Week

Topics

Study Materials

1

points, oriented segments, parallel translation, vectors, collinear and coplanar vectors,

Textbooks 
2

linear operations with vectors, linear dependence, coordinates of vectors and points. 
Textbooks

3

scalar(dot) product of vectors, projection, direction cosines, cosine theorem. Vector product, orientation of plane, 
Textbooks

4

Lagrange identity, area, collinear points, triple (mixed) product, 
Textbooks

5

volume, double vector product. A definition of affine and Euclidean spaces. 
Textbooks

6

curves and surfaces, parametric, explicit and implicit equations, geometric locus. Equations of straight lines and planes, normal vectors. 
Textbooks

7

geometric problems with lines and planes. Menelaos and Ceva theorems. Intersections, angles, skew lines, distances, pencils. 
Textbooks

8

review and midterm exam, 
Textbooks 
9

circles and spheres, parametric equations, polar, cylindrical and spherical coordinates, 
Textbooks

10

intersection with a line, secant and tangent, normal, polar line and plane. 
Textbooks

11

conics: canonical equation of ellipse and hyperbola, focuses and vertices, asymptotes. Directrix, eccentricity, parabola. Parametric equations. 
Textbooks

12

quadrics: ellipsoid of revolution, hyperboloids, asymptotic cone, elliptic and hyperbolic paraboloids, 
Textbooks

13

conics and quadrics: affine classification theorem of Gauss. 
Textbooks

14

review and midterm exam 
Textbooks
