Week

Topic(s)

1

Elements of Analytic Geometry, Cartesian Coordinates in the Plane: Lines in the Plane, Review of Trigonometry

2

Polar Coordinates, Change of Coordinates: Rotation and Translation

3

Vectors in the Plane: Directed Line Segments and Vectors, Algebra of Vectors

4

Scalar Product, Angle Between Two Vectors, Lines, Half Lines and Line Segments

5

Distance, Bisectors, Symmetry, Convex Sets, Half Planes, Polygons

6

Conic Sections: Fundamental Definitons, The Parabola, Central Conics

The Ellipse, The Hyperbola, Asymptotes of an Hyperbola

7

Conic Sections: Fundamental Definitons, The Parabola, Central Conics

The Ellipse, The Hyperbola, Asymptotes of an Hyperbola

8

Conic Sections: Fundamental Definitons, The Parabola, Central Conics

The Ellipse, The Hyperbola, Asymptotes of an Hyperbola

9

Algebra of Vectors in 3-Space, Scalar Product and Cross Product of Vectors in 3-Space

10

Planes and Lines in 3-Space, Distance from a Point to a Plane or to a Line

11

The General Quadratic Equation, Tangents and Polars

Families of Planes and Lines, Vectors in n-Space, Vectors with Complex Components

12

Surfaces: Spheres and Cylinders, Surfaces of Revolutions

13

Canonical Equations of Quadratic Surfaces, Change of Coordinates in 3-Space, Cylindrical Coordinates

14

Spherical Coordinates, The General Quadratic Equations