Dave's Web Corner

MTH-261 Week 10 (October 27-November 2)

recommended exercises
- 5, 9, 11, 17, 19, 21, 23, 25, 29
learning objectives
- evaluate a triple integral by changing to cylindrical coordinates
additional notes
- visualizing symmetry when converting to cylindrical coordinates
- converting integrands and limits of integration
  - the cylindrical and spherical transformation triangles
- the price of conversion
  - rectangular: \( dV=dx\,dy\,dz \)
  - cylindrical: \( dV=r\,dr\,d\theta\,dz \)
  - spherical: \( dV=\rho^{2}\sin\phi\,d\rho\,d\phi\,d\theta\)

recommended exercises
- 3, 7, 9, 11, 13, 15, 17, 23, 25, 29, 39, 40, 46
learning objectives
- evaluate a triple integral by changing to spherical coordinates
additional notes
- visualizing symmetry when converting to spherical coordinates
- converting integrands and limits of integration
  - the cylindrical and spherical transformation triangles
- the price of conversion
  - rectangular: \( dV=dx\,dy\,dz \)
  - cylindrical: \( dV=r\,dr\,d\theta\,dz \)
  - spherical: \( dV=\rho^{2}\sin\phi\,d\rho\,d\phi\,d\theta\)

Deadlines
- All homework is due at the beginning of class on the date indicated.
- All exams are given in class on the date indicated.
- Late homework is not accepted and there are no make-ups for missed exams. Contact me before the deadline if you have a conflict with a deadline and we will find a mutually agreeable solution.
- Solutions are posted under these links after the deadline.
Homework
- due Thursday, October 31:
  - 15.4 - , 15.5 - , 15.6 -
- due Tuesday, November 5:
  - 15.7 - , 15.8 - , 15.9 -
- due Thursday, November 14:
  - (none)
Exams
- Thursday, November 7: Exam 2
  - Exam 2 (solutions)
  - Exam 2 covers sections 14.4-14.8 and 15.1-15.7