# Math 21a - Homework

Here is the homework policy in a nutshell:
• Homework must be turned in to your CA at the start of section. If you miss a class, you are responsible for getting it to your CA on time. (It's a good idea to let your CA know how you intend to do this, to avoid miscommunications.)
• Late homework is never accepted.
• Your lowest homework score will be dropped at the end of the semester. (You can earn additional homework drops by taking quizzes in problem session.)
• You are welcome to work with other students. However, you should only turn in work that you understand yourself, and that you have written up yourself and explained in your own words. Any help you receive must be acknowledged.

Hour and topic Assignment Relevant reading Due date Solutions
0. Warm-Up Problem Set 0

Here are the Mathematica files you'll need for some of the problems:

(You can also find PDF versions of the last two handouts on the Handouts page.) M 9/10 Solutions
1. Visualizing Functions of Two Variables Problem Set 1
W 9/12 Solutions
2. Surfaces in $$\mathbb{R}^3$$ Problem Set 2 Strategies for Sketching Surfaces, §9.6, Dimension F 9/14 Solutions
3. Polar, Cylindrical, and Spherical Coordinates Problem Set 3 Polar Coordinates, §9.7 M 9/17 Solutions
4. Partial Derivatives Problem Set 4
If you're feeling pressed for time because of the mini-exam, you may turn this in with PS 5 (on F 9/21). But please start it before Wednesday so that you don't have to do 2 full problem sets between Wednesday and Friday!
§11.3 W 9/19 Solutions
5. Double Integrals Problem Set 5 Double Integrals F 9/21 Solutions
6. Calculating Double Integrals over General Regions Problem Set 6 Review Suggestions, Double Integrals, Vectors M 9/24 Solutions
7. Double Integrals in Polar Coordinates Problem Set 7 §12.4 through Example 1, Vector operations W 9/26 Solutions
8. Triple Integrals Problem Set 8 §12.7 F 9/28 Solutions
9. Triple Integrals, Continued Problem Set 9 §12.8 M 10/1 Solutions
10. Vector Fields and Lines Problem Set 10 Vectors (or §9.2), §13.1 through Example 5, §9.5 through Example 3 W 10/3 Solutions
11. The Dot Product and Planes Problem Set 11 §9.3 and the Planes part of §9.5 through Example 4 F 10/5 Solutions
12. The Cross Product Problem Set 12 §9.4 through Example 5 and the Planes section of §9.5 W 10/10 Solutions
13. Vector-Valued Functions (Parametric Curves) Problem Set 13 §10.1 - 10.3 through Example 2 on pg. 709 F 10/12 Solutions
14. Parametric Curves and Parametric Surfaces Problem Set 14 §10.1 (especially Examples 5 and 6), 10.5 To give you flexibility in studying for the exam, you may turn this in either M 10/15 or W 10/17 Solutions
15. 2-Dimensional Curl There is no Problem Set 15! (This material will be on Problem Set 16.) in-class worksheet
16. Parametric Surfaces, Continued Problem Set 16 §10.5 F 10/19 Solutions
17. Surface Area and Scalar Surface Integrals Problem Set 17 §12.6 through Example 1 and §13.6 through Example 1 M 10/22 Solutions
18. Line Integrals Problem Set 18 §18.1, 18.2 from Calculus by Hughes-Hallett W 10/24 Solutions
19. Directional Derivatives Problem Set 19
§11.6 F 10/26 Solutions
20. Tangent Planes and Linear Approximation Problem Set 20 §11.4 but skip the part on differentials M 10/29 Solutions
21. Calculating Directional Derivatives, The Gradient Problem Set 21 §11.6 W 10/31 Solutions
22. Using the Gradient, The Chain Rule Problem Set 22 §11.5 through Example 7 F 11/2 Solutions
23. Maxima and Minima Problem Set 23
Updated 11/2 to clarify wording in #2 and add a Mathematica tip.
§11.7, (optional) Why is the Second Derivative Test true? M 11/5 Solutions
24. Lagrange Multipliers Problem Set 24 §11.8 You may turn this in either W 11/7 or F 11/9 Solutions
25. Exam 2 Review There is no Problem Set 25.
26. More Optimization Problem Set 26 §11.7 and 11.8 M 11/12 Solutions
27. Flux Integrals Problem Set 27 §13.6 W 11/14 Solutions
28. Flux Integrals, Continued Problem Set 28 §13.6 F 11/16
29. Gradient vector fields Problem Set 29 Conservative Vector Fields or §13.3 through Theorem 5 M 11/19
30. Green's Theorem Problem Set 30 §13.4 M 11/26

Note: Solutions to in-class worksheets can all be found on the worksheets page.