Class Meets MWF 12:30–1:20

Room Keller Hall 303

See here for the syllabus.

## Announcements

• (5/1) The final exam will be Monday, May 6th at 12:00pm in the usual room. Here are your grades going into the final, taking into account the final homework assignments and after I dropped your lowest two homework scores.

• (4/25) Things you should know for the final:

• Fubini’s theorem, in its various forms.

• How to determine limits for regions of integration.

• How to compute double and triple integrals in rectangular coordinates.

• How to convert integrals in rectangular coordinates to polar, cylindrical, and spherical coordinates.

• How to calculate the average value of a function.

• How to calculate first moments and center of mass.

• How to use coordinate transforms to compute integrals.

• How to compute path integrals.

• How to compute flux and flow/circulation integrals.

• How to check whether a vector field is conservative, how to find a potential function for a conservative vector field, and how to evaluate a path-independent integral using a potential function.

• How to calculate gradients, divergences, and curls.

• How to use Green’s theorem.

• How to set up and compute surface integrals.

• How to use Stokes’ theorem.

• How to use the divergence theorem.

• And everything you’ve learned in Calculus I, II, and III.

• (4/25) Here is the final from last semester’s Calculus IV class. For extra practice problems, there are additional problems at the end of chapters 14 and 15 in the textbook.

• (4/23) Here are your tentative grades going into the final, by student ID. This is not 100% accurate, as it does not account for your last two homework assignments and me dropping your lowest two scores. But it should give you an idea of where you are.

• (4/17) I will be offering the chance to makeup points you lost from the second midterm. Here are six problems. They correspond to the six problems from the in-class portion of the midterm. Choose up to three problems from the midterm and do the corresponding problem. Turn them into me on Monday, April 22 to get back up to 70% of the points you lost.

• (4/4) A study guide for the second midterm is here. As a reminder, the midterm will be next Friday, April 12.

• (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 sub-selection 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.

• Week 15: (Due Monday, April 22) 15.7: 4, 11, 20, 26; Ch 14 practice exercises (p. 838): 15, 30, 36.

• Week 16: (Due Friday, April 26) 15.8: 6a, 8, 14; Ch 15 practice exercises (p. 917): 5, 18, 28, 40.

• Week 17: No homework! Review for the final!