# Analytic Geometry

**Math 115, 2006–2007, Fall Semester**

**Textbook:** *Analytic Geometry,* H. I.
Karakaş, METU, 1994. (*Note:* The paragraph spanning
pp. 42–43 needs to be corrected.)

**Suggested problems** from the Karakaş book:

- Section 4.1 # 1a, 1b, 1d, 4, 5
- Section 4.2 # 1, 3b, 3c, 3d, 6-1, 8, 9
- Section 4.4 # 2b, 2c, 3, 7-1, 7-2, 7-4, 11
- Section 4.5 # 2a, 2b, 2d, 5b, 5e, 6c, 6d, 7b,7d, 8-1,8-2
- Section 4.6 # 1a,1b, 2
- Section 4.7 # 1a, 1b, 6, 7a, 10a, 11a
- Section 8.1 # 1b, 1c, 1d, 1e, 1g, 3a, 3e, 3f, 3g, 3i
- Section 8.3 # 1a, 1b, 1c, 1d, 1e, 1f, 1g, 1h, 1i, 1j, 1k, 2, 6, 7,9, 15a, 15c
- Section 8.4 #1

**References:** Any Calculus and Analytic Geometry book.

- on defining angles in analytic geometry;
- on conic sections.

**Tentative Course Outline:**

Week | Topics | Sections |
---|---|---|

1 | Fundamental Principle of Analytical Geometry. Cartesian coordinates in the plane | 1.5, 2.1, 2.7 |

2 | Lines in the plane | 2.2, 2.3 |

3 | Review of trigonometry | 2.4 |

4 | Polar coordinates | 2.5 |

5 | Rotation and translation in the plane. Directed segments and vectors | 2.6, 3.1,5.1 |

6 | Algebra of vectors, scalar product | 3.2, 3.3, 5.2, 5.3 |

7 | Cross product, lines in 2 and 3-space, distance | 5.4, 3.4, 3.5, 5.5 |

8 | Lines in 3-space (cont.), planes | 5.5, 5.6 |

9 | Planes(cont.) | 5.7 |

10 | Conic sections, parabola, ellipse | 4.1, 4.2, 4.3, 4.4 |

11 | Hyperbola | 4.5, 4.6 |

12 | General quadratic equations | 4.7 |

13 | Spheres, cylinders, surfaces of revolution | 8.1, 8.2 |

14 | Canonical equations of quadratic surfaces | 8.3 |

**Grading:** There will be two midterm exams which will be
of weight 30% each. The final exam will be of weight 40%. The letter
grade will be assigned by the instructor according to the distribution
of weighted total grades.

**Results** of the
second midterm exam (xls file)

**Dates of Exams:**

- Midterm 1: November 16 (Thursday), covering weeks 1–6 above
- Midterm 2: December 14 (Thursday), covering weeks 7–9 above
- Final: covers all weeks listed above (see in particular the suggested problems near the top of this page)
- Make-up: January 24 (Wednesday), 14.00, in M-214.
**postponed from Tuesday because of a conflict**

Section | Instructor | When | Where |
---|---|---|---|

1 | Sergey Finashin | Monday 11:40–12:30 | M102 |

Wednesday 13:40–15:30 | |||

2 | Turgut Önder | Monday 11:40–12:30 | M103 |

Wednesday 13:40–15:30 | |||

3 | David Pierce | Monday 12:40–13:30 | M102 |

Wednesday 10:40–12:30 |