the exam questions.


Good luck for the next week exams!

Viimeksi muutettu: torstaina 15. helmikuuta 2024, 08.42