# Math 53: Multivariable Calculus, Fall 2008

Math 53 with prof. Hutchings, Fall 2008

Discussion sections 111 and 108 with Anton Geraschenko

Hutchings' Math 53 site (no longer exists) (go here for announcements, course policies, schedule, and assignments)

**GSI:**Anton Geraschenko**Office (hours):**1044 Evans, Tuesdays 12:30 PM to 1:30 PM and Wednesdays 12 PM to 1 PM.

If you have questions outside of office hours, the best way to reach me is to email me.

**Midterm Solutions/Extra Credit:** You can get extra credit points for writing up solutions to old exam problems. The old exams can be found here. You can either submit a paper copy of your solution, or you can send me a pdf. Your write-up should include the statement of the problem (including which midterm the problem is taken from), and it should make it clear how the solution works. If your solution is unclear (e.g. skips too many steps or is difficult to read) or incorrect, I will ask you to redo it.

Hutchingsfinal07f | 1, 2, 4, 6, 3, 4, 5, 7, 8, 9, 10 |

Hutchingsfinal07s | 1, 2, 3, 4, 5, 6, 7, 6, 7, 8, 9, 10 |

F03_Second_Midterm-M.Hutchings | 1, 2, 3, 4, 5, 6 |

F03_First_Midterm-M.Hutchings | 1, 2, 3, 4, 5, 6 |

F03_Final_Exam-M.Hutchings | 1, 4, 6, 9, 2, 2 (different solution), 3, 4, 5, 7, 8, 9, 10, 11, 12 |

F03_Final_Exam-K.Hare | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 |

S03_Final_Exam-L.Evans | 1, 2, 3, 4, 6, 5, 7, 8, 9, 10, 11, 12, 13, 14 |

F02_Second_Midterm-K.Kedlaya | 1, 2, 3, 4, 5, 6 |

F96_Final_Exam-G.Bergman | 1, 2, 3, 4, 5 |

F96_Second_Midterm-G.Bergman | 1, 2, 3 |

**Groupwork Problems/Quizzes:** Here are the quizzes and solutions, along with the problems we did in section to prepare for each quiz (starting with quiz 9). When you're studying for the midterm or final, I recommend trying to do all the quizzes again. I also encourage you to look at old quizzes and worksheets posted by some of the other GSI's: René Quilodrán, Scott Cramer, and Cameron Hill.

Groupwork problems | Quizzes |

Quiz 1 and solutions | |

Quiz 2 and solutions | |

Quiz 3 and solutions | |

Quiz 4 and solutions | |

Quiz 5 and solutions | |

Midterm 1 review sheet | |

Quiz 6* (this was not a graded quiz) | |

Quiz 6 and solutions | |

Quiz 7 and solutions | |

Quiz 8 and solutions (and here's problem I decided was too hard for this quiz) | |

11-04, 11-06 | Quiz 9 and solutions |

11-13 | old quiz (solved) with good example problem |

Midterm 2 review sheet, and Misha Berger's review sheet | |

11-18 11-20 | Quiz 10 and solutions |

12-02 12-04 | Quiz 11 and solutions |

12-09 | |

Final review sheet and review session problems |

If you want to look at the review sheets I made last time I was a GSI for Math 53, I see no reason to stop you. But be warned that the schedule for the class was different last time, so the material for the midterms and final may not agree with Hutchings' class.

**Box of Death:** If you make these mistakes while solving a problem, you're dead; you should be grateful if you get any credit at all.

**Challenge problems:** If you want, you can try solving some of the following problems. They don't all require calculus.

- Your pet kangaroo is tied to a pole in your yard with an extremely elastic leash. It sees a spider on the pole. Being afraid of spiders, it jumps 1km away from the pole (now the leash is length 1km). The spider decides to chase after the kangaroo by walking 1cm along the leash; Then the kangaroo jumps another kilometer in the same direction (stretching the leash by a factor of 2); then the spider steps another centimeter along the leash; and so on (kangaroo and spider alternate jumping 1km and 1cm, respectively). Does the spider ever catch up to the kangaroo (assuming the Earth is flat and infinite)? If yes, how long does it take?
- You are a camel at a banana market. The market is at one end of a 1000km desert, and your camel family is at the other end. You need to get 1000 bananas to your family, but you have the following problem: you can only carry up to 1000 bananas on your back, and you need to eat one banana per kilometer as you walk through the desert. Assuming you can leave bananas in the middle of the desert to be picked up later (the don't go bad or get stolen), what is the minimum number of bananas you need to buy?
- Your pet kangaroo bakes a perfectly spherical loaf of bread, and slices it evenly (all slices have the same thickness). If you want the maximum amount of crust (the crust is the best part!), should you ask for a piece near the middle, near the end, or a piece somewhere in between?
- Compute lim
_{x→∞}(√(x^{2}+x)-x) - The circumference of a circle of radius 1 is 2π. The surface area of a sphere of radius 1 is 4π. What is the "surface volume" of a sphere of radius 1 in four dimensions, given by the equation x
_{1}^{2}+x_{2}^{2}+x_{3}^{2}+x_{4}^{2}=1? What is the "surface hypervolume" of a sphere of radius 1 in n dimensions? - Integrate sin(√x) with respect to x.