# Syllabus

 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