**Class meets at:** Goldsmith 317,
TF 12:30-1:50 PM (block J)

**Lecturer:** Dmitry Kleinbock

**Office:** Goldsmith 207, phone 6-3059

**Office Hours:** MTh 2-3:30 PM

**E-mail address:** kleinboc@brandeis.edu

**Graders:** Matthew Cordes mcordes@brandeis.edu, office hours: Mon
1-2 PM in Goldsmith 306;

Yurong Zhang ray8511@gmail.com, office hours: Wed 2-3, Goldsmith 116

**Class Home Page:**
http://people.brandeis.edu/~kleinboc/20a/intro.html

**Syllabus in PDF:**
http://people.brandeis.edu/~kleinboc/20a/math20as12-syllabus.pdf

**Text:** Multivariable Calculus, Concepts & Contexts, 4th edition, by James Stewart,
Brooks/Cole. We will
cover Chapters 9-13 with some omissions.

Quiz 1: Friday, February 10, covering
Sections 9.1-9.7 and 10.1-10.2; Solutions (PDF)

Midterm 1: Tuesday, February 28, covering
Sections 9.1--11.4; Review Sheet (PDF) Solutions (PDF)

Quiz 2: Tuesday, March 6, covering
Sections 11.2-11.4; Solutions (PDF)

Quiz 3: Friday, March 23, covering
Sections 11.5-11.8; Solutions (PDF)

Quiz 4: Tuesday, April 3, covering
Sections 12.1-12.3; Solutions (PDF)

Midterm 2: Tuesday, April 17, covering
Sections 11.5--12.3; Review Sheet (PDF) Solutions (PDF)

Quiz 5: Tuesday, April 24, covering
Sections 12.4-12.8; Solutions (PDF)

Quiz 6: Tuesday, April 31, covering
Sections 13.1-13.3; Solutions (PDF)

**FINAL**: Wednesday, May 9, 1:30 PM, covering
everything up to section 13.4; Review Sheet (PDF)

**Homework** assignments and deadlines:

1 |
Read Sections 9.1-9.3; Problems 7, 8, 14, 24, 31 in Section 9.1 (for the last two, draw a picture of the region); 6ce, 10, 16, 17, 22 in Section 9.2; 4, 7, 10 in Section 9.3 (there will be more on this section on the next assignment). |
January 24 |

2 | Problems 22, 30, 33, 34 in Section 9.3; 8, 9, 16, 20, 22 in Section 9.4; 2, 3, 8, 25, 26, 38 in Section 9.5. | January 31 |

3 | Problems 2, 7, 8, 15, 16 in Section 9.6; 4, 6, 8, 17, 18, 26 in Section 9.7; 6, 9, 16, 19-24 in Section 10.1. | February 7 |

4 |
Problems 4, 10, 16, 24, 34, 38 in Section 10.2;
2, 3, 14 (here the first step should be to find the arc length function s(t), i.e. the length of the curve between 0 and t, as a function of t) in Section 10.3; 12, 16(a), 17 in Section 10.4. |
February 14 |

5 | Problems 22, 24 in Section 10.3; 18, 28 in Section 10.4; 19, 20, 30 (only the equation is required, but feel free to try the graph) in Section 10.5; 5, 20, 23 in Section 11.1; 5, 7 in Section 11.2; 16, 24, 40 in Section 11.3. | February 28 |

6 | Read Sections 11.4-11.5; Problems 28, 30, 41, 54, 56, 60 in Section 11.3; 4, 6, 14, 19, 42 in Section 11.4; 2, 6, 14, 36 in Section 11.5. | March 6 |

7 |
Problems 22, 27, 30, 41 in Section 11.5;
10, 11, 16, 22, 23, 26, 30, 39, 41, 44 (the normal line can be in either symmetric or parameterized form), 50 in Section 11.6. Note that in some of the problems in 11.6, to get the directional derivative in the direction of some vector v, you may have to rescale it to make it into a unit vector. |
March 13 |

8 | Read Sections 11.7-11.8; Problems 2, 4, 6, 10, 13, 17, 27, 30, 31, 38 in Section 11.7; 4, 6, 9, 12 in Section 11.8. | March 20 |

9 | Problems 43, 46 in Section 11.7 (use a method of your choice); 18, 19 in Section 11.8; 12, 14 in Section 12.1; 4, 8, 14, 16, 20, 21 (choose the order of integration carefully!), 26, 30 in Section 12.2. | March 27 |

10 | Problems 36, 38 in Section 12.2; 6, 8, 14, 16, 17, 18, 23, 26, 29, 44, 49, 50, 58 in Section 12.3. | April 3 |

11 | Problems 6, 10, 11, 13, 22, 27 in Section 12.4; 6, 7, 9 in Section 12.6; 8, 11, 12, 17 in Section 12.7; 7, 10, 17, 20, 24 in Section 12.8. | April 17 |

12 | Problems 11-14, 22, 23 in Section 13.1; 3, 4, 9, 16, 20, 22, 39, 40 in Section 13.2; 1, 12, 15, 18 in Section 13.3. | April 27 |

13 | Problems 6, 8, 10 in Section 13.3; 1, 3, 6, 7, 9, 10, 11, 12, 18, 19 in Section 13.4. | May 7 |

**Grades** will be based on homework, quizzes, two 1-hour tests,
and a final exam (scheduled by the registrar for this time block), weighted as follows:

Two midterm exams, in class, dates TBA | 40% |

The final exam, as scheduled by registrar | 40% |

Quizzes, once every 1-2 weeks | 10% |

Graded homework | 10% |

The dates of the **midterm exams** and **quizzes** will be
announced in advance. Each quiz will take 15-20 min. **Homework** is
assigned once a week and is due the following week. You may discuss the homework
problems with other students in the class; however, if you do, you should write on your
homework submission the students with whom you discussed the assignment. (You do not need to
mention any help you received from the TA's or instructor.) You may not copy the written work
of another student or allow another student to copy your written work. What you
submit should be your own work.
Late
homework will not be accepted. Students
who miss a quiz (or exam) will not be granted a make-up quiz (or exam) unless there is a
documented medical or other emergencies.
.

If you are a student who needs academic accommodations because of a documented disability, please contact me and present your letter of accommodation as soon as possible. If you have questions about documenting a disability or requesting academic accommodations, you should contact Beth Rodgers-Kay in Academic Services (x6-3470 or brodgers@brandeis.edu). Letters of accommodation should be presented at the start of the semester to ensure provision of accommodations. Accommodations cannot be granted retroactively.

You are expected to follow the University's policy on academic integrity, which is distributed annually as section 4 of the Rights and Responsibilities Handbook. Instances of alleged dishonesty will be forwarded to the Department of Student Development and Conduct for possible referral to the Student Judicial System. Potential sanctions include failure in the course and suspension from the University. If you have any questions about how these policies apply to your conduct in this course, please ask.