**Course: MATH 32B, Calculus of Several Variables**, Lecture 3,
Winter 2015

**Prerequisite:** MATH 31B and MATH 32A, with grades of C- or
better..

**Course Content:** Introduction to integral calculus of several
variables, line and surface integrals.

**Syllabus:** Here.

*Last update:* 25 February 2015

**Instructor:** Steven Heilman, heilman(@-symbol)ucla.edu

**Office Hours:** Mondays, 10AM-12PM, Wednesdays, 1PM-2PM, MS
7370

**Lecture Meeting Time/Location:** Monday, Wednesday and Friday,
2PM-250PM, Rolfe 1200

**TA:** Ohrt, C. J., cohrt(@-symbola)ucla.edu; Shani, A.,
assafshani(@-symbol)ucla.edu; Keneda, J., jkeneda(@-symbol)math.ucla.edu

**TA Office Hours:** Ohrt: Tuesdays 12PM-1PM, Thursdays 3PM-4PM, MS
3915E; Keneda: Tuesdays and Thursdays, 11AM-12PM, MS 2951; Shani: Thursdays
3PM-4PM, MS 2344

**Discussion Session Meeting Time/Location:**

- 3A, Tuesday, 2PM-250PM, MS 5137. Ohrt, C. J. www.math.ucla.edu/~cohrt
- 3B, Thursday, 2PM-250PM, Royce 160. Ohrt, C. J. www.math.ucla.edu/~cohrt
- 3C, Tuesday, 2PM-250PM, PAB 1749. Shani, A. www.math.ucla.edu/people/grad/assafshani
- 3D, Thursday, 2PM-250PM, PAB 1749. Shani, A. www.math.ucla.edu/people/grad/assafshani
- 3E, Tuesday, 2PM-250PM, PAB 1434A. Keneda, J. T. www.math.ucla.edu/~jkeneda/teaching.html
- 3F, Thursday, 2PM-250PM, PAB 1434A. Keneda, J. T. www.math.ucla.edu/~jkeneda/teaching.html

- My email address for this course is heilman(@-symbol)ucla.edu.
- It is your responsibility to make sure you are receiving emails from heilman(@-symbol)ucla.edu, and they are not being sent to your spam folder.
- Do NOT email me with questions that can be answered from the syllabus.
- Homework questions sent to me by email will be answered altogether in the form of a "digest." I will get to every question, but I cannot reply to every email. This digest will be sent out typically two days before the homework is due.

- Late homework is not accepted.
- You may not use the internet to try to find answers to homework problems.
- The lowest two homework scores will be dropped. This policy is meant to account for illnesses, emergencies, etc.
- Do not submit homework via email.
- There will be 9 homework assignments, assigned weekly on Friday
and turned
in at the
**beginning**of class on the following Friday. In the second and eighth week of the quarter, the homework will not be turned in, and instead there will be quiz in the discussion section. - A random subset of the homework problems will be graded each week. However, it is strongly recommended that you try to complete the entire homework assignment.
- Collaboration on the homeworks is allowed and encouraged.
- All homework assignments must be
**written by you**, i.e. you cannot copy someone else's solution verbatim. - Label your homework with the lecture number and discussion section number.
- Homework solutions will be posted ... (time)
- Reading the syllabus counts as one homework grade. In order to receive credit for reading the syllabus, you must read the syllabus by January 9th, noon, PST.

- There will be two quizzes, administered in the second and sixth weeks of class. In the second and sixth weeks of class, the homework will not be turned in, and instead, the quiz will count for the homework grade. The problems from the quiz will closely resemble or be identical to problems from the homework from that particular week.
- Quizzes will be administered in your discussion section, which is on either Tuesday or Thursday. Each quiz should last about 15 minutes.

- The final grade is weighted as the larger of the following two schemes. Scheme 1: homework (15%), the first midterm (20%), the second midterm (25%), and the final (40%). Scheme 2: homework (15%), largest midterm grade (35%), final (50%). The grade for the semester will be curved. However, anyone who exceeds my expectations in the class by showing A-level performance on the exams and homeworks will receive an A for the class.
- We will use the MyUCLA gradebook.
- If you cannot attend one of the exams, you must notify me within the first two weeks of the start of the quarter. Later requests for rescheduling will most likely be denied.
- You must attend the final exam to pass the course.

** Tentative Schedule**: (This schedule may change slightly during the course.)

Week | Monday | Tuesday | Wednesday | Thursday | Friday |

1 | Jan 5: 16.1, Integrals in two variables | Jan 7: 16.2, Integrals over general regions | Jan 8 | Jan 9: Homework 1 due. 16.3, 12.3, Polar coordinates | |

2 | Jan 12: 16.4, 13.7, Integrals in polar coordinates | Quiz in section | Jan 14: 16.2, 16.3, Triple integrals | Quiz in section | Jan 16: Homework 2 (ungraded). 16.4, Cylindrical and spherical coordinates |

3 | Jan 19: No class | Jan 21: 16.5, Applications of multiple integrals | Jan 22 | Jan 23: Homework 3 due, 16.6, Change of variables | |

4 | Jan 26: Midterm #1 | Jan 28: 16.6, Change of vars, 17.1, Vector Fields | Jan 29 | Jan 30: Homework 4 due. 17.2, Scalar line integrals | |

5 | Feb 2: 17.2, Vector line integrals | Feb 4: 17.3, Conservative Vector Fields | Feb 5 | Feb 6: Homework 5 due. 17.3, Conservative Vector Fields | |

6 | Feb 9: 17.4, Parametric Surfaces | Quiz in section | Feb 11: 17.4, Surface Area, Surface Integrals | Quiz in Section | Feb 13: Homework 6 (ungraded). 17.5, Surface Integrals of Vector Fields |

7 | Feb 16: No class | Feb 18: 18.1, Green's Theorem | Feb 19 | Feb 20: Homework 7 due, 18.1, Green's Theorem | |

8 | Feb 23: 18.2, Stokes' Theorem | Feb 25: 18.2, Stokes' Theorem | Feb 26 | Feb 27: No homework due. Midterm #2 | |

9 | Mar 2: 18.2, 18.3, Stokes' Theorem, Divergence Theorem | Mar 4: 18.3, Divergence Theorem | Mar 5 | Mar 6: Homework 8 due. 18.3, Divergence Theorem | |

10 | Mar 9: Leeway/review | Mar 11: Leeway/review | Mar 12 | Mar 13: Homework 9 due. Review of course |

**Advice on succeeding in a math class:**

- Review the relevant course material
**before**you come to lecture. Consider reviewing course material a week or two before the semester starts. - When reading mathematics, use a pencil and paper to sketch the calculations that are performed by the author.
- Come to class with questions, so you can get more out of the
lecture. Also, finish your homework at
least
**two days**before it is due, to alleviate deadline stress. - Write a rough draft and a separate final draft for your homework. This procedure will help you catch mistakes.
- If you are having difficulty with the material or a particular homework problem, review Polya's Problem Solving Strategies, and come to office hours.

- (removed)

- 32B Lecture Notes (typos fixed 01/28/2015)