2018 June 7,

Carleton College, Spring 2018, Joshua R. Davis, , CMC 325, x4095

This course continues your education in calculus — a subject on which much of our modern technological world is based. Specifically, this course extends the vector techniques, that you learned in Math 120, from 2D to 3D. That's important, because our world isn't 2D. The course then develops the calculus of vector fields, which underlie applications such as electromagnetism, fluid dynamics, and structural geology. Finally, it presents sequences and series, which find applications throughout statistics, physics, and other fields. The course materials are

*Calculus: Early Transcendentals*, 8th Ed, by James Stewart. It is important that you use exactly this version of the text. Other versions may have different section and problem numbering.- Here are some exercises to help us with basic math writing.
- An equation is a statement
- A sequence of equations is a sequence of statements
- The arrow "=>" indicates that one equation implies another
- Here are our exams from this term.
- Exam A, Solutions (Quartiles: 47/56, 43/56, 40/56)
- Exam B, Solutions (Quartiles: 52/60, 47/60, 40/60)
- Exam C, Solutions (Quartiles: 73/84, 64/84, 51/84)
- Here are some exams from my spring 2017 Math 211 course. The content overlaps with that of Math 210. They should give you an idea of how I write exams. You might find parts of them useful as review or practice.
- Exam A, Solutions (Quartiles: 37/52, 32/52, 28/52)
- Exam B, Solutions (Quartiles: 45/57, 34/57, 28/57)
- Exam C, Solutions (Quartiles: 56/66, 48/66, 44/66)
- Similarly, here are some exams from my fall 2014 Math 211, which was unusually difficult.

Our class meets in CMC 319 during period 2A (MonWed 9:50-11:00, Fri 9:40-10:40). If you want to meet with me outside class, then try to make my office hours, which are

- Mon 1:50-3:00 (5A),
- Tue 10:00-11:00,
- Wed 11:10-12:20 (3A),
- Thu 9:30-10:30.

If you cannot make my office hours, then e-mail me to make an appointment, listing several possible times.

Final grades (A, B, C, etc.) are assigned according to an approximate curving process. By this I mean that there are no predetermined percentages (90%, 80%, 70%, etc.) required for specific grades. The advantage of this system is that student grades don't suffer when I write a difficult exam. The disadvantage is that you cannot compute your own grade. Visit me in my office, if you want me to estimate your current grade for you. The following elements contribute.

- Participation: You are expected to attend every class meeting promptly, take notes, and participate in discussion and group work. You can make up for a deficiency in class participation by discussing the course with me in office hours or generally demonstrating exceptional effort and interest. Participation is used to make small adjustments to the final course grade. Additionally, a requirement for passing this course is that you visit me in my office at least once during the first two weeks.
- Assignments: Assignments are the core of the course; they are where you learn the material. Altogether they count for 25% of your grade.
- Exam A: The first midterm exam is given in class sometime around the fourth week. It counts for 25% of your course grade.
- Exam B: The second midterm is given in class sometime around the eighth week. It counts for 25% of your grade.
- Exam C: The final exam is scheduled for Saturday 2018 June 2, 3:30-6:00, in our usual room. The exam counts for 25% of your course grade. Self-scheduled final exams are not allowed.

You are expected to spend about 10 hours per week on this course outside class. Some students need to spend more than 10 hours. If you find yourself spending more than 15 hours, then talk to me.

On homework, you are encouraged to figure out the problems with other students. However, you should always write/type your solutions individually, in your own words. You may not copy someone else's work or allow them to copy yours. Presenting someone else's work as your own is a violation of Carleton's Academic Integrity standards.

Writing is not just for English and history majors. Written and oral communication skills are essential to every academic discipline and are highly prized by employers. In this course, your written work is evaluated both for correctness and for presentation.

Although homework is assigned every day, it is usually collected only on Fridays. When handing in a week's homework, *staple* your pages into a single packet, in the correct order. Multi-sheet packets that are not stapled are unacceptable. I will not accept packets that are not stapled. Is there a stapler in the classroom? Often not, so staple ahead of time. Is a paper clip okay? No.

Depending on time constraints in any given week, perhaps not all of your homework will be graded. In order to ensure full credit, do all of the assigned problems.

During the term, you have one free pass to hand in a week's homework packet late, no questions asked. Simply hand in your late packet when the next packet is due, writing "Late Pass Used" prominently at the top of the late packet. Once you have used your late pass, no late assignments are accepted, except in extreme circumstances that typically require documentation by physicians or deans.

If some medical condition affects your participation in class or your taking of exams, let me know in the first week of class. You may need to make official arrangements with Disability Services for Students.

This schedule is tentative. It will be adjusted as we proceed. To help you decode the schedule, here is an example. On Day 2 we discuss triple integrals. Section 15.6 of the textbook covers that material; read it if you want another treatment. You have six homework problems, which are due on Day 3.

Date | Day | Reading | Topics | Assignment | Due | Notes |
---|---|---|---|---|---|---|

M 3/26 | 1 | review | Day 1 | 1, 2 | ||

W 3/28 | 2 | 15.6 | triple integrals | 15.6 #10, 12, 22, 28, 32, 48ab | 3 | |

F 3/30 | 3 | 15.7 | cylindrical coordinates | 15.7 #7, 10, 16, 28, 30, 31 | 6 | cylindricalSpherical.pdf |

M 4/02 | 4 | 15.8 | spherical coordinates | 15.8 #6, 13, 18, 22, 28, 46 | 6 | |

W 4/04 | 5 | 4.4, 7.8 | L'Hopital's rule, improper integrals | 4.4 #16, 18, 24, 80; 7.8 #10, 16, 40, 69 | 9 | |

F 4/06 | 6 | 13.1 | vector functions, space curves | 13.1 #8, 18, 21-26, 32 | 9 | |

M 4/09 | 7 | 13.2 | derivatives, integrals of vector functions | Day 7 | 9 | |

W 4/11 | 8 | 13.3 | arc length but not curvature | 13.3 #4, 15, 16, 67 | 12 | |

F 4/13 | 9 | 16.1 | vector fields | Day 9 | 12 | |

M 4/16 | 10 | 16.2 | line integrals | Day 10 | 12 | |

W 4/18 | 11 | 16.3 | fundamental theorem for line integrals | 16.3 #1, 4, 18, 20, 25, 26, 28, 36c | 15 | |

F 4/20 | 12 | 16.4 | Green's theorem | 16.4 #1, 6, 12, 21, 27 | 15 | |

M 4/23 | 13 | review | ||||

W 4/25 | 14 | Exam A | ||||

F 4/27 | 15 | 11.1 | sequences | 11.1 #3, 14, 24, 26, 28, 38, 46, 68 | 17 | |

M 4/30 | Midterm Break | |||||

W 5/02 | 16 | 11.2 | series | Day 16 | 17, 20 | |

F 5/04 | 17 | catching up | none | |||

M 5/07 | 18 | 11.3 | integral test | Day 18 | 19, 20 | |

W 5/09 | 19 | 11.4 | comparisons | 11.4 #4, 6, 14, 16, 24, 30, 38 | 23 | |

F 5/11 | 20 | 11.5 | alternating series | 11.5 #6, 7, 18, 20, 26, 34 | 23 | |

M 5/14 | 21 | 11.6 | absolute convergence, ratio test, root test | Day 21 | 22, 23 | |

W 5/16 | 22 | 11.8 | power series | 11.8 #4, 10, 22, 24, 26, 30, 36a, 38, 42 | 26 | |

F 5/18 | 23 | review | ||||

M 5/21 | 24 | Exam B | ||||

W 5/23 | 25 | 11.9 | power series as functions | 11.9 #8, 14, 16, 18, 26, 36a, 38 | 28 | arctan.nb |

F 5/25 | 26 | 11.10 | Taylor series | 11.10 #10, 18, 20, 22, 26, 44, 54 | 28 | |

M 5/28 | 27 | 17.4 | series in differential equations | a few of 17.4 #1-#12 | never | |

W 5/30 | 28 | series in probability, conclusion | ||||

S 6/02 | Exam C, 3:30-6:00 |