Geometry & Vectors

	Geometry & Vectors MA 1607 (Andreas Fring) course syllabus

The novel to the course

Lecture Notes

These notes are only additional material and can not replace your own notes
taken in the lecture. If you do find it difficult to take notes and make sense
of them afterward contact the academic learning support unit.

Content:

1) Axioms for Geometry

1.1) What is geometry?
1.2) Some literature
1.3) The Axioms of Incidence
1.4) Measurement Axioms

2) Vectors

2.1) The Notion of a Vector
2.2) Addition and Scaling of Vectors
2.3) Vectorspaces
2.4) The Length of a Vector
2.5) The Dot or Scalar Product (angles)
2.6) Euclidean Geometry
2.7) The Cross or Vector Product (orientation)
2.8) Triple Products
2.9) Quadruple Products
2.10) Vectorfields

3) Analytic (coordinate) geometry (2D)

3.1) Points
3.2) Lines

3.2.1) The Equation of a straight Line
3.2.2) The Angle between two straight Lines
3.2.3) The Distance of a Point from a Line

3.3) Conic Sections

3.3.1) The Ellipse (e<1)
3.3.2) The Hyperbola (e>1)
3.3.3) The Parabola (e=1)

3.4) Curves of Degree >2

3.4.1) Descartes Folium
3.4.2) Fermat Curves

4) Analytic (coordinate) geometry (3D)

4.1) Points
4.2) Lines

4.2.1) Intersection of Lines

4.3) Planes

4.3.1) The Equation of a Plane
4.3.2) Intersection of a Plane and a Line
4.3.3) Shortest distance of a point from a plane
4.3.4) The line of intersection of two planes

4.4) Spheres

4.4.1) The Equation of the sphere
4.4.2) The tangent plane of the sphere

Exercises:

Courseworks:

Past Papers:

The academic leaning support unit offers regularly workshops on revision and examination techniques.

A.Fring@city.ac.uk

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