Math 244: Calculus IV (Spring 2019)
Class Meets MWF 12:30–1:20
Room Keller Hall 303
See here for the syllabus.
Announcements

(2/7) The first midterm, next Friday, February 15, will be over sections 11.5, 11.6, and 14.1–14.6. Calculations you should know how to perform for the midterm:

Determine equations for lines and planes;

Compute double integrals using rectangular coordinates;

Convert double integrals into polar coordinates and compute them;

Compute triple integrals using rectangular coordinates.
Things you should know:

How to identify quadric surfaces by their graphs or equations;

The various versions of Fubini’s theorem;

The connection between multiple integrals and area/volume;

How to define first and second moments, and center of mass.
You may find it helpful to look at this midterm from last semester. (Answer key.)


(1/14) Office hours for Thursday, January 17 will be moved up one hour earlier, from 9:30 to 10:20.

Tentative exam dates:

February 15 Midterm 1

April 12 Midterm 2

May 6, 12–2pm Final Exam


Important dates:

January 15 Last day to register for a course, last day to change course grading mode.

January 30 Last day to drop a course without a W grade.

Homework
I will grade a subselection of the bolded problems.

Week 1: Stop by my office some time during office hours and introduce yourself. Please do this by Thursday, January 17.

Week 2: (Due Friday, January 18) 11.5: 1, 4, 7, 13, 18, 23, 57, 68, 71.

Week 3: (Due Friday, January 25) 14.1: 1, 3, 7, 15, 19; 14.2: 2, 10, 20, 24, 30.

Week 4: (Due Friday, February 1) 14.3: 2, 4, 5, 14, 15, 17; 14.4: 1, 2, 7, 15.

Week 5: (Due Friday, February 8) 14.4: 18, 22; 14.5: 6, 10, 22, 37; 14.6: 26 (only find the center of mass, not the moments of inertia).

Week 6: No homework, due to exam on Friday, February 15. Instead you should spend your time reviewing for the exam!

Week 7: (Due Friday, February 22) 14.7: 3, 12, 17, 32, 34, 67.

Week 8: (Due Friday, March 1) 14.8: 3, 7, 9, 17, 18, 20.

Week 9: (Due Friday, March 8) 15.1: 1–8 (you don’t need to show any work for these), 9, 12, 15, 17; 15.2: 2, 4, 14, 20.

Week 10: (Due Friday, March 15) 15.3: 2, 4, 6, 10, 14, 19, 33, 36, 37.

Week 11: Spring break!

Week 12: (Due Friday, March 29) 15.4: 4, 6, 12, 20, 24

Calculate the following, where $f(x,y,z) = x\sin(yz)$ and $\vec G = (xyz,0,x+y+z)$:

$\operatorname{div} \vec G$

$\operatorname{grad} f$

$\operatorname{curl} \vec G$

$\operatorname{grad} \operatorname{div} \vec G$

$\operatorname{div} \operatorname{grad} f$

$\operatorname{div} \operatorname{curl} \vec G$


It makes sense to take the divergence of the curl of a vector field, because $\operatorname{curl} \vec F$ is a vector field and divergence is applied to vector fields. But it doesn’t make sense to take the curl of the divergence of a vector field, because $\operatorname{div} \vec F$ is a scalar function and curl is applied to vector fields. Which of the following make sense?

$\operatorname{grad} \operatorname{curl} \vec F$

$\operatorname{curl} \operatorname{grad} f$

$\operatorname{grad} \operatorname{div} \operatorname{curl} \vec F$

$\operatorname{curl} \operatorname{div} \operatorname{grad} \operatorname{curl} \operatorname{curl} \vec F$

$\operatorname{curl} \operatorname{curl} \operatorname{curl} \operatorname{grad} \operatorname{div} \operatorname{curl} \vec F$


(It may help to think of curl, div, and grad as spam, bacon, and eggs.


Week 13: (Due Friday, April 5) 15.5: 4, 6, 14, 20, 24, 31b (use the parameterization from 31a); 15.6: 3, 13, 18.

Week 14: No homework, due to exam on Friday, April 12.